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<p><img src="http://i.stack.imgur.com/IBHdy.png" alt="enter image description here"></p>
<p>This is an excerpt from "Modern mathematical statistics with applications" by Devore et al.
What puzzles me is that the estimator cannot help being dependent on $\theta$, since the sample depends on the parameter.</p>
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] |
<p>I have a mixed model built using Data A below, and now I want to validate the model using Data B. What should I do to actually "validate" the model?</p>
<pre><code>model <- lme(Y~1+X1+X3, random=~1|School, method="ML", data=A)
</code></pre>
<p>I know how to use "predict(model,B) - B$Y" to get residuals, but what else should I also perform in this validation process?</p>
<p>(I will not apply the cross-validation technique since my data are hierarchical structured.)</p>
|
g35718
|
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<p>I have some project categories $(PC_1, ... ,PC_n)$ and some institutions $(I_1, ..., I_n)$ and would like to determine how fairly projects are assigned to institutions and their project categories by some external sources.</p>
<p>I was thinking about using some chi square based measure for this. Basically I have a two dimensional contingency table where one dimension corresponds to the project categories and the other to the institutions. Each cell of the contingency table counts the number of projects that each institution ‘runs’ for a particular project category.</p>
<p>I could determine $(O – E)\cdot|O-E|/E$ for each cell. Here:</p>
<ul>
<li>$O$ is the observer number of projects</li>
<li>$E$ is the expected number of projects</li>
</ul>
<p>IMHO this would give me a value for each cell which indicates how much the observed value differs from the expected value and thus how fairly the resources were assigned for an institution and project category. In other words a negative value indicates ‘unfairness’, a positive value indicates ‘favouritism’ and a value close to zero indicates ‘fairness’. What do you think?</p>
|
g35719
|
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<p>I'm playing with support vector machines (SVM) using the e1071::svm() function in R, and I encountered a scenario where I asked it for a leave-one-out cross-validated classification of a 2-category response and obtained a total accuracy of 38% (35/90), which, given 90 samples, ends up with a 95% confidence interval that is <strong>below</strong> chance. Should I consider this a fluke, and if not, how is it possible for an SVM to become anti-predictive?</p>
<p>In case it matters, I used default values for the cost and gamma parameters, and the data predicting the response was a 8192 item vector representing 500 milliseconds of electroencephalogram data collected across 64 electrodes. </p>
|
g35721
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<p>I am trying to compare 2 ideas to see which one is better/more effective - I am looking to see if a significant difference. (2 conditions)</p>
<p>We used a questionnaire to gather feedback from hundreds of people.
(Questions include: how likely would you buy it, how likely would you tell your friends and family, I want to learn more about this product...etc. An
swers are multiple choice: strongly agree,somewhat agree, neutral, somewhat disagree, strongly disagree & no advantage, some advantage, slight advantage, a great advantage)</p>
<p><strong>WHAT SHOULD I DO? AND IS THIS THE RIGHT WAY OF DOING IT? (using SPSS)</strong></p>
<ol>
<li>t-test: by combining the data (would I just give each answer a value like 1-4, add values up for total score for each participant)</li>
<li>Run cross tabs and then do something?</li>
<li>Other suggestions?</li>
</ol>
<p>THANKS! :) </p>
|
g73385
|
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<p>When you are trying to fit models to a large dataset, the common advice is to partition the data into three parts: the training, validation, and test dataset.</p>
<p>This is because the models usually have three "levels" of parameters: the first "parameter" is the model class (e.g. SVM, neural network, random forest), the second set of parameters are the "regularization" parameters or "hyperparameters" (e.g. lasso penalty coefficient, choice of kernel, neural network structure) and the third set are what are usually considered the "parameters" (e.g. coefficients for the covariates.)</p>
<p>Given a model class and a choice of hyperparameters, one selects the parameters by choosing the parameters which minimize error on the training set. Given a model class, one tunes the hyperparameters by minimizing error on the validation set. One selects the model class by performance on the test set.</p>
<p>But why not more partitions? Often one can split the hyperparameters into two groups, and use a "validation 1" to fit the first and "validation 2" to fit the second. Or one could even treat the size of the training data/validation data split as a hyperparameter to be tuned.</p>
<p>Is this already a common practice in some applications? Is there any theoretical work on the optimal partitioning of data?</p>
|
g73386
|
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<p>I was thinking of this problem.</p>
<p><a href="http://en.wikipedia.org/wiki/Two_envelopes_problem" rel="nofollow">http://en.wikipedia.org/wiki/Two_envelopes_problem</a></p>
<p>I believe the solution and I think I understand it, but if I take the following approach I'm completely confused.</p>
<p>Problem 1:</p>
<blockquote>
<p>I will offer you the following game. You pay me \$10 and I will flip a fair coin. Heads I give you \$5 and Tails I give you \$20.</p>
<p>The expectation is \$12.5 so you will always play the game.</p>
</blockquote>
<p>Problem 2:</p>
<blockquote>
<p>I will give you an envelope with \$10, the envelope is open and you can check. I then show you another envelope, closed this time and tell you: This envelope either has \$5 or $20 in it with equal probability. Do you want to swap?</p>
<p>I feel this is exactly the same as problem 1, you forgo \$10 for a \$5 or a \$20, so again you will always switch.</p>
</blockquote>
<p>Problem 3:</p>
<blockquote>
<p>I do the same as above but close the envelopes. So you don't know there are $10 but some amount X. I tell you the other envelope has double or half. Now if you follow the same logic you want to switch. This is the envelope paradox.</p>
</blockquote>
<p>What changed when I closed the envelope??</p>
<p>EDIT:</p>
<p>Some have argued that problem 3 is not the envelope problem and I'm going to try and provide below why I think it is by analysing how each views the game. Also, it gives a better set up for the game.</p>
<p>Providing some clarification for Problem 3:</p>
<p>From the perspective of the person organising the game:</p>
<blockquote>
<p>I hold 2 envelopes. In one I put \$10 close it and give it to the player. I then tell him, I have one more envelope that has either double or half the amount of the envelope I just gave you. Do you want to switch? I then proceed to flip a fair coin and Heads I put \$5 in and Tails I put \$20. And hand him the envelope. I then ask him. The envelope you just gave me has twice or half the amount of the envelope you are holding. Do you want to switch?</p>
</blockquote>
<p>From the perspective of the player:</p>
<blockquote>
<p>I am given an envelope and told there is another envelope that has double or half the amount with equal probability. Do I want to switch. I think sure I have $X$, hence $\frac{1}{2}(\frac{1}{2}X + 2X) > X$ so I want to switch. I get the envelope and all of a sudden I am facing the exact same situation. I want to switch again as the other envelope has either double or half the amount.</p>
</blockquote>
|
g73387
|
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] |
<p>We are measuring data with a high sample rate (20 kHz) and calculated a big standard error due to our system setup. Currently we are only interested in slow signals (in the order of Hz's) is it valid to use averaging (once per 20.000 samples) and thus lower our standard error with an order 20.000?</p>
|
g41569
|
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] |
<p>I have four numeric variables. All of them are measures of soil quality. Higher the variable, higher the quality. The range for all of them is different:</p>
<p>Var1 from 1 to 10</p>
<p>Var2 from 1000 to 2000</p>
<p>Var3 from 150 to 300</p>
<p>Var4 from 0 to 5</p>
<p>I need to combine four variables into single soil quality score which will successfully rank order.</p>
<p>My idea is very simple. Standardize all four variables, sum them up and whatever you get is the score which should rank-order. Do you see any problem with applying this approach. Is there any other (better) approach that you would recommend?</p>
<p>Thanks</p>
<p><strong>Edit:</strong></p>
<p>Thanks guys. A lot of discussion went into "domain expertise"... Agriculture stuff... Whereas I expected more stats-talk. In terms of technique that I will be using... It will probably be simple z-score summation + logistic regression as an experiment. Because vast majority of samples has poor quality 90% I'm going to combine 3 quality categories into one and basically have binary problem (somequality vs no-quality). I kill two birds with one stone. I increase my sample in terms of event rate and I make a use of experts by getting them to clasify my samples. Expert classified samples will then be used to fit log-reg model to maximize level of concordance / discordance with the experts.... How does that sound to you?</p>
|
g49470
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<p><strong>INTRO</strong></p>
<p>I have trained a SVM model based on 300 training cases in order to build a filter that should help me extract a bigger and evenly balanced training set, that is to be validated by human judges.</p>
<p><strong>DATA</strong></p>
<p>My training set is:</p>
<pre><code>288 negative cases
12 positive cases
</code></pre>
<p>My model performance is:</p>
<pre><code>True positives = 6
False positives = 0
True negatives = 288
False negative = 6
</code></pre>
<p>I have used this model on a 440000 cases data set and I am given confidence values for zeroes and ones (confidence.1. = 95% -> confidence.0. = 5% and confidence.1. = 50% -> confidence.0. = 50%)</p>
<p>When the model is applied to the 440000 cased it predicts 1499 of the cases to be positive.</p>
<p><strong>PROBLEM</strong></p>
<p>As explained I am about to take a random sample of 3000 cases that will hopefully be balanced in order to train a better model. Thus my formal problem becomes:</p>
<p><em>"How can one extract a random sample of 3000 and approximate the balance of the dataset given the information I have stated?"</em></p>
<p><strong>OWN THOUGHTS</strong></p>
<p>I am fairly good with R but I simply do not have the knowledge or the skills to figure this out. I dont even know if it is possible. The only thing I do know is that it seems a bit doll to just put a finger in the air and guess on which cases to extract. The easy way would be to take the top 3000 sorted on confidence.1. which is nothing more that a qualified guess.
Happy new year
Kasper </p>
|
g47744
|
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<p>I am doing cross-validation using the leave-one-out cross-validation method (total 10 runs). I have predicted $\hat{y}$ and observed $y$ from all the runs. I have applied the following equation to calculate $R^2$. Can anyone please confirm whether I am doing right? I am confused because the $R^2$ value appeared negative.
\begin{align}
SSE&=∑(y-\hat{y})^2 \\
SST&=∑(y–\bar{y})^2 \\
R^2&=1-(SSE/SST)
\end{align}
(N.b., $\bar{y}=$ is the average of $y$.)</p>
|
g27748
|
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<p>I understand supervised and unsupervised learning well, and would be able to identify some 'basic' examples of, for example, supervised classifcation as:</p>
<ul>
<li>SVMs</li>
<li>Random Forests</li>
<li>Logistic Regression</li>
</ul>
<p>These are key works in the field which have lots of code and publications available.</p>
<p>I am now starting to look at domain adaptation in supervised learning, where the distribution over the data at learning and testing time are known to be different. Despite reading some of the literature, I haven't spotted any similar 'basic' methods which come up time and time again. In contrast, there seem to be a wild array of completely different methods for achieving the goal, many of which have only been in the literature for a few years.</p>
<p>Are there such key, established methods for domain adaptation? What are the most popular methods currently used?</p>
|
g35729
|
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0.01732386089861393
] |
<p>I have a data table T1, that contains nearly a thousand variables (V1) and around 200 million data points. The data is sparse and most of the entries are NA. Each datapoints have a unique id and date pair to distinguish from another.</p>
<p>I have another table T2, which contains a separate set of variables (V2). This table also has id and date pair that uniquely identify entries in T2. </p>
<p>We suspect that the data in T1 can be used to predict values of variables in T2. </p>
<p>To prove this, I thought to apply 'glm' model in R and check if we can really find some variable in T2 that is dependent on variables in T1. </p>
<p>For each variable in T2, I started pulling out all data in T1 having same id and date pair which resulted in much smaller ~50K data points for some of test variables. </p>
<p>The problems that I am facing now with application of glm is as follows. </p>
<ol>
<li><p>In some cases, it shows me an error 'fit not found' and warning 'glm.fit: algorithm did not converge '. I am not sure why is it shown? </p></li>
<li><p>How the NAs are treated in glm? Does it remove all records involving 'NA' first and then perform fitting?</p></li>
<li><p>Is it a good strategy to remove all NAs first and then call 'glm'. I fear that this may reduce the datapoints significantly as most of them are NAs. </p></li>
<li><p>Which method is used to calculate the coefficients. I couldnot find any website or paper or book that discuss how the output is calculated.</p></li>
</ol>
<p>I tested glm with and without 'NAs' and found difft answers which points that NAs are considered while fitting the data:</p>
<p>Example 1:</p>
<pre><code>> tmpData
x1 x2 x3 Y
1 1 1 1 3
2 1 0 4 5
3 1 2 3 6
4 0 3 1 4
Call: glm(formula = as.formula(paste(dep, " ~ ", paste(xn, collapse = "+"))),
na.action = na.exclude)
Coefficients:
(Intercept) as.numeric(unlist(tmpData["x1"])) as.numeric(unlist(tmpData["x2"]))
5.551e-16 1.000e+00 1.000e+00
as.numeric(unlist(tmpData["x3"]))
1.000e+00
Degrees of Freedom: 3 Total (i.e. Null); 0 Residual
Null Deviance: 5
Residual Deviance: 9.861e-31 AIC: -260.6
</code></pre>
<p>Example 2:</p>
<pre><code>'x1' 'x2' 'x3' 'Y'
100000 1 NA 2
1 1 1 3
1 NA -1124 2
1 0 4 5
1 2 3 6
0 3 1 4
Coefficients:
(Intercept) as.numeric(unlist(tmpData["x1"])) as.numeric(unlist(tmpData["x2"])) as.numeric(unlist(tmpData["x3"]))
-2.3749044 -0.0000625 0.6249899 1.8749937
Degrees of Freedom: 5 Total (i.e. Null); 2 Residual
Null Deviance: 13.33
Residual Deviance: 1.875 AIC: 20.05
</code></pre>
|
g73388
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] |
<p>There are several packages that can apply the Durbin-Watson test for serial correlation. However, I do not see a package that supports the calculation in the case that once has a GLS weighted regression.</p>
<p>For example, CRAN package <a href="http://cran.r-project.org/web/packages/lmtest/index.html" rel="nofollow">lmtest</a> notes in their <a href="http://cran.r-project.org/web/packages/lmtest/NEWS" rel="nofollow">changelog</a> that they explicitly do not support weighted regressions (yet). Before the recent release, lmtest would not throw an error when passing weighted regressions. </p>
<p>My concern is that the other dwtest packages may also not be explicitly dealing with this scenario.</p>
|
g1008
|
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<p>I have <strong>6</strong> masses as input data which they are expressed as m+/- delta m.
Via a complicated processes I calculate <strong>decay width</strong> as a final result.
It takes a long time for the code to compute decay width for example for <strong>m</strong> values. Let's call it <strong>(decay width)_central</strong>.
Let's call <strong>m + delta m= m_max</strong> and <strong>m- delta m =m_min</strong>. (For 6 masses: For
example m_max means I substitute all 6 masses with their maximum value).
Then decay width for m_max is <strong>(decay width)_max</strong> and decay width for m_min
is <strong>(decay width)_min</strong>.
Can I have an estimate for error bar with only these 3 values of decay widths?
(It is very time consuming to find more than these 3 results.)
Or may be you suggest a better way?
Thanks a lot.</p>
<p>My problem is how to calculate error bars for decay width. Errors originate from 6 experimental data which I used as inputs. The question is that how should I find error bars for decay width? I can't use the usual methods such as deviation for errors, because it is so time consuming to calculate decay width for the masses in experimental range and then find mean value. Can I find an estimate for error bars only with 3 values of decay width? The decay width which I found by substituting all the masses with m + delta m, The one by substituting all the masses with m - delta m and the one which I found by substituting the mean values for m? </p>
|
g35730
|
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] |
<p>Given a data matrix like this:</p>
<pre><code> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 9.520 11.137 16.576 18.225 20.576 25.861 NA
[2,] 9.005 9.491 11.106 16.530 18.184 20.495 25.773
[3,] 9.437 11.050 20.393 25.711 NA NA NA
[4,] 9.442 11.058 20.411 25.711 NA NA NA
[5,] 9.431 11.045 20.421 25.707 NA NA NA
[6,] 9.461 11.052 20.319 25.657 NA NA NA
[7,] 9.245 10.819 20.253 25.628 NA NA NA
[8,] 9.229 10.801 20.216 25.594 NA NA NA
[9,] 9.234 10.805 20.258 25.619 NA NA NA
[10,] 9.241 10.814 20.264 25.626 NA NA NA
[11,] 9.248 10.819 20.281 25.649 NA NA NA
[12,] 9.231 10.800 20.219 25.567 NA NA NA
</code></pre>
<p>How do I get a data frame like this?:</p>
<pre><code> S p1 p2 p3 p4 p5 p6 p7
1 NA 9.520 11.137 16.576 18.225 20.576 25.861
2 9.005 9.491 11.106 16.530 18.184 20.495 25.773
3 NA 9.437 11.050 NA NA 20.393 25.711
4 NA 9.442 11.058 NA NA 20.411 25.711
5 NA 9.431 11.045 NA NA 20.421 25.707
6 NA 9.461 11.052 NA NA 20.319 25.657
7 NA 9.245 10.819 NA NA 20.253 25.628
8 NA 9.229 10.801 NA NA 20.216 25.594
9 NA 9.234 10.805 NA NA 20.258 25.619
10 NA 9.241 10.814 NA NA 20.264 25.626
11 NA 9.248 10.819 NA NA 20.281 25.649
12 NA 9.231 10.800 NA NA 20.219 25.567
</code></pre>
<p>In the matrix, each row represent the timepoints from 1 sample. The matrix is balanced with an arbitrary number of NAs as needed. In the dataframe, each column represents all the timepoints that are functionally equivalent. Timepoints in a single sample cannot be functionally equivalent. </p>
<p>I think I should be able to solve this with some form of kmeans clustering that restricts each cluster from having more than one member from each sample. Any ideas?</p>
|
g73389
|
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<p>I am trying to fit a model investigating the amount of the loan (or a transformation of it) as a function of the the variables <code>income</code>, <code>gender</code>, <code>customer</code> and <code>age</code>.</p>
<p>Fitting a standard linear regression gives poor results (R-squared of only 0.27). Besides, the relationship between income and loan seems quite weird. It has a sort of left-rotated Z-shape</p>
<p>Would be appropriate to use a semiparametric model here? And so yes, how would you model it?</p>
<p>I tried this: </p>
<pre><code>model <- spm(loan~f(income, basis="trunc.poly")+age+factor(gender)+factor(customer))
</code></pre>
<p>But this gave poor results (no significant variables).</p>
<p>Anyone has suggestions?</p>
<p>Many thanks in advance.</p>
|
g73390
|
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<p>I am an anthropology student. I am researching the inter-relatedness of most if not all humans as part of my studies. I personally have an interest in statistics and probability theory and I have used it in regards to this topic. Before I explain my theory, I received the following from a computer scientist that I wish to share to better give a background idea of what I’m trying to put forward:<br>
If there were random intermixing, then we would each have ~1 million ancestors living in 1500 AD, out of a world population of ~500 million.
So the fractional overlap between two people would be about 1/500th.</p>
<p>But the probability that two people share at least one common ancestor would be essentially 100%. Basically, you are choosing a random number between 1 and 500 a million times and you're asking whether you ever choose number 500. In a million trials, we expect this to happen 2000 times. So that it happens at least once is guaranteed.</p>
<p>If we get rid of the random intermixing, the fractional overlap will drop to much less than 1/500th. But I suspect that the probability of at least one overlap will remain very high.
If the population in 1500 was 500 million, and it is 6 billion today (12x larger).
If the average generation length is 30 years, there are 17 generations in 500 years.
So the average number of surviving children per mother is $\exp((\log 12)/17) = 1.157$
Since a child has two parent, the average number of surviving children per person is 2 * 1.157 = 2.315
So this is the average growth rate per generation for the descendants of a person in 1500.
$2.315^{17}$ = 1.575 million. So an average person in 1500 has about 1.5 million offspring alive today. Sampling from the whole world, the probability that a random person from 1500 is an ancestor of a random person in 2000 would be 1.5 million / 6 billion = 0.025%.
If you were only considering people in a region like Europe, it would probably be something like 1.4 million / 700 million = 0.2%.</p>
<p>As I have said above, this is from a computer scientist. Next, is my own theory. From a probabilistic standpoint, due to the Law of Large Numbers, me, you or *almost anyone alive today had an ancestor in like say feudal Japan in 1500 CE. I chose Japan because of its remoteness yet it still had contact with the rest of the world at that time and I chose the year 1500 because of each person had in theory about a million ancestors- lower than that because of inbreeding but still a sizable number nonetheless. I have shared this theory with several of my colleagues and they are intrigued by it yet I have not yet shared it with an actual statistician. I know it seems unlikely, but from a strictly statistical standpoint, what do you think of it?</p>
<p>*please note, this excludes populations that have not have had contact. </p>
|
g73391
|
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<p>I trained a few different models, (Perceptron, Stochastic Gradient Descent and Naive Bayes), each with different parameters. I then scored their accuracy on a cross validation set.</p>
<p>The scores on the best parameter Perceptron, SGD and NB models were 93%, 91% and 94% respectively. </p>
<p>I didn't expect such similar results and I'm at a bit confused because I feel that the possibility of variance makes choosing the NB as the best model questionable.</p>
<p>Am I supposed to test all 3 on the test set and use the model with the best unbiased error? Or is that implicitly cherry picking the best model ?</p>
|
g35733
|
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] |
<p>This is in reference to the <a href="http://en.wikipedia.org/wiki/Girsanov_theorem" rel="nofollow">Girsanov theorem</a> however question is general. If $X$ is a standard normal variable $N(0,1)$, why is expectation of $e^{-\mu X - \mu^2/2}$ equal to 1?</p>
<p>Shouldn't it be $e^{-\mu^2/2}$?</p>
|
g47133
|
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<p>I have data on commute times over a specified route over different days during different conditions. Some of the conditions are categorical (e.g., weather, traffic), and some of them are numeric (e.g., time departing from origin). I'd like to find out which of these conditions most strongly correlate with the shortest commute times on any given day of the week (M-F).</p>
<p>Is there a decision tree-like algorithm that would discover the conditions most strongly correlated with the shortest commute times?</p>
|
g73392
|
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<p>I would like to compare two linear regression models which represent degradation rates of a mRNA over time under two different conditions. The data for each model collected independently. </p>
<p>Here is the dataset.</p>
<pre>
Time (hours) log(Treatment A) log(treatment B)
0 2.02 1.97
0 2.04 2.06
0 1.93 1.96
2 2.02 1.91
2 2.00 1.95
2 2.07 1.82
4 1.96 1.97
4 2.02 1.99
4 2.02 1.99
6 1.94 1.90
6 1.94 1.97
6 1.86 1.88
8 1.93 1.97
8 2.12 1.99
8 2.06 1.93
12 1.71 1.70
12 1.96 1.73
12 1.71 1.76
24 1.70 1.46
24 1.83 1.41
24 1.62 1.42
</pre>
<p>These are my models:</p>
<pre><code>Exp1.A.lm<-lm(Exp1$Time~Exp1$(Treatment A))
Exp1.B.lm<-lm(Exp1$Time~Exp1$(Treatment B))
</code></pre>
<pre>
Call:
lm(formula = Exp1$Time ~ Exp1$(Treatment A))
Residuals:
Min 1Q Median 3Q Max
-6.8950 -1.2322 0.2862 1.2494 5.2494
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 74.68 6.27 11.91 2.94e-10 ***
Exp1$(Treatment A) -36.14 3.38 -10.69 1.77e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.97 on 19 degrees of freedom
Multiple R-squared: 0.8575, Adjusted R-squared: 0.85
F-statistic: 114.3 on 1 and 19 DF, p-value: 1.772e-09
Call:
lm(formula = Exp1$Time ~ Exp1$(Treatment B))
Residuals:
Min 1Q Median 3Q Max
-7.861 -3.278 -1.444 3.222 11.972
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 88.281 16.114 5.478 2.76e-05 ***
Exp1$(Treatment B) -41.668 8.343 -4.994 8.05e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5.173 on 19 degrees of freedom
Multiple R-squared: 0.5676, Adjusted R-squared: 0.5449
F-statistic: 24.94 on 1 and 19 DF, p-value: 8.052e-05
</pre>
<p>To compare these two models, I used this following code. </p>
<pre><code>anova(Exp1.A.lm,Exp1.B.lm)
</code></pre>
<pre>
Analysis of Variance Table
Model 1: Exp1$Time ~ Exp1$Exp1$(Treatment A)
Model 2: Exp1$Time ~ Exp1$Exp1$(Treatment B)
Res.Df RSS Df Sum of Sq F Pr(>F)
1 19 167.60
2 19 508.48 0 -340.88</pre>
<p>My question is why the ANOVA analysis doesn't show an F statistics and a p.val. My apologies if this is a naive question. </p>
<p>Based on different slopes, the rate of degradation is different in these two models, but I would like to know how statistically significant this difference is. I hope that this makes sense. </p>
<p>Thank you-</p>
|
g37528
|
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<p>I am confused between what types of problems these three models capture, and their applications:</p>
<ul>
<li><a href="http://en.wikipedia.org/wiki/Latent_Dirichlet_allocation" rel="nofollow">Latent Dirichlet Allocation (LDA)</a></li>
<li><a href="http://en.wikipedia.org/wiki/Dirichlet_process" rel="nofollow">Dirichlet Processes</a> and <a href="http://en.wikipedia.org/wiki/Pitman%E2%80%93Yor_process" rel="nofollow">Pitman-Yor processes</a></li>
<li><a href="http://en.wikipedia.org/wiki/Hierarchical_Dirichlet_process" rel="nofollow">Hierarchical Dirichlet Process</a> (HDP) & Hierarhical Pitman-Yor Processes</li>
</ul>
<p>More than formal definitions (which I can find on Wikipedia), I am looking for the <strong>intuition</strong> behind each of them ( how they build on each other).</p>
<p>Perhaps, more specifically:</p>
<ul>
<li>Is the difference between LDA and HDP that LDA is parameteric (i.e. I need to pre-specify the number of topics) whereas HDP is non-parametric? (and therefore I don't need to know how many topics I have)</li>
<li>What is the difference between a Dirichlet Processes and Pitman-Yor Processes? </li>
<li>What is the difference between a non-parametric process (e.g. DP) and a hierarhical non-parametric process (e.g. HDP)?</li>
</ul>
|
g73393
|
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] |
<p>I have been trying to use <a href="http://cran.r-project.org/web/packages/sspir/index.html" rel="nofollow">sspir</a> R package to estimate the following Poisson model:</p>
<p>$Y_{t}\sim Po(\exp(\lambda_{t}));$ such that $\lambda_{t}=X_{t}\beta
+\gamma_{t}$ and $\gamma_{t}=\theta\gamma_{t-1}+u_{t},u_{t}\sim NID(0,\sigma
^{2}).$</p>
<p>In State-space form, we have $\lambda_{t}=Z_{t}F_{t},$ $Z_{t}=\left[
X_{t}\: 1\right] ,$ $F_{t}=\left[ \beta^{\prime}\: \gamma_{t}\right]
$</p>
<p>Then, $F_{t}=\left(
\begin{array}
[c]{ll}%
1 & 0\\
0 & \theta
\end{array}
\right) F_{t-1}+\left(
\begin{array}
[c]{l}%
0\\
u_{t}%
\end{array}
\right) $. Standard initial conditions are also set.</p>
<p>I have been trying to use <code>sspir</code> package in R to estimate this model, but I was not able to. If I let $\gamma_{t}$ to be a random walk, then it is standard.</p>
<p>Any suggestion? I am kind of new with this models so any help is very much appreciated.</p>
|
g35735
|
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<p>I'm trying to plot forecast and real data on the same plot. But there is always gap between them on the image :</p>
<p><img src="http://i.stack.imgur.com/ni7FR.png" alt="enter image description here"></p>
<p>I use for the forecasting following code:
y=boardings[,1]
## Simple Exponential smoothing
#predict existing values
results=HoltWinters(y,beta=FALSE, gamma=FALSE)
#print data
print(cbind(y,results$fitted))
#draw the plot with fitted values
plot(results)
#predict future values
results2=forecast.HoltWinters(results,h=12)
print(results2)</p>
<pre><code>#draw the plot with prediction
plot.forecast(results2,lwd=1,xlab='time',ylab='log.boardings',main='12-month prediction by Exponential Smoothing')
</code></pre>
<p>The data is taken from the <a href="http://cran.r-project.org/web/packages/timeSeries/index.html" rel="nofollow">timeSeries</a> package with name <code>boardings</code>.</p>
<p>I would really appreciate any help.</p>
|
g73394
|
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<p>Assume the model $ \ y = X\beta + u \ $ with $\ W \ $ is a $ \ n\times l \ $ so called matrix of instruments. </p>
<p>The following assumptions hold. There is a law of large numbers (LLN) for 1.,2.,3. and 4. such that</p>
<ol>
<li><p>$\text{plim}_{n\to\infty} \ \left(\frac{X^TX}{n}\right) = m_{X^TX}$</p>
<p>holds where $m_{X^TX}$, a finite, non stochastic matrix with full
column rank, exsists.</p></li>
<li><p>$\text{plim}_{n\to\infty} \ \left(\frac{W^TW}{n}\right) =
\text{lim}_{n\to\infty} \left(\frac{{\mathbb
E}\left(W^TW\right)}{n}\right)$</p>
<p>where we assume, that the RHS exists and is finite as well as
positive definite.</p></li>
<li><p>$\text{plim}_{n\to\infty} \ \left(\frac{W^TX}{n}\right)$</p>
<p>where we assume, that the limit $W^TX$ exists, is finite and $W^TX$
has full column rank i.e. $\text{rk}\left(W^TX\right)=k$.</p></li>
<li><p>$\text{plim}_{n\to\infty} \ \left(\frac{W^Tu}{n}\right) =
\text{lim}_{n\to\infty} \left(\frac{{\mathbb
E}\left(W^Tu\right)}{n}\right) = 0$</p>
<p>where we assume that $\text{lim}_{n\to\infty} \left(\frac{{\mathbb
E}\left(W^Tu\right)}{n}\right)$ is equal to $0$.</p></li>
</ol>
<p>The asymptotic variance for OLS will, under the assumption of homoscedastic errors $u$ i.e. that ${\mathbb E}\left(uu^T|X\right) = \sigma^2_0 I_n$ and that the model is actually correctly specified , be</p>
<p>$\text{plim}_{n\to\infty} \text{Var}\left[ n^{\frac{1}{2}}\left(\boldsymbol{\widehat{\beta}}_{\text{KQ}} - \boldsymbol{\beta_0}\right)\big| X\right] = \sigma_0^2 \ m_{X^TX}^{-1}$</p>
<p>The corresponding asymptotic variance for the 2SLS case will look like</p>
<p>$\text{plim}_{n\to\infty} \text{Var}\left[ n^{\frac{1}{2}}\left(\boldsymbol{\widetilde{\beta}_{\text{2SLS}}} - \boldsymbol{\beta_0}\right)\big| X\right] = \sigma_0^2 \ \text{plim}_{n\to\infty} \left(\frac{X^TP_W X}{n}\right)^{-1}$</p>
<p>If I now consider the precision matrix rather then the variance matrix and take their difference I'll get </p>
<p>$\text{plim}_{n\to\infty} \ \left(\frac{X^TM_WX}{n}\right) = \left(\text{plim}_{n\to\infty} \ \frac{X^TX}{n}\right) - \left(\text{plim}_{n\to\infty} \ \frac{X^TP_WX}{n}\right)$</p>
<p>which is a positive semidefinite matrix.</p>
<p><strong>My question: When are both asymptotic variances of OLS and 2SLS equal</strong></p>
<p>My guess is that we need to set $X^TX = X^T P_W X$. The only possibility for such a thing is when $P_WX=X$. So all the columns of $X$ must be in the image of $P_W$. This means that all the columns of $X$ are actually viable instruments. By that I conclude that there are (at least asymptotically) no endogenous regressor within $X$ if their asymptotic variances are equal. But this seems to good to be true. There are downfalls of using a 2SLS-approach if theres no endogeneity involved. Again, this would mean that if the variances of the 2SLS and OLS estimator are equal asymptotically it does not matter if we choose 2SLS or OLS since both estimators are consistent for $\beta$.</p>
<p>Any thoughts about this proble would be very much appreciated
Druss</p>
|
g73395
|
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] |
<p>From what I read the <a href="http://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator" rel="nofollow">Theil-Sen estimator</a> seems to be a really cool estimator; robust and easy to understand. <strong>Would it be possible to device (or does it already exists) a Bayesian "version" of the Theil-Sen estimator so that you provide a prior for the slope and get a probability density back instead of just a point estimate? How would such an estimator look/work?</strong></p>
|
g73396
|
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<p>I've been using a Metropolis/Gibbs sampler combination to generate a joint density for some parameters(it is a hierarchical model, with $y_i\sim Poisson(\lambda_i)$, $\lambda_i\sim Gamma(\alpha,\beta)$). What techniques can I use to lower autocorrelation(it is present in $\alpha$ and $\beta$)? I have been using thinning, but even when I use huge lags(4950, which is reaching the memory limit on my computer to use) there is still significant autocorrelation. Is there something I could do with my step size distribution to help with this? I have been drawing the new values of $\alpha$ and $\beta$ from a normal distribution, with mean the current parameter value, and standard deviation 1. Thanks!</p>
|
g47141
|
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<p>I'm familiar with very basic plotting in R, but I'm not sure how best to create the reasonably-complicated plot described below.</p>
<p>I have developed a density estimation method that essentially fits an empirical distribution to multiple univariate samples, under distinct conditions. To be clear, let $\mathbf{x}_i^\mathrm{j}$ be a vector of univariate values for the $i^\mathrm{th}$ sample under condition $j$. My method allows me to approximate the distribution from which the values in $\mathbf{x}_i^\mathrm{j}$ were drawn. Although in principle, $j$ could take on many values, in practice I am interested in just two conditions (e.g., $j$ specifies whether the sample is for a pre- or post-intervention condition).</p>
<p>In particular, the method I have developed attempts to establish correspondences between common features of the fitted density estimates (e.g., modes). I want to be able to plot curves for all the density estimates in such a way as to allow comparison between the two conditions, and between corresponding features of the distributions.</p>
<p>I would like to create a grid of subplots (e.g., <em>m</em> × <em>n</em> if there are a total of 2 × <em>m</em> × <em>n</em> samples; note that <em>m</em> and <em>n</em> are only specified so that the overall plot has a convenient aspect ratio, they do not relate to the design of the experiment etc.). Each subplot would show two curves: one for the distribution underlying $\mathbf{x}_i^\mathrm{pre}$ and the other for $\mathbf{x}_i^\mathrm{post}$. Further, to allow the correspondences to be compared, I would like to color the line used to draw the curves using a “rainbow” (or other color map), so that one could, for example, look at the red regions of two curves and visually determine whether they do in fact correspond. To this end, I can provide vectors (<em>x</em>, p(<em>x</em>), <em>c</em>), where <em>x</em> is an arbitrary value on the horizontal axis of the density estimate plot, p(<em>x</em>) is the density estimate for <em>x</em>, and <em>c</em> is a value in (0, 1), such that a particular value of <em>c</em> should correspond across all density estimates, and should, therefore, be plotted in the same color (e.g., a value of 0.2 might sit at the peak of the mode of the distributions).</p>
<p>Lastly, in order to allow the two curves in each subplot to be distinguished, I'd like to be able to style each differently, for example by using a thin line for the pre condition and a thick line for the post condition.</p>
<p>Thanks.</p>
|
g31078
|
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://stats.stackexchange.com/questions/26970/validation-techniques-for-hierarchical-model">Validation techniques for hierarchical model</a> </p>
</blockquote>
<p>I already posted <a href="http://math.stackexchange.com/questions/135641/validation-techniques-for-hierarchical-model">this to Math.SE</a>, but I realized this would probably be a better place to post to. </p>
<p>I have a hierarchical model that I need to validate. My model is as follows: we have a collection of $λ_i$ that we draw from ${\rm Gamma}(α,β)$. Then, we draw our data point yi from ${\rm Poisson}(λ_i)$. I get a joint distribution of $α,β,λ_i$ via a Gibbs sampler combined with a Metropolis step. This part is fine, no problems with implementation. My question is how do I validate such a model? I have my set of data, each one corresponding to one particular $λ_i$. I'm not sure what statistical tests/ other steps I should take to check are.
Thanks!</p>
|
g49336
|
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] |
<p>I've been searching for a way to combine two hazard ratios from the same study for a meta-analysis, but found nothing. Does anyone know how to do this?</p>
<p>Any thoughts would be great.</p>
<p>Good Day,</p>
<p>Simon</p>
|
g73397
|
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] |
<p>I have spent a fair amount of time trying to solve this problem but I can't find the solution. More specifically, I have the following matrix:</p>
<pre><code>P(D|E&F) = [ 0.5 0.3 0.5 0.2 ;
0.5 0.7 0.5 0.8 ]
</code></pre>
<p>All the variables are binary (two states)
D, E and F are nodes of a Bayesian network. E and F are the parents of D and they are independent. </p>
<p>Now, new evidence comes in and we know that D and E are independent as well (the link between D and F remains but the arc from E to D is removed). How do I go about finding P(D|F) from P(D|E&F) ?</p>
|
g35743
|
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<p>I used the MATLAB interface of libsvm for doing binary classification of 997-dimensional training data. I am trying to understand how the resulting model is used to compute the predicted output (which we get by calling <code>svmpredict</code>)</p>
<p>The model contains fields (it has linear kernel):</p>
<pre><code>nSV = [546; 246]; totalSV=792; rho = 0.093
and svCoeff [792x1 double] and SVs [792x997 double]
</code></pre>
<p>I thought that we must be simply multiplying svCoeff with SVs to get a [997x1] matrix which we then multiply with the actual feature, before shareholding by rho. But that's not the case.
Can someone illustrate with a simple equation how these parameters are used to do classification?</p>
|
g73398
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] |
<p>How can I measure separability between different number of instance of one feature vector? For example the main vector is <code>V=[1 1 2 3 4 5 7 8 10 100 1000 99 999 54]</code> and three sub-vector with different sample lengths are <code>t1=[1 1 2 3 99 1000]</code> or <code>t2=[1 10 1000]</code> or <code>t3=[2 3 4 10 100 99 999 54]</code>.</p>
<p>Which one is more separable and more informative? I mean I am looking for a sub-vector with minimum length and maximum separability power.</p>
<p>If I put it in GMM, the sub-vector with less samples has better probability which is not fairly approach.</p>
<pre><code>train=[1 2 1 2 1 2 100 101 102 99 100 101 1000 1001 999 1003];
No_of_Iterations=10;
No_of_Clusters=3;
[mm,vv,ww]=gaussmix(train,[],No_of_Iterations,No_of_Clusters);
test1=[1 1 1 2 2 2 100 100 100 101 1000 1000 1000];
test2=[1 1 2 2 100 99 1000 999];
test3=[1 100 1000];
[lp,rp,kh,kp]=gaussmixp(test1,mm,vv,ww);
sum(lp)
[lp,rp,kh,kp]=gaussmixp(test2,mm,vv,ww);
sum(lp)
[lp,rp,kh,kp]=gaussmixp(test3,mm,vv,ww);
sum(lp)
</code></pre>
<p>The results are as follow :</p>
<pre><code>ans =
-8.0912e+05
ans =
-8.1782e+05
ans =
-5.0381e+05
</code></pre>
<p>I will really appreciate, if you could help me.</p>
|
g73399
|
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] |
<p>What are the most significant annual conferences focusing on quantitative methods in psychology?</p>
<p>This could include but is not limited to psychometrics, mathematical psychology, and statistical methods in psychology.</p>
<p>Rules:</p>
<ul>
<li>One conference per answer</li>
<li>Include a link to the conference</li>
</ul>
|
g35748
|
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] |
<p>I have two samples, one with $n_1 = 41,000$ and the other with $n_2 = 881$; the larger sample has a standard deviation of $13.74$, and the smaller has an $SD=10.75$. The means are different, and when I run a Welch's t-test, I get a $p < .001$. I'm not sure if that's the appropriate test. I checked the skew for both samples; it was $29$ for the large sample and $9$ for the small one. Should I use a Mann-Whitney U test, or do I have enough data to assume normally distributed samples? In the end I need to know if the means of the samples are statistically different and be able to say one mean is $X$ times larger than the other. </p>
|
g73400
|
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] |
<p>This may be a stupid question but... is there a specific name for normalizing some data so that it has mean=0 and sd=1? </p>
<p>Or do I just say "data was normalized to have mean=0 and sd=1"?</p>
<p>thanks
nico</p>
|
g47158
|
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<p>Lately, I have been interested in phenomenons related to omission of variables. For example, it can be shown that the expected value of the sample variance under the inclusion of one variable $x_1$ but omission of one variable $x_2$ is $\mathbb{E}(s^2|x_1,x_2)= \sigma^2 + \frac{\sigma^2}{n-1} RSS_{x_1, \beta_2 x_2}$ where $\beta_2$ is the true coefficient of $x_2$ and $RSS_{x_1, \beta_2 x_2}$ is the residual sum of squares when running a regression with $x_1$ as predictor and $\beta_2x_2$ as outcome. Now, I am interested in getting a better expression for this when we have an $AR(2)$ process.</p>
<p>Let an $AR(2)$-process be given by $x_t = ax_{t-1}+bx_{t-2} + \epsilon_t$ (with the $\epsilon_i$ being independent and normal with standard deviation $\sigma$).</p>
<p>If we run a regression with $(x_2,\ldots, x_T)$ as the response vector and $(x_1,\ldots, x_{T-1})$ as the predicting variable, what can be said about the residual sum of squares? That is, if we (falsely) think that the process is an $AR(1)$-process, what can be said about the expected residual sum of squares?</p>
<p>Since I am quite unschooled in statistics (my only academic background is in mathematics), I would be interested in references (articles and books) as well as answers, even if they are only tangentially related to this question.</p>
|
g35751
|
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<p>Am I correct to understand that the order in which variables are specified in a multifactorial ANOVA makes a difference but that the order does not matter when doing a multiple linear regression?</p>
<p>So assuming an outcome such as <strong>measured blood loss, y</strong> and two categorical variables</p>
<ol>
<li><strong>adenoidectomy method, a</strong></li>
<li><strong>tonsillectomy method, b</strong></li>
</ol>
<p>The model <em>y~a+b</em> is different to the model <em>y~b+a</em> (or so my implementation in R seems to indicate).</p>
<p>Am I correct to understand that the term here is that ANOVA is a <strong>hierarchical</strong> model since it first attributes as much variance as it can to the first factor before trying to attribute residual variance to the second factor?</p>
<p>In the example above the hierarchy makes sense because I always do the adenoidectomy first before doing the tonsillectomy but what would happen if one had two variables with no inherent order?</p>
|
g47159
|
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<p>I have numerous road segments that belong to a city. Each road segment as a weight that is given to it due to its level of 'connectivity' (‘impact’from a small side street to a motorway). So, small neighbourhood road networks won’t have much weight at the regional level. These are calculated at different radii from each segment going from 400 meters at 400 meter intervals to 20,000 m. So each line segment will have a ‘measure’ at each radius (400, 800, 1200m) that indicate its level of impact on the total network. </p>
<p>Now here’s my question: </p>
<p>I want to be able to 'cluster' these so I can say that these segments 'cluster' around the R400 (400m) radius and therefore are local BUT also have activity around 800m and 1000m so could be local and a little peripheral activity. So below are 6 records just showing the activity at 400, 800 and 1200 meters - in reality it'll go up to 20,000m at 400m intevals.</p>
<pre><code> 400m 800m 1200m
</code></pre>
<p>1 1.2982806 1.3231481 1.3453017
2 1.2048655 1.2961186 1.3369008
3 1.2557751 1.3028713 1.341819
4 1.3692737 1.367762 1.3970656
5 1.3519189 1.3815914 1.3904856
6 1.3940601 1.3942301 1.4031725</p>
<p>So the higher the score the greater the 'connectivity' at that level of radius. So 400m radius of the 2nd record start at 1.20 then at 1200m is 1.33 - so it has a higher connectivity at 1200m.</p>
<p>Therefore, I think the 'shape' of the 'line' and how it clusters with similar lines is important. But I want the data to dictate this and not me starting to create 'categories' by forcing the data to do things that I want to see - this is my concern.</p>
<p>I was thinking using the K Mean measure (But this asks for number of categories...which I think dictates to the data what I want to see) or comparing areas under the curves Or shapes of the curves once of plotted them out – basically grouping the once that look similar, but I know that there are issues where because they could be same areas and shapes but inverted. </p>
<p>thanks for your patience, clearly, I am rather lost...
would be grateful for any advice!
with kindest regards,
Atakan</p>
|
g73401
|
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<p>I have two bacterial markers, I'll just call them <em>X</em> and <em>Y</em>. <em>X</em> codes for virulence, whereas <em>Y</em> just indicates the bacteria is present. Consequently, <em>X</em> will not show up without <em>Y</em> although not all bacteria have <em>X</em>. Both also have a detection limit, although I only care about the detection limit for <em>X</em> because I want to know the probability distribution for the ratio of <em>X</em> / <em>Y</em> (pathogenic to normal bacteria if present).</p>
<p>Because the data are censored and a ratio, I was considering fitting a censored beta distribution. However I realized that the ratio itself is not censored - for example, <em>X</em> could be below detection limit but still some large % of <em>Y</em> if <em>Y</em> is also fairly low. </p>
<p>Does anyone have any suggestions for how to address this problem? I am assuming using a ratio distribution won't work because <em>X</em> and <em>Y</em> are obviously not independent. </p>
|
g73402
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<p>I perform prequential evaluation like this: start with a training set, classify a number of examples, then add the correctly classified examples in the training set and continue to classifying the next number of unseen examples. Is this supposed to increase performance as examples are added to the training set or this doesn't apply to every case? By increasing performance I mean if the average F1, not only accuracy, of the second piece of unseen examples must be higher than that of the first or is it possible for a latter piece to have worse average F1 than a former? And if it has worse, what does this could be possibly mean? Could it mean a problem with training data?</p>
<p>This paper <a href="http://www.cs.waikato.ac.nz/~eibe/pubs/Twitter-crc.pdf" rel="nofollow">Sentiment Knowledge Discovery in Twitter Streaming Data</a> describes prequential evaluation. It experiments with Naive Bayes and not SVMs, probably for the reasons mentioned in comments below.</p>
<p>Thanks a lot in advance! </p>
|
g73403
|
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] |
<p>I have a set of observations. When I do an OLS I get a $\beta$. After I remove some values I also get a $\beta$. Now I want to test if the properties of two betas are the same? Please give me a hint how to do that?</p>
|
g35760
|
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<p>I am looking at the spatial patterns of turnover in aquatic assemblages using gradient forest and generalized dissimilarity models in R. I have species and environmental data for more than 400 sites sampled from streams across the country. However, I also have many missing values in my predictor (environmental) variables, up to 30% for some variables, so removing the cases with incomplete data sets or replacing them by the mean will result in bias and loss of information. About the missingness pattern, my data is really an assembly of data collected by different county administrations, and the decisions about which variables to sample are made at the county level. For example, some counties have monitored total and dissolved nutrients but others have only routinely monitored total nutrients. The missingness pattern is thus affected by those decisions. The next matrix is an example of how my data would look like:</p>
<pre><code> County V1 V2 V3 V4 V5 V6
[1,] 10 52 6 35 294 48 25
[2,] 10 22 7 41 53 42 NA
[3,] 10 118 NA 55 82 59 NA
[4,] 10 150 8 13 91 63 15
[5,] 10 500 NA NA NA 102 9
[6,] 9 58 7 NA 22 73 7
[7,] 9 9 6.5 NA 38 152 17
[8,] 9 9 7 NA 14 224 11
[9,] 9 142 5.5 NA 57 64 11
[10,] 9 90 6 NA 102 66 NA
[11,] 6 30 7 9 NA NA 11
[12,] 6 420 4.5 8 NA NA NA
[13,] 6 43 4.5 3.5 NA NA NA
[14,] 6 50 6.5 116 NA NA 14
[15,] 6 10 NA 13 NA NA 8
>
</code></pre>
<p>where "County" is the different county administrations that have provided data, and "V1 to V6" are the environmental variables.
In county 10 all variables are sampled but some are missing at random.
In county 9 variable V3 is not routinely monitored.
In county 6 variables V4, and V5 are not monitored, in addition there are missing values in the routinely measured variables due to, e.g. failure in the sampling device.</p>
<p>I cannot forget to mention that my data are also spatially autocorrelated at small spatial scales (<10 to 100km).
I would like to estimate those missing values but I don’t know which method is the most appropriate to do so, and which R packages are recommended. </p>
|
g35761
|
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<p>I'm writing a proposal for a restrospective cohort study using registry data. Am I right to think of the registry data as the whole population?</p>
<p>If it is the population, then am I right in thinking there is no need to calculate required sample size (as is required for other cohort studies) or confidence intervals?</p>
<p>If it is a sample, what would be the study population, and how would I go about calculating sample size?</p>
<p>Additionally, with this in mind, how do I treat missing data? If there are 1000 heart transplant patients in a registry but only 500 of them have complete data (i.e. all the variables have values), do I treat these 500 patients as a sample? Furthermore, if it is a sample, it isn't random. Therefore is it worth calculating the confidence intervals from this actual sample size?</p>
|
g73404
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] |
<p>What is meant by subscripting the expectation with some distribution, e.g. $\mathrm{E_{f}}[h(X)]$? </p>
<p>If it's any help, here's the context:</p>
<p>In M.C. Simulation, we wanted </p>
<blockquote>
<p>$\mathrm{E[h(X)] = \int{h(x)f(x)dx}}$ </p>
</blockquote>
<p>so we used the law of large numbers and central limit theorem based on samples:</p>
<blockquote>
<p>$\frac{1}{n} \sum_{i=1}^{n}h(X_i) \longrightarrow E_{f}[h(X)]$, with $X_{1}, \ldots, X_{n} \sim f$</p>
</blockquote>
|
g73405
|
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] |
<p>I have a dataset that is clearly increasing as time goes on (exchange rate of a currency, monthly data over 20 years), my question is: Can I detrend the data and then difference it also to make it stationary, if the detrending in itself doesn't achieve this? And if so, would this be considered twice differenced, or just detrended and once differenced? </p>
|
g35763
|
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] |
<p>This is similar to question <a href="http://stats.stackexchange.com/questions/17602/caret-re-sampling-methods">Caret re-sampling methods</a>, although that really never answered this part of the question in an agreed upon way.</p>
<p>caret's train function offers <code>cv</code> and <code>repeatedcv</code>. What is the difference in say doing:</p>
<pre><code>MyTrainControl=trainControl(
method = "cv",
number=5,
repeats=5
)
</code></pre>
<p>vs</p>
<pre><code>MyTrainControl=trainControl(
method = "repeatedcv",
number=5,
repeats=5
)
</code></pre>
<p>I understand <code>cv</code> breaks the set into k-folds (parameter <code>number</code>), and then starts over and runs it parameters <code>repeats</code> number of times. </p>
<p>The only thing I could think of is that maybe regular <code>cv</code> with <code>repeats</code> uses the same exact indexes for the folds each time? essentially running the <code>cv</code> on the same exact folds each time, vs perhaps <code>repeatedcv</code> selects new folds each times?</p>
<p>Can someone clarify?</p>
|
g73406
|
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] |
<p>The biological data is listed as following: </p>
<pre><code> V1 V2 V3 V4 V5 V6
0.064 0.014 0.016 0.012 0.013 0.023
0.056 0.000 0.000 0.008 0.010 0.000
0.042 0.014 0.024 0.008 0.017 0.023
0.031 0.014 0.016 0.008 0.013 0.023
0.068 0.000 0.008 0.004 0.020 0.000
0.081 0.000 0.000 0.004 0.010 0.000
0.060 0.014 0.016 0.006 0.010 0.023
</code></pre>
<p>or you can download the data from <a href="http://www.mediafire.com/?6yp9l9m47jv433a" rel="nofollow">http://www.mediafire.com/?6yp9l9m47jv433a</a>.</p>
<pre><code>A<- dat[,1]
B<- dat[,2:6]
</code></pre>
<p>I want to compare the difference between the first column to other columns of the data.Because only dat[,2] and dat[,6] not subject to normal distribute,I used wilcox.test instead of t.test function to caculate in R. But the warning messages rised up,such as "In wilcox.test.default(A, B[, 1]) : cannot compute exact p-value with ties". Could you give me some suggestions? Thank you.</p>
<pre><code>wilcox.test(A,B[,1])
Wilcoxon rank sum test with continuity correction
data: A and B[, 1] W = 49, p-value = 0.00184 alternative hypothesis: true location shift is not equal to 0
Warning message: In wilcox.test.default(A, B[, 1]) : cannot compute exact p-value with ties
</code></pre>
|
g73407
|
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] |
<p>Dear all,
I was encouraged to ask this question here as well as on stackoverflow and would be very appreciative of any answers...</p>
<p>Due to hetereoscedasticity I'm doing bootstrapped linear regression (appeals more to me than robust regression). I'd like to create a plot along the lines of what I've done in the script here. However the <code>fill=int</code> is not right since <code>int</code> should (I believe) be calculated using a bivariate normal distribution. </p>
<ul>
<li>Any idea how I could do that in this setting? </li>
<li>Also is there a way for <code>bootcov</code> to return bias-corrected percentiles?</li>
</ul>
<p>sample script:</p>
<pre><code>library(ggplot2)
library(Hmisc)
library(Design) # for ols()
o<-data.frame(value=rnorm(10,20,5),
bc=rnorm(1000,60,50),
age=rnorm(1000,50,20),
ai=as.factor(round(runif(1000,0,4),0)),
Gs=as.factor(round(runif(1000,0,6),0)))
reg.s<-function(x){
ols(value~as.numeric(bc)+as.numeric(age),data=x,x=T,y=T)->temp
bootcov(temp,B=1000,coef.reps=T)->t2
return(t2)
}
dlply(o,.(ai,Gs),function(x) reg.s(x))->b.list
llply(b.list,function(x) x[["boot.Coef"]])->b2
ks<-llply(names(b2),function(x){
s<-data.frame(b2[[x]])
s$ai<-x
return(s)
})
ks3<-do.call(rbind,ks)
ks3$ai2<-with(ks3,substring(ai,1,1))
ks3$gc2<-sapply(strsplit(as.character(ks3$ai), "\\."), "[[", 2)
k<-ks3
j<-dlply(k,.(ai2,gc2),function(x){
i1<-quantile(x$Intercept,probs=c(0.025,0.975))[1]
i2<-quantile(x$Intercept,probs=c(0.025,0.975))[2]
j1<-quantile(x$bc,probs=c(0.025,0.975))[1]
j2<-quantile(x$bc,probs=c(0.025,0.975))[2]
o<-x$Intercept>i1 & x$Intercept<i2
p<-x$bc>j1 & x$bc<j2
h<-o & p
return(h)
})
m<-melt(j)
ks3$int<-m[,1]
ggplot(ks3,aes(x=bc,y=Intercept,fill=int)) +
geom_point(,alpha=0.3,size=1,shape=21) +
facet_grid(gc2~ai2,scales = "free_y")+theme_bw()->plott
plott<-plott+opts(panel.grid.minor=theme_blank(),panel.grid.major=theme_blank())
plott<-plott+geom_vline(x=0,color="red")
plott+xlab("BC coefficient")+ylab("Intercept")
</code></pre>
|
g47164
|
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] |
<p>I conducted a multilevel analysis using repeated measures across four time points. The model contains intercept, linear slope and quadratic slope. I am interested in examining the extent to which variable A interacts with other identified variables in my model, so I added the interaction terms to intercept, linear slope and quadratic slope to estimate the fixed effects of these interactions. I then eliminated the non-significant interactions and retan the model until the interaction terms in the model were all significant. </p>
<p>My questions are:</p>
<ol>
<li><p>When delete non-significant interactions from the model, if the interaction was significant on linear slope but not quadratic slope, should I still keep the non-significant one on quadratic slope? Or should I only keep the significant one on linear slope?</p></li>
<li><p>How should I interpret an interaction on linear slope but not quadratic slope (or vice versa)?</p></li>
</ol>
<p>Thank you for your response in advance! Any advice is appreciated.</p>
|
g73408
|
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<p>I am trying to apply a GLM in R. I have a binary response (success vs failure), and 3 categorical explanatory variables : Sex (male or female), Food (present or absent) and Wind (none, low, high). I arranged my data to end up with a count of number of success for each possible combination of explanatory variables. (<em>*</em> Sorry for the pictures instead of codes, but I wasn't able to format it so it could be understandable...)</p>
<p><img src="http://i.stack.imgur.com/ZZd6m.png" alt="enter image description here"></p>
<p>I tried to run a GLM on this, taking the Success column as the response variable and treating it as count data : </p>
<p><code>model2<-glm(Success~Wind*Sex*Food, data=data, family=poisson)</code></p>
<p>But the summary of it gives something unexpected : The residual deviance shows 0 degrees of freedom.
<img src="http://i.stack.imgur.com/8H0ko.png" alt="enter image description here"></p>
<p>Why is it the case ? (i.e. is it unusual as I think or I'm just freaking out for nothing) Am I using an inapropriate model or distribution ? Is the trouble coming from the way I managed my dataset ? I don't know if I am using an appropriate technique... Basically, I want to know if any of my explanatory variables or their interaction has an effect on the success of the trial. I don't know how else I could get that info...</p>
<p>Thanks</p>
|
g73409
|
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] |
<p>$\chi^n_k=\sum_{i=1}^kx_i^n$ where $x_i$ are Gaussian variables and $n>2$?</p>
|
g35766
|
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<p>I have a question regarding a small investigation that I have been conducting into the relationship between the length of observation sequence, T, on which two decoders (BCJR and classic Viterbi) decode in a fixed small (2 state, 3 symbol) HMM.</p>
<p>When I plot $T$ against the average decoding rate accuracy, I get unsurprising results, the BCJR algorithm moderately outperforms the Viterbi on symbol-by-symbol decoding and the data shows essentially no relationship between $T$ and accuracy rate.</p>
<p>However, for the same sequences, I have plotted T against $\log P(O,Q\vert\lambda)$, for both the sequence from the BCJR decoder and the sequence from the Viterbi decoder, where $O$ is the observation sequence. I have also plotted $T$ against $\log P(O\vert Q,\lambda)$. In both cases, for the same set of results, there is a 'perfect' negative linear relationship between $T$ and these log probabilities. This would accord to a 'perfect' relationship: as the length of observation sequence increases, the log probabilities exponentially decrease and the exponential decrease does not vary over $T$, which would be surprising to say the least. </p>
<p>Does anyone have any reasons as to how we know these results are wrong? What would be the expected relationship between $T$ and these log probabilities? Any help, no matter how small or trivial - even if just an idea or a thought, would be really appreciated as I just would like to understand this situation further.</p>
|
g73410
|
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<p>Does anyone know of research which investigates the effectiveness (understandability?) of different visualization techniques? </p>
<p>For example, how quickly do people understand one form of visualization over another? Does interactivity with the visualization help people recall the data? Anything along those lines. An example of visualizations might be: scatter plots, graphs, timelines, maps, interactive interfaces (like Parallel Coordinates) etc.</p>
<p>I'm particularly interested in research within a lay-person population.</p>
|
g47168
|
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] |
<p>This is a soft question: How can the order of a sample univariate data be reversed while preserving the variance?</p>
|
g35767
|
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] |
<p>Hello I'm running anova with R and I am wondering what the differce is between multiway anova and single anova. I know single anova gives a different answer than multiway anova but I dont know how to quantify multiway anova.
Could someone explain in words the difference between:</p>
<ul>
<li>base~col1</li>
<li>base~col1+col2</li>
<li>base~col1*col2</li>
</ul>
<p><a href="http://www.gardenersown.co.uk/Education/Lectures/R/anova.htm#anova_1" rel="nofollow">http://www.gardenersown.co.uk/Education/Lectures/R/anova.htm#anova_1</a></p>
<p>How do I interpret the results of col1+col2 and col1*col2
because col2 is giving a P(>F) of 0.473 on single anova but P(>F) 4.21e-07 in multiway anova. col2 does correlate well with base having only a 2% coloration for 711 individuals. According to <a href="http://vassarstats.net/rsig.html" rel="nofollow">http://vassarstats.net/rsig.html</a> 2% coloration isn't significant.
Thank you</p>
<p>edit:
i know my col1 and col2 have some interactions is that causing the low multiple anova p value?</p>
<p>i am using </p>
<pre><code>aov.ex2 <- aov(base~col1+col2,data=data1)
summary(aov.ex2)
aov.ex2 <- aov(base~col1,data=data1)
summary(aov.ex2)
aov.ex2 <- aov(base~col1,data=data1)
summary(aov.ex2)
</code></pre>
<p>and the results are not simular</p>
|
g73411
|
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<p>I am using random forests for a class.</p>
<p>I am predicting weight training.</p>
<p>In scikit learn I always used a rule of thumb of a depth of 5, the depth x features rounded.</p>
<p>I had 53 features, rounded to 50 x 5 and got 250 for number of trees.</p>
<p>I picked 250 trees and 5 node depth and got great results.</p>
<p>I got 98% accuracy for my test set (100% for training). </p>
<p>The data set is for coursera machine learning. The data set is at d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv I removed seven features that were unrelated. The predictor is classe. </p>
<p>Well, it works again, but I have no formal basis. I would appreciate any guidance,</p>
|
g27350
|
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<p>I want to make a 4 question, multiple choice survey in which each question asks about an analogous range of actions for slightly different scenarios. Each participant would only be administered the survey once. For example: </p>
<p>"In situation W how would you behave? (5[very aggressively] -- 1 [not aggressively])."
"In situation X how would you behave? (5[very aggressively] -- 1 [not aggressively])."
"In situation Y how would you behave? (5[very aggressively] -- 1 [not aggressively])."
"In situation Z how would you behave? (5[very aggressively] -- 1 [not aggressively])."</p>
<p>I then wanted to sum the responses to the 4 questions, and use that total score as my DV.</p>
<p>I plan to have 2 IVs. </p>
<p>The first will be relationship status, and consist of 7 levels (e.g. Married, single, divorced, dating, widowed, etc).</p>
<p>The second will be, say, partner hair-color preference, and will consist of 3 levels (e.g. blond, brunet, redhead).</p>
<p>So, my understanding is that this will be a 3x7 factorial design, with a total number of 21 individual conditions, and an ordinal DV. </p>
<p>Ideally, I'd like to do a 3x7 factorial ANOVA to test for main effects and interaction effects, but I don't think my summed, ordinal survey response DV is amenable to this. Is there some other analysis i could use in this situation? Would the Kruskal-Wallis be appropriate? Thanks!</p>
|
g73412
|
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<p>Please help! </p>
<p>I have developed a logistic regression model for prediction of a binary outcome at a range of different times following a set point. This gave me different models with different variables lists, although many variables overlapped and were seen to be significant at different times. I've then created a combined model to use the same set of variables at all time points and have run this for each of the 6 times in question. This model is therefore not the best-fit for any individual time point, but is the best-fit across all time points. </p>
<p>I've been looking at how to internally validate this model within SPSS, and am stuck. I have been able to bootstrap to obtain variable estimates at each of the time points, but am looking for a measure of overall model performance (i.e. a mean AUC to calculate model optimism or similar). However, my attempts at 10-fold cross-validation have failed as I cannot work out how to apply the model created on 9/10th of the dataset to the other 1/10th. Every time I save an .xml file, SPSS tells me it is not recognised and cannot be used. The additional problem is that the model was tested on different population numbers at different time points, due to missing data issues. </p>
<p>Is there a simple way to obtain overall model performance data to internally validate a logistic regression model in SPSS, given the problems I have outlined? </p>
<p>Thanks</p>
|
g35771
|
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<p>I posted this to mathoverflow and no one's answering:</p>
<p><a href="http://en.wikipedia.org/wiki/Scheff%C3%A9%27s_method">Scheffé's method</a> for identifying statistically significant contrasts is widely known. A <b>contrast</b> among the means $\mu_i$, $i=1,\ldots,r$ of $r$ populations is a linear combination $\sum_{i=1}^r c_i \mu_i$ in which $\sum_{i=1}^r c_i=0$, and a scalar multiple of a contrast is essentially the same contrast, so one could say the set of contrasts is a projective space. Scheffé's method tests a null hypothesis that says <em>all</em> contrasts among these $r$ populations is $0$, and given a significance level $\alpha$, rejects the null hypothesis with probability $\alpha$ given that the null hypothesis is true. And if the null hypothesis is rejected, Scheffé points out that his test tells us <em>which</em> contrasts differ significantly from $0$ (I'm not sure the Wikipedia article I linked to points that out).</p>
<p>I would like to know if one can do something similar in a different sort of situation. Consider a simple linear regression model $Y_i = \alpha + \beta x_i + \varepsilon_i$, where $\varepsilon_i\sim\operatorname{i.i.d.}N(0,\sigma^2)$, $i=1,\ldots,n$.</p>
<p>The null hypothesis I want to consider concerns a different sort of contrast. It says there is no subset $A\subseteq\lbrace 1,\ldots,n\rbrace$ such that $E(Y_i) = \alpha_1 + \beta x_i$ for $i\in A$ and $E(Y_i) = \alpha_2 + \beta x_i$ for $i\not\in A$, where $\alpha_1\ne\alpha_2$. If the subset $A$ is specified in advance, then an ordinary two-sample $t$-test does it, but we want something that considers all subsets and holds down the probability of rejecting a true null hypothesis.</p>
<p>One could figure this out if efficiency were not a concern: find a test that goes through all $2^{n-1}-1$ possibilities. Even then it's problematic; two contrasts would not be independent. I asked an expert on outlier detection about this and he just said it's a combinatorial nightmare. Then I asked if one could <em>prove</em> that there's no efficient way to do it, perhaps by reducing an NP-hard problem to it. He just said he stays away from NP-hard problems.</p>
<p>So: Can one prove either that this problem is "hard" or that it's not?</p>
|
g73413
|
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] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://stats.stackexchange.com/questions/12386/machine-learning-cookbook-reference-card-cheatsheet">Machine learning cookbook / reference card / cheatsheet?</a> </p>
</blockquote>
<p>I wonder if there is a good self-learning textbook for machine learning? I am particularly looking for those in application-level, not so much theoretical. I wouldn't mind a math-heavy book, as long as you guys think it is suitable for self-learning. </p>
<p>Thanks! </p>
|
g49363
|
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<p>I have a database of users with a field of the last time they logged in. Would this kind of data be considered "censored", and if so is there anything I can do with it beyond a histogram/density of how many people logged in within the last month, two months, etc? (To be clear: I only know the last time they logged in, so they could have logged in every day for years, up until a week ago, and all I know is they haven't logged in since last week.)</p>
<p>It feels to me that this is censored data, but in a reverse sort of way from the definitions I read online. But perhaps this is just left-censored data? Or is this some kind of logit problem?</p>
<p>For now, all I'm able to say is the percentage of users who have logged in during the last month, two months, etc, but I know people will want to hear more than that, and I also fear that it's easy to misinterpret what this data means. (It feels very particular, like explaining a confidence interval.) Ultimately, I may have to (manually) dump the data on a weekly basis to be able to take it any farther.</p>
<p>Any references appreciated.</p>
|
g35775
|
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] |
<p>I have logs for users and posts in a blog platform for 3 years. I can easily find out how many posts each user have made per day/month/year/etc.</p>
<p>What I want to find out is if the frequency of posts is growing or not, in other words, if the users are contributing more over time or not. New users could join at any time and old ones could abandon the system (only the first one is logged). Is a trend estimation (<a href="http://en.wikipedia.org/wiki/Trend_estimation" rel="nofollow">http://en.wikipedia.org/wiki/Trend_estimation</a>) suitable for this ? </p>
<p>More over, is there a python package for this kind of time analyse ? </p>
|
g35977
|
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] |
<p>What is the purpose of the link function as a component of the generalized linear model? Why do we need it?</p>
<p>Wikipedia states:</p>
<blockquote>
<p>It can be convenient to match the domain of the link function to the range of the distribution function's mean</p>
</blockquote>
<p>What's the advantage of doing this?</p>
|
g73414
|
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<p>I am interested in finding a leading indicator of $Y_t$. Is it sufficient to find a variable $X$ for which its lagged value is correlated with $Y$? Do I have to give consideration to the spurious regression phenomenon? Or is it correct to say that when it comes to forecasting, I can ignore this problem?</p>
|
g35777
|
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] |
<p>Suppose you have $n$ players play a round robin tournament. A win adds 1 to the winning score of a player while a loss adds nothing. After the round robin tournament is finished the players are assigned ranks based on their scores, with ties being broken at random, the top player receiving a rank of $n-1$ and the bottom player receiving a rank of 0. What is the relationship between the expected value of the $\textbf{score}$ of player $i$ and the expected value of the $\textbf{rank}$ of player $i$?</p>
<p>Sample result of a tournament with 5 players: $scores=(3,3,2,1,1)$ and $ranks=(3,4,2,1,0)$</p>
<p>Addition information: A player $i$ has an attribute $\lambda_i$. The probability that player i beats player $j$ in a game is $\frac{\lambda_i}{\lambda_i+\lambda_j}$.</p>
<p>Numerical simulations suggest that taken across players, the two quantities perfectly correlated, but I don't know how to prove this. Any references would be appreciated.</p>
|
g73415
|
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<p>Consider a set of observations $ \{ y_i \}$ and assume a Gaussian model for these data: $y_i \sim \mathcal{N}(\mu, \sigma^2)$. Suppose the mean parameter $\mu$ is known, but the variance parameter $\sigma^2$ is not. The conjugate prior for $\sigma^2$ is then the scaled inverse chi-squared distribution; consequently, we have a nice posterior. Now, suppose instead of $\mathcal{N}(\mu, \sigma^2)$ our model is $\mathcal{N}(\mu, \sigma^2 + \sigma_0^2)$ where $\sigma_0^2$ is known. What can we say regarding the prior and posterior distributions of $\sigma^2$ in this case? Thank you.</p>
<p>Regards,
Ivan</p>
|
g73416
|
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<p>I am working on monthly seasonally adjusted data. To the best of my knowledge (maybe I'm wrong), data is seasonally adjusted to take out any form of seasonality. </p>
<p>After doing an ACF of the second difference of my data with R, I saw a spike from the lag one point that crosses the horizontal dashed line. This led me to suggest a nonseasonal MA(1) component. I then saw a lag from the 12th point that lies right on the horizontal dashed line. Can this mean there is a seasonal MA(1) component with period 12? And if so, can monthly seasonally adjusted data still exhibit seasonality? </p>
|
g73417
|
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] |
<p>I am working on a data set. After using some model identification techniques, I came out with an ARIMA(0,2,1) model. </p>
<p>I used the <code>detectIO</code> function in the package <code>TSA</code> in R to detect an <em>innovative</em> outlier (IO) at the 48th observation of my original data set. </p>
<p>How do I incorporate this outlier into my model so I can use it for forecasting purposes? I don't want to use the ARIMAX model since I might not be able to make any predictions from that in R. Are there any other ways I could do this? </p>
<p>Here are my values in order:</p>
<pre><code>VALUE <- scan()
4.6 4.5 4.4 4.5 4.4 4.6 4.7 4.6 4.7 4.7 4.7 5.0 5.0 4.9 5.1 5.0 5.4
5.6 5.8 6.1 6.1 6.5 6.8 7.3 7.8 8.3 8.7 9.0 9.4 9.5 9.5 9.6 9.8 10.0
9.9 9.9 9.8 9.8 9.9 9.9 9.6 9.4 9.5 9.5 9.5 9.5 9.8 9.3 9.1 9.0 8.9
9.0 9.0 9.1 9.0 9.0 9.0 8.9 8.6 8.5 8.3 8.3 8.2 8.1 8.2 8.2 8.2 8.1
7.8 7.9 7.8 7.8
</code></pre>
<p>That is actually my data. They are unemployment rates over a period of 6 years. There are 72 observations then . Each value is to at most one decimal place</p>
|
g73418
|
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] |
<p>I am using Logistic Regression in a <code>low event rate</code> situation.<br>
Overall universe: 46,000<br>
Events: 420</p>
<p>Conventional logistic regression models divide the data into training and test sets and compute the error rates. The final coefficients and threshold levels are chosen and a model is created.</p>
<p>OTH, I'm just trying to prove that so and so coefficient is significant and has positive association with the event in study. I'm not developing a model as of now. I don't focus on error rates (too many true negatives!) and chose my threshold level ~ hit rate. </p>
<p>Should I consider dividing my universe into 2 samples, the conventional way? With such a low event rate, I'm worried that doing this to bias my coeff. estimates.</p>
|
g73419
|
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] |
<p>I'm working on a software and need to do some statistics. In my case I'm comparing two different networks that have a certain number of nodes with attributes and want to test with a Fisher's exact test if some of these attributes are enriched in the smaller one.<br>
I also have a good math library that is able to calculate hypergeometric distributions and want to use it.</p>
<p>So after reading a bit it seemed to me that you need to calculate the probabilities for your obtained data and more extreme cases and then add these.</p>
<p>If this is correct and my table looks e.g. like</p>
<pre><code>-------------------------------------
| |Network1|Network2|
-------------------------------------
|has Attribute |a=7 |b=10 |
-------------------------------------
|has not Attribute|c=17794 |d=1107 |
-------------------------------------
</code></pre>
<p>How more extreme tables do I have to calculate for a one-tailed test? I guess until a=0, b=17, c=17801 and d=1100?</p>
<p>Thanks a lot!</p>
|
g35782
|
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] |
<p>Why are measures of dispersion calculated relative to some central point? Why wouldn't, for instance, all possible non-repeated, pairwise differences in the dataset be a valid measure of spread?</p>
|
g35784
|
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] |
<p>I am new to statistics and within the last two days I tried to get my head around PCA plots. Now, I kind of understand what they are showing but I am still not sure about the 95% confidence ellipse that is very often shown in such plots. The 2 dimensional PCA plot displays the two biggest variances (whatever these are) in the data but I don't know what the ellipse is trying to tell me and what it means if a sample/dot (whatever is displayed) is lying outside that ellipse.</p>
<p>Help is very much appreciated.</p>
|
g73420
|
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<p>I am building a scoring model for rating an individual on trustworthiness. The parameters of the model are not fixed and I have no historical data to test. So to test the validity of the parameters and their weightings, I have built random samples using Monte Carlo simulation. I have now came across the term predictive modeling (logistic regression, etc). So here, does Monte Carlo or any other technique work?<br>
Could anyone clarify when to use simulation and when to use predictive modeling?</p>
|
g73421
|
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<p>I was studying Deep Belief Network (DBN) and have questions. </p>
<p>1) According to the definition of DBN, DBN is formed by stacking RBM on top of each other such that the hidden layer in a lower layer becomes the input layer in the above layer. However, when I read the papers by Geoff Hinton (for example, "a fast learning algorithm for deep belief nets"), his DBN doesn't seem to have multiple RBMs. His DBN has only one RBM (i.e., undirected Markov Random Field with two layers) which sits on top while the other layers have only directional edges. I am confused by this difference. </p>
<p>Are these two architectures essentially same? When the term, "DBN" is used in literatures, does it refer to Geoff Hinton's DBN? Or does it refer to a general class of multi-layer architectures with one or multiple RBMs.</p>
<p>2) Following up the above question, does anybody know why Geoff Hinton's DBN has undirected RBM (called associative memory) on top? What role does it play? What would happen if, instead of undirected edges, directed edges are used on top?</p>
<p>Thanks,</p>
|
g451
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] |
<p>Is there a standard hypothesis test for differences in the mean of a continuous dependent variable with respect to a single ordered categorical variable. </p>
<p>By specifying that the independent variable is ordered, I also mean to impose the assumption that the dependent variable is monotonic in the independent variable.</p>
|
g14632
|
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<p>Last week I had an interesting discussion with a good friend of mine. He had been playing some <a href="http://en.wikipedia.org/wiki/Online_poker">online poker</a> and suggested that there is a relationship between new subscription/additional money transfer and the cards that you're dealt, i.e. you get good cards to get hooked. The sites would probably be risking a lot if this was true but the problem still fascinates me.</p>
<p>My first approach to this was to ask my friend to define "good cards" and do a simple <a href="http://en.wikipedia.org/wiki/Binomial_test">binomial test</a>. My friend had though a hard time defining what exactly good cards are. If he gets really bad cards he knows to fold while if he gets good cards he knows to go all in - the bad cards are the ones in between.</p>
<p>My other approach would be to calculate the exact probability of each given hand and then to see if it differs from the expected, perhaps using a <a href="http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test">Wilcoxon signed-rank test</a> since this should detect a different distribution shape as well as a true shift. I guess the hard part is to calculate the exact probability. </p>
<p>The data would consist of the first 0-100 dealt cards compared with 300-400 dealt cards a week later (or a friend that's been on the site for a while).</p>
<p><strong>Question</strong>: How would you suggest to approach the issue?</p>
<p><strong>How Texas hold'em works</strong></p>
<p>I'm no expert gamer (I've only played Texas hold'em 3-4 times) but it's fairly simple, you can find more details on the Wikipedia page <a href="http://en.wikipedia.org/wiki/Texas_hold_%27em">here</a>. </p>
<p>The main difference from regular poker is that you only get 2 cards at start. You don't get to switch these cards. On the table are another 5 cards face down. By combining your two with the tables 5 you choose the best possible 5 card-poker hand. </p>
<p>For instance if you get 2 aces you have a good start and you will probably go in strong, likewise if you have a 7 and a 2 your chances to win are very slim and you quickly fold. The hard part is perhaps a queen and a 9 where you might end up without anything although your cards are above the "average". You can find a list of the poker hands <a href="http://en.wikipedia.org/wiki/List_of_poker_hands">here</a>.</p>
|
g73422
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<p>For a linear regression fit for a problem with p variables X_i ranging between 0 and 1, where p>20 (I don't know if that is relevant or not), and the number of samples is about 1000, I wanted to estimate the variance contribution for each of the variables using the regression coefficients. If I understood correctly var(A*X) = A^2*var(X), and therefore I thought that taking the square of the regression coefficients and multiplying that with the variance for each of the variables should give a vector containing all the variance contributions of the different variables. </p>
<p>The problem is that I expected the sum of those variance contributions to be equal to the sum of the total regression model variance, but it isn't. The sum of the variances is some times up to 50% larger, then the total variance of the regression model.</p>
<p>here some <code>Matlab</code> like pseudo code to explain the problem more in detail. </p>
<pre><code>X %sample matrix
Y %output sample matrix
Linmodel=polyfitn(X,Y) %fit a model
for ii=1:nr_colsX
VARCONT(ii)=var(Linmodel.COEF(ii)*X(:,ii))) %variance of the contributions
VARRC(ii)=(Linmodel.COEF(ii)).^2*var(X(:,ii)) %variance based on Reg. Coef.
end
SVC=sum(VARCONT(ii)) %sum of the variance contributions
SVSRC=sum(VARRC)
VY=var(Y) %sum of the variance of the samples
VYmod=var(polyvaln(Linmodel,X)) %sum of the variance of the model on the samples
XR=rand(100000,nr_colsX) %sum of the variance of the model with large number of samples
VYmodR=var(polyvaln(Linmodel,XR))
</code></pre>
<p>for one of the models that are supposed to be almost linear, VY is almost equal to VYmod.
but SVC is about 50% largen then that. and VYmodR comes more in the direction of SVC. </p>
<p>1) Could some body please explain me why the sum of the variance contributions from the Regression coefficients, can be quite a bit larger then the variance of the regression model? </p>
<p>2) If this is so as it seems to be the case should there then not be some sort of upper bound for the sum of the square of the regression coefficients, such that the sum of their squares, multiplied by the variances of the input, should not be larger then the total variance of the output? Because it seems strange to me that the output of an interpolation model could result in a larger variance, then the variance of the data output points used for the interpolation. </p>
<p>Any help is highly appreciated, but any help that is written in a way, such that also just a silly engineer as me can understand it is appreciated even more. </p>
|
g35792
|
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0.027088414877653122
] |
<p>The <code>chisq.test</code> function in R includes a <code>y =</code> argument, which is to <code>NULL</code> by default. The help page doesn't explain what this argument does, and playing round with numbers doesn't give any clues, for example all these give exactly same results:</p>
<pre><code>chisq.test(x=c(20, 10, 5, 3, 2, 1, 0), y = 100:106)
chisq.test(x=c(20, 10, 5, 3, 2, 1, 0), y = 0:6)
chisq.test(x=c(20, 10, 5, 3, 2, 1, 0), y = 5:11)
</code></pre>
|
g18145
|
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] |
<p>The dependent variable of my problem is highly concentrated around zero. Here is a stemplot</p>
<pre><code> The decimal point is 6 digit(s) to the right of the |
-2 | 511
-1 | 92221
-0 | 87777666666665555555555555555444444444444444444444444444444433333333+2428
0 | 00000000000000000000000000000000000000000000000000000000000000000000+2113
1 | 00000000000000000000000000000000000011111111111111111111111111111122+110
2 | 0000000000111111233333444444555666666677778889
3 | 00112457778889
4 | 11233456999
5 | 0000389
6 | 01477
7 | 259
8 | 033
9 | 002356
10 | 9
11 |
12 |
13 | 069
14 |
15 |
16 |
17 | 13
</code></pre>
<p>Normally when I have a dependent variable (DV) that looks like this I apply a logarithmic transformation for reasons both economical and mathematical. But obviously this will not work in this case as I have values below zero.</p>
<p>Is there another monotonically increasing transformation function that will reduce the peakedness of this distribution?</p>
|
g73423
|
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<p>IMDB uses a Bayesian estimate to compute its top 250 films. Let's say I know all the variables needed to compute this Bayesian estimate for these films. I also have the production company associated with each film. How could I fairly rank the production companies based on the weighted rank (and review counts) of their films? I'd be using all films with a more than m reviews. As a refresher, IMDB uses <code>weighted rating (WR) = (v / (v+m)) × R + (m / (v+m)) × C</code>.</p>
<p>It probably doesn't matter, but I'm using R to do the analysis in case there are some packages that can help solve this.</p>
|
g73424
|
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] |
<p>Official stats on how many videos (rather than how many hours or what volume of data) seem quite hard to come by. </p>
<p>My current idea is something like this:</p>
<p>A youtube URL is like: <a href="http://www.youtube.com/watch?v=w1sjRD7NSec" rel="nofollow">http://www.youtube.com/watch?v=w1sjRD7NSec</a></p>
<p>where</p>
<pre><code> id = w1sjRD7NSec
</code></pre>
<p>Assuming that each character in the id can be upper (26) or lower (26) case letter or number (10)</p>
<p>the number of combinations should be</p>
<pre><code> = (26 + 26 +10 ) ^ 11
= 62^11
= 5.2 x 10 ^19
</code></pre>
<p>So if I write a script to try random urls of 100/1000/whatever videos, and Z% are successful, then will </p>
<pre><code> Z% x 5.2 x 10 ^19
</code></pre>
<p>give me the number of videos that exist (or at least are downloadable), albeit with a very low confidence?</p>
|
g12795
|
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<p>I am measuring the evolution of the brain response to a visual stimulation over time. The measures are done every seconds from 1 second to 14 seconds (each measure at time t gives a value summarizing the magnitude of the brain response from time 0 to time t). I have 8 subjects and 2 experimental conditions. For each subject and condition I replicate the measurement 12 times. I obtain therefore for each subject and condition 12 growth curves.</p>
<p>My aim is to assess the influence of the experimental condition on the response profile. The responses appear to be fairly linear in time. Additionally, a noticeable aspect of the obtained results is the increase of the response variability over time (for each subject individually as well as between subjects).
I am not sure about how to specify properly my random effect for the linear mixed model (using the nlme package).</p>
<p>My initial idea was to start with the following model (time being coded as an integer and condition and subject as factors):<code>lm0 <- lme( response ~ time*condition, random = ~time | subject/condition, data = psdData)</code>.</p>
<p>Now due to the increase of variability of the response over time, I also get an increase of variability of the residuals over time.
I initially wanted to try correcting for this using correlation structures, unfortunately, due to the replications, it seems that I cannot use the correlation option; when trying <code>lm1 <- update(lm0, corr = corCAR1(form = ~time))</code> or <code>lm1 <- update(lm0, corr = corCAR1(form = ~time | subject/condition))</code>, I obtain the error:</p>
<pre><code>Error in Initialize.corCAR1(X[[2L]], ...) : covariate must have unique values within groups for "corCAR1" objects
</code></pre>
<p>and when trying <code>lm1 <- update(lm0, corr = corCAR1(form = ~time | replicate/subject/condition))</code>, I obtain the error:</p>
<pre><code>Error in lme.formula(response ~ time * condition, data = psdData, : incompatible formulas for groups in 'random' and 'correlation'
</code></pre>
<p>As I didn't manage to use correlation structures, I tried to use variance functions to model heteroscedasticity: <code>lm1 <- update(lm0, weights = varPower(form = ~ time))</code></p>
<p>But when looking at the residuals, it still displayed an increased variance over time. Same thing happened when using "varExp" or "varConstPower".</p>
<p>I tried then another model, this time considering trials as units of measurements (and not subject as previously) and including the trial to trial variability within each subject.
I created the factor <code>trialInSub <- condition:replicate</code> which list all 24 trials of each subject (12 per condition) and wrote the model:</p>
<pre><code>lm0 <- lme( response ~ time*condition, random = ~time | subject/trialInSub, data = psdData)
</code></pre>
<p>giving a random intercept and slope for each subject and for each trial within subject.</p>
<p>As this model fits a line for each replicate, I don't have anymore the issue about increasing variance over time.
However when looking at the autocorrelation of the models residuals, I would suspect something is wrong with the model: from lag 2 to 7, the autocorrelation decreases from 0.5 to -0.5 and from lag 7 to 10 increases back to 0.04.
Additionally I have a clear linear trend when plotting residuals against fitted values of the model for time = 1 (it looks fairly normally distributed for all other times) I tried different correlation structures but it didn't change much my results.</p>
<p>I am really not sure that I handle the problem in a proper way and that the models I tried really reflect the design of the experiment and the structure of the data.
I hope someone can direct me towards a solution that would be statistically sound.</p>
|
g35796
|
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<p>I'm very in to Sports analysis and am keen to look at finessing my analysis models that I have worked up (I don't have a great maths background, I've just done a little bit of reading).</p>
<p>Standard deviation of Game Results about prediction from a Ratings system (in this case least squares regression with a few tweaks) equals the stochastic element in a normal distribution function where:</p>
<p>x = the margin of victory that you are trying to get a % against (e.g. it could be a point spread e.g. % to cover)
the mean = the predicted margin of victory derived in this case from my least squares regression to create power ratings for teams
sigma = standard deviation of error on the difference between the predicted margin of victory and actual margin of victory based on past results.</p>
<p>Based on the above I would treat in Excel terms a win % for team A as:</p>
<p>1-NORMDIST(0.5,mean,sigma,true) - with the mean and sigma having values obviously.</p>
<p>Based on Stern "The Probability of Winning an American Football Game" American Statistician (August 1991) - the sigma value (stochastic element? - sorry this isn't my usual thing) is approximately 13.86. How would you go about refining this for other sports? - e.g. Australian Rules Football. I said this could be done for any sport (and I believe it can within reason unless the results or the sport doesn't lend itself to this type of analysis).</p>
<p>Looking at past AFL results from the end of the season point of view the standard deviations are as follows (have only started looking at these in the last two days):</p>
<p>2009: 31.34 (150+ results)
2010: 33.44 (150+ results
2011: 34.91 (150+ results)
2012: 25.62 (only approximately 70 results so far as it is mid season)</p>
<p>As you feed more data into the model for 2012 it will build up a more accurate picture but looking at past data I'm putting the sigma value for AFL at around 33.5 (above the 25.62 value). Is there anyway of defining a best fit value? Where I don't have a great background in this kind of thing, if someone could give me some gentle nudges in the right direction in terms of where I should be looking or what I could be applying I would be grateful.</p>
<p>I believe this can definitely be applied to other sports as well e.g.:</p>
<p>English Premiership:</p>
<p>2008/2009: 1.45 (Season with over 300+ results)
2009/2010: 1.52
2010/2011: 1.54
2011/2012: 1.64 (but when looking over the last 100 results around the 1.50 mark)</p>
<p>I've also looked at the percentages that this then gives for home wins, away wins and draws and they are virtually identical to the percentages for bookmakers odds (except they work to 105-106% instead of 100% so they have an edge which accounts for the small differences).</p>
<p>NBA:</p>
<p>2008/2009: 11.30 (Season with 1000+ results)
2009/2010: 11.56
2010/2011: 10.88
2011/2012: 11.36</p>
<p>Thanks in advance for any advice,</p>
|
g73425
|
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] |
<p>I have multiple (finitely-many) variables with independent posterior pdfs $f_{x_1}...f_{x_n}$ based on Bayesian updating treating them as independent with independent evidence.</p>
<p>If I subsequently discover conditional evidence relating the variables and need a joint prior, is there an analogue to a maximum-entropy prior forming a joint pdf $f_{x_i}(x_1, ...x_n)$ from the individual $f_{x_1}...f_{x_n}$?</p>
<p>Sorry if this question is boring, obvious, nonsensical, or underdetermined. If the latter, what extra information is required to make it meaningful?</p>
|
g73426
|
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] |
<p>I'm want to show that a customer who buys paper books is more likely to buy an e-reader than a customer who does not buy paper books. Note that the number of e-readers purchased in the past is small (1,000) compared to the total set of events (1,000,000).</p>
<p>Here's the historical data that I have:</p>
<pre><code>Customer Name
| Month
| Purchased Books in Last Month
| Purchased Books in Last 12 Months
| Purchased Books in Last 3 Years
| Purchased Book this Month
| Purchased e-Reader this Month
Joe Smith | 1/12 | 0 | 0 | 0 | 1 | 0
Joe Smith | 2/12 | 1 | 1 | 1 | 0 | 0
Joe Smith | 3/12 | 0 | 1 | 1 | 0 | 1
...
</code></pre>
<p>Using these historical data, I'd like to demonstrate that book-buyers are more likely to buy e-readers, especially if they have recently purchased a book.</p>
<ol>
<li><p>When I do a linear regression on the binary events for "Purchased Books in Last 12 Months" and "Purchased e-Reader this Month", I get r < 0.1.</p></li>
<li><p>However, if I compare P(purchased e-reader) to P(purchased e-reader | purchased books in last 12 months), the probability of a previous-book-buyer purchasing an e-reader is 10x higher than a random customer purchasing an e-reader</p></li>
</ol>
<p>How do I reconcile these two results? Am I using the right tools to answer this question with confidence?</p>
|
g35800
|
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] |
<p>I'm hoping someone can explain this bit of R code for me related to <code>glm()</code>. I don't understand the diagnostic plot that has been suggested. It seems a more informative plot would be to plot against the fitted values, but maybe I don't understand something.
Here's the code:</p>
<pre><code>result <- glm(survive~age, data=donner, family=binomial)
# Why is this plotted against the respondent index?
plot(residuals(result,type="pearson"), main="pearson residual plot")
</code></pre>
<p>Data to reproduce the above example:</p>
<pre><code>> dput(donner)
structure(list(age = c(23L, 40L, 40L, 30L, 28L, 40L, 45L, 62L,
65L, 45L, 25L, 28L, 28L, 23L, 22L, 23L, 28L, 15L, 47L, 57L, 20L,
18L, 25L, 60L, 25L, 20L, 32L, 32L, 24L, 30L, 15L, 50L, 21L, 25L,
46L, 32L, 30L, 25L, 25L, 25L, 30L, 35L, 23L, 24L, 25L), sex = c(1L,
0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L,
0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 0L,
1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L), survive = c(0L,
1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L,
1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L,
0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L)), .Names = c("age",
"sex", "survive"), class = "data.frame", row.names = c(NA, -45L
))
</code></pre>
|
g73427
|
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<p>this is a rather elemental question, but any help would be appreciated anyway.</p>
<p>This <a href="http://www.gifted.uconn.edu/siegle/research/Correlation/alphaleve.htm" rel="nofollow">webpage</a> gives a method of finding the p-value of Pearson's correlation coefficient, using a table. However, the methods listed in <a href="http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient" rel="nofollow">Wikipedia's article</a> suggest that <em>using a table</em> is only valid if the variables are special in some sense, or if there is enough data.</p>
<p>So, my question is: under no assumptions for the random variables for which Pearson's correlation is calculated, is it correct to use a pre-computed table?</p>
|
g35803
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] |
<p>I would like to compute the Wilcoxon rank-sum test in Stata for two countries of my sample with the dummyvalue 3 and 6. </p>
<p>Can anyone give the right code for Stata? </p>
|
g73428
|
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] |
<p>I have calculated the correlation between A and B for 10 different subjects. For averaging purposes, I've converted the r-values to z-values using Fisher's z-transformation. </p>
<pre><code>subj zvalue
s1 -0.04
s2 -0.14
s3 -0.29
s4 -0.20
s5 -0.37
s6 -0.01
s7 -0.09
s8 0.20
s9 -0.15
s10 0.09
</code></pre>
<p>I want to test if the correlation between A and B is significantly different from zero. Do I use a paired sample t-test against 0 with the z-values, then report the r-value converted from the mean z-value? Or should I convert each subject's z-value back to an r-value before doing the t-test?</p>
<p>Edit:
Critically, is a paired t-test against 0 appropriate to test if this correlation is significant across subjects?</p>
|
g47199
|
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<p>I am implementing a Fine & Gray competing risk model. The model includes covariates that are static for each person (e.g. location) as well as covariates that change over time (such as local unemployment rates).</p>
<p>The issue I have is: how do you generate cumulative incidence curves, assuming covariates that change over time? It is straightforward to use the STATA command "stcurve" and generate a CI curve that assumes fixed values for covariates (e.g. covariate value X for all times), but there is no functionality to generate a CI curve assuming covariate value X in time t, and then covariate value Y in time t + 1. </p>
<p>Is there a paper that discusses this, or a package in R/SAS/STATA that lets you generate curves assuming different values of covariates over time? Thanks very much for any help!</p>
|
g35805
|
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<p>I would like to know how to move forward in establishing a baseline on multiple observed years of retrospective data. My intent is to first identify the 10% of a given group to include in a study, and then establish a baseline.</p>
<p>One concern of the data is that some observations may have an extremely large score in one year due to "bad luck". To attempt to take this into account, what I had done was look back at three years of data, and ranked each observation from lowest to highest (in a year). I then summed the ranks across three years, which would get me a final "ranking". I then took the highest 10%. My question is, would it be wise to use the mean as baseline given that some observations actually had a lower score in the third year OR should I use the third year score as "baseline"? If neither, what would be a better way of establishing a baseline?</p>
<p>I've provided some code to replicate what I have done thus far. </p>
<p>Thanks in advance.</p>
<p>X1-X3: year 1, year 2, year 3 <br>
x1.1 - x3.1: year 1 rank, year 2 rank, year 3 rank <br>
total: total sum for year 1, year2 and year 3. <br>
mean: mean of year 1, year2 and year 3.
rank: final ranking</p>
<pre><code>x = c('dplyr', 'ggplot2')
lapply(x, require, character.only=T)
props = function(ncol, nrow, var.names=NULL){
if (ncol < 2) stop("ncol must be greater than 1")
p = function(n){
y = 1
z = sapply(seq_len(n), function(i) {
x = sample(seq(0, 10000-y, by = 1), 1)
y = y + x
return(x)
}
)
w = c(z)
return(w)
}
DF = data.frame(t(replicate(nrow, p(n = ncol))))
if (!is.null(var.names)) colnames(DF) = var.names
return(DF)
}
set.seed(9213)
df = props(ncol = 3, nrow = 100)
df$id = rownames(df)
df = df[,c(ncol(df),1:(ncol(df)-1))]
df.w = data.frame(df, apply(df[2:4], 2, rank, ties.method = 'min'))
df.rank = df.w %.%
group_by(id, X1, X2, X3, X1.1, X2.1 , X3.1) %.%
summarise(
total = sum(c(X1, X2 , X3)),
mean = mean(c(X1, X2 , X3)),
rank = sum(c(X1.1, X2.1 , X3.1))) %.%
arrange(id)
df.rank$rank = rank(df.rank$rank, ties.method = 'min')
df.rank = df.rank[order(df.rank$rank), ]
percent.10 = subset(df.rank, rank > quantile(rank, prob = 1 - 10/100))
</code></pre>
|
g73429
|
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] |
<p>In maximum likelihood estimation (MLE) a useful result is that the standard errors for some estimated coefficient vector can be computed as the square roots of the diagonal entries of the inverse of the negative expected information matrix. </p>
<p>In other words, let the empirical estimate <em>of the expectation</em> of the information matrix be: $$I(\theta) =-\frac{1}{N}\sum_{i=1}^{N}\mathcal{H}(Z_{i},
\theta)$$ for parameter vector $\theta$, and data points $Z_{i}$, where $\mathcal{H}(Z_{i},\theta)$ denotes the Hessian matrix of the log-likelihood function, evaluated at the single datum $Z_{i}$ and the parameter vector estimate $\theta$.</p>
<p>Then the matrix given by $I(\theta)^{-1}$ contains the variance/covariance structure of the MLE estimates, and its diagonal entries in particular are the variances of the estimated MLE parameters.</p>
<p>In my specific application, the $Z_{i}$ are consumer data about price preferences for different heating options, and the model is a logit probability model. I've done all the work of estimating the MLE and there are standard formulas for the derivative vector and Hessian matrix in this logit scenario. I have about 250 data samples, which is large enough that I expect the MLE estimate to be fairly accurate.</p>
<p>However, when I numerically compute the information matrix and the corresponding variances, I am seeing very large numbers. The estimated coefficients range in absolute value from 0.5 to 22, but the smallest standard error is about 7.2, which makes me question what I'm doing.</p>
<p>I know that the empirical estimate of the Hessians are correct, as I've used my code on a separate data set to confirm that I'm computing the derivatives and second-derivatives correctly, so I think it's unlikely to be a coding mistake.</p>
<p>Does anyone have any advice on what might yield such large standard deviations in practice?</p>
|
g35807
|
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<p>I've got a online classification problem where I predict a class label <code>{+1, -1}</code> for an object and then show it to a user to get a real label. My task is to minimize a number of <code>-1</code> objects shown to a user.</p>
<p>Obviously, the algorithm will not converge if it learns only on <code>+1 -> -1</code> missclassifications, so a certain ammount of <code>-1</code> objects needs to be shown to users anyway. The problem is to minimize a number of <code>-1</code> objects shown to a user by selecting only the ones most valuable for learning.</p>
<p>The above problem is being solved in a field of 'active learning', where a learner gets to decide whether to request a laber for an object from user or not. Searching for a solution that does not imply i.i.d., I've found <a href="http://jmlr.csail.mit.edu/papers/volume7/cesa-bianchi06b/cesa-bianchi06b.pdf" rel="nofollow">this work</a>, where the learner decides on whether to require a label for an object by its margin. This is intuitive: the lesser margin means that we're more likely to make an error, which makes an object more valuable for learning. The probability to require an object depends on a margin and some parameter <code>b</code>, the optimal value for which is given for a linearly separable case, which applies for my problem.</p>
<p>The algorithm is simple and goes as follows:</p>
<pre><code>initialize weight vector w(t) with zeros
for every input vector x(t):
calculate margin p(t) = w(t-1) * x(t)
predict a class with Hebb's rule y(t) = sgn(p(t))
toss a coin with P(heads) = b / (b + |p(t)|)
if Heads:
query the label y' of x
if y' != y:
update weights w(t+1) = w(t) + y'*x
else:
w(t+1) = w(t)
</code></pre>
<p>Basically, I need to use this rule for querying user only if object prediction is <code>-1</code>, and if it is <code>+1</code>, I require a label anyway. My question is: would my algorithm converge in that setting? The perceptron algorithm itself and the modified version from the above article are symmetrical in respect to class labels. In my setting there will surely be more errors on <code>+1</code> objects, than on <code>-1</code>'s. <strong>Does it hurt convergence? If it does, what modification to that algorithm can bring it back to 'symmetry' between positive and negative weight updates?</strong></p>
<p>The modified algorithm querying <code>+1</code>s in all cases is as follows:</p>
<pre><code>initialize weight vector w(t) with zeros
for every input vector x(t):
calculate margin p(t) = w(t-1) * x(t)
predict a class with Hebb's rule y(t) = sgn(p(t))
toss a coin with P(heads) = b / (b + |p(t)|)
if Heads or y(t) == +1:
query the label y' of x
if y' != y:
update weights w(t+1) = w(t) + y'*x
else:
w(t+1) = w(t)
</code></pre>
<p>Is this algorithm going to converge? If not, what modifications can be made? </p>
<p>The first idea was to decrease a learning rate for +1's, but still, I don't know how to prove convergence. Do you have any ideas on how to design an algorithm so that <strong>it will surely find a linear separator in a finite number of iterations</strong>?</p>
<p>Thanks.</p>
<p><strong>Update</strong>. If don't know how to answer the question, but have any thoughts on where you would look for a solution or any pointers to publications/books/etc, please, let me know!</p>
|
g73430
|
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] |
<p>This question is somewhat of a continuation from an earlier posting:
<a href="http://stats.stackexchange.com/questions/50526/using-em-algorithm-for-record-linking">Using EM algorithm for record linking</a></p>
<p>I have two data sets of individual some of whom are in both but a prior it is not know which are and there are no identification id's that are common to both. What we know are the individual's first name, last name, birth year, and birth country. Since I still do not understand how to apply EM to link them, I am converting the name string to Soundex or NYSIIS and requiring exact matches. That is, linking individuals only if their NYSIIS-equivalent first names match, last names match, birth years match, and birth countries match, and this match is unique both within and across data sets. </p>
<p>Would it make sense to then assess the match quality by say computing the Jaro-Winkler of the names of the match pairs? So say a pair has names Jon Smith and Jonn Smith and NYSIIS(Jon) == NYSIIS(Jonn), does it make sense to compute Jaro-Winkler (Jon Smith, Jonn Smith)? And if so, should I weigh by the corresponding analyses by the Jaro-Winkler estimates?</p>
|
g35810
|
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<p>I aim to discriminate between three populations by using a maximum likelihood classifier. The idea is that every population has a unique distribution $\hat{f_i} (x)$. The pdf $\hat{f_i}(x)$ has been estimated on a set of training data. A new set of observations $(x_1,...x_p)$ will be assigned to the population for which
$\log(q_i)+\sum_{j=1}^p \log(\hat{f_i}(x_j))$ is maximized. I want to investigate if the difference in the likelihoods are significant. How should I a perform a likelihood ratio test? I could of course perform the "standard" test in which I test $\lambda=\frac{L_0}{L_1} $ and then take $\chi^2= -2 \log \lambda$, but as I understand this test is used when there is a difference in the number of parameters between $L_1$ and $L_0$ . </p>
<p>"Let L0 be the maximum value of the likelihood when the parameters are restricted (and reduced in number) based on the assumption. Assume k parameters were lost (i.e., L0 has k less parameters than L1)." </p>
<p>Or is this correct? Otherwise how should the test be performed? </p>
|
g73431
|
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] |
<p>I want to generate some spatial data where the points/location in the space form a multivariate gaussian distribution. I want these points to have certain autocorrelation given by the variogram model like spherical with spill 0.025 and range 15. I then want to generate some sample for this </p>
<p>How can I do it?</p>
<p>I then want to plot the empirical variogram and again fit a model variogram to check if they come out to be similar. How can I do it?</p>
|
g73432
|
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<p>I've read <a href="http://www.evanmiller.org/how-not-to-sort-by-average-rating.html" rel="nofollow">How Not to Sort By Average Rating</a> regarding how to average binary positive/negative ratings in a way that takes the number of ratings into account. The author uses the "lower bound of Wilson score confidence interval for a Bernoulli parameter". However, the items I'm dealing with have continuous ratings from 0 to 1. Is there an analogous averaging technique for this case?</p>
<p>My ratings collection is long-tailed: the median item has only 2 ratings, but the average one has 80, and the most-rated item has 36,000 ratings. Intuitively ten ratings of 0.8 should "average" higher than one of 0.9, but I'd like a precise formulation of this intuition.</p>
<p>(I'm using this to design a recommender system, which has to deal with 50,000 users and 10,000 items. I'm evaluating various known recommenders, like GroupLens and LSI, and have to design one that doesn't perform too much worse than those (and hopefully better). I was reminded of this blog post on averages when using users' average ratings for a baseline RMSE calculation.)</p>
|
g73433
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<p>I have a question about Bayesian Information Criteria. (GARCH models)</p>
<p>I have looked for so many hours but still very confused about this BIC especially a negative one. As far as I am concerned it is okay to have a BIC that is negative, but the interpretation of them are different in each book on website. I am not looking for sophisticated answer just a normal explanation as if you were to explain someone who is not math or statisticians.</p>
<p>Given same data,length and number of observation which model is better, based on BIC?</p>
<blockquote>
<ol>
<li><p>-4.98749 </p></li>
<li><p>-4.995782 </p></li>
<li><p>-4.9864</p></li>
</ol>
</blockquote>
<p>Thank you in advance.</p>
<p>I am using R software and running 3 models, GARCH-t, GJR model, and simple GARCH (1,1) model. So, I am trying to see which model is better, based only on BIC.
I have already concluded what model is better based on other factors but this makes me confused.</p>
|
g12798
|
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