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<p>When a <a href="http://en.wikipedia.org/wiki/Queueing_theory" rel="nofollow">queueing system</a> is modeled as an M/M/1 queue, it is assumed that the arrival time of jobs has Poisson distribution and the service rate has exponential distribution. I am wondering what features a system should have in order to model the arrival rate as Poisson? I known that Poisson is the only distribution that its inter-arrival time of jobs is exponentially distributed which is memoryless. Are there any better and more intuitive features for it?</p>
<p>Also even in a more complex modeling (M/G/1), only the service rate is changed to general which means that the Poisson arrival rate is good enough where G/M/1 or G/G/1 is not as appealing as the previous ones.</p>
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] |
<p>Quick question: I have found <a href="http://www.r-tutor.com/elementary-statistics/analysis-variance/randomized-block-design" rel="nofollow">this tutorial</a> which recommends a two-factorial design for the following setup: three menu items (fixed factor) are tested in six restaurants (random factor). The guide recommends using</p>
<pre><code>aov( response ~ item + restaurant )
</code></pre>
<p>I think that the correct way of doing that would be</p>
<pre><code>aov( response ~ item + Error( restaurant / item ) )
</code></pre>
<p>I am confused. </p>
<p><strong>My question: am I right, or am I wrong and the author of the tutorial is right?</strong></p>
|
g73318
|
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] |
<p>Given a R.V $X$ and that $\ E(X) = 0 $ and $\ E(X^2) = \sigma^2 $. Is there anyway to compute $\ E(X^3) $ without knowing the density function of $X$? </p>
|
g73319
|
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] |
<p>I do experiments with a certain parameter x. The result is y. I assume y is linearly related to x.</p>
<p>Suppose I can do 1000 experiments, which method will give me a better estimation of the linear relation?</p>
<ul>
<li>Select 1000 different values of x, get a single y for each x, and do linear regression?</li>
<li>Select 100 different values of x, run 10 experiments for each x, average the y values for each x, and then do linear regression on the 100 averages?</li>
<li>Select 100 different values of x, run 10 experiments for each x, and do linear regression without averaging first?</li>
</ul>
<p>What if I am not sure that the relation is linear?</p>
|
g73320
|
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] |
<p>I'm fitting a generalized linear mixed model in R using the Laplace approximation. I'm looking for a reference for the Laplace approximation used for that, or a reference regarding the comparison between the PQL and Laplace methods for fitting generalized linear mixed models.</p>
|
g73321
|
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] |
<p>This figure:</p>
<p><img src="http://i.stack.imgur.com/Q5Lrp.jpg" alt="odds ratios"></p>
<p>shows my odds ratios. I believe they have to be linear for logistic regression to work and am wondering how to pre-process these data. Thanks.</p>
|
g38209
|
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] |
<p>Is there any reason of what I can think of, to transform the data with a square root? I mean what I always observe is that the R^2 increases. But this is probably just because of centering the data! Any thought is appreciated!</p>
|
g73322
|
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<p>I have hundreds of explanatory variables and under 100 observations (saturated data set). I'd like to create a linear model in which I have two or so composite variables made up of a dozen of the explanatory variables each. How do I find the best variables to use for the composites without going through every combination?</p>
<p>Currently my $R^2 = .64$, I'd like to improve that. </p>
<p>The model looks something like this:</p>
<p>$$Y = B_1(v_1 + v_2 + \dots + v_{12}) + B_2(v_{13} + v_{14} + \dots +v_{24})$$</p>
<p>where $B_1$ and $B_2$ are the coefficients and the entirety of ($v_1 + v_2 + \dots + v_{12}$) is acting as one variable.</p>
|
g73323
|
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<p>This is pretty hard for me to describe, but I'll try to make my problem understandable. So first you have to know that I've done a very simple linear regression so far. Before I estimated the coefficient, I watched the distribution of my $y$. It is heavy left skewed. After I estimated the model, I was quite sure to observe a left-skewed residual in a QQ-Plot as wel, but I absolutely did not. What might be the reason for this solution? Where is the mistake? Or has the distribution $y$ nothing to do with the distribution of the error term? </p>
|
g73324
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] |
<p>Question was originally posted <a href="http://stackoverflow.com/questions/6172746/calculate-variance-of-3-or-more-attributes-with-known-frequecies">on Stack Overflow</a>. </p>
<p>I want to calculate variance of data at a given time where I know the frequency of the conditional and decision attributes.
At time $t$ every conditional attribute can have 3 possible values while decsion attribute consists of two classes. </p>
<p>See the picture below for more details:
<img src="http://i.stack.imgur.com/XZnue.png" alt="enter image description here"></p>
<ul>
<li>How can I calculate the variance of this data snapshot?</li>
<li>Sample code or an algorithm would be most appreciated.</li>
</ul>
|
g73325
|
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<p>I'm trying to implement the extended binomial density function with support on c( 0 : (floor(N) + 1)), but I'm running into (I think) precision issues, as running:</p>
<pre><code>########################
#---DENSITY FUNCTION---#
########################
debinom <- function(k, n, p, sum) {
if (k <= n) {
return( choose(n, k) * p^k * (1-p)^(n-k) )
} else {
return (1.0 - sum)
}
}#END: pebinom
##########################################
#---CUMULATIVE DISTRIBUTION FUNCTION 2---#
##########################################
pebinom <- function(x, n, p) {
# point mass at 0
totalDensity = cumProb = debinom(0.0, n, p, 0.0)
k = 0
while (k <= (x)) {
density2 = debinom(k, n, p, totalDensity)
totalDensity = totalDensity + density2
cumProb = cumProb + density2
k = k + 1
}
k = k + 1
density = debinom(k, n, p, totalDensity)
cumProb = cumProb + density * (x - k)
return (cumProb)
}#END: debinom
############
#---TEST---#
############
for (i in 0:10) {
x = i + runif(1)
cat(x, " ", pebinom(x, 100, 0.1), "\n")
}
</code></pre>
<p>gives a negative probabilities for tail values. </p>
<h1>EDIT</h1>
<p>I have changed, and mostly simplified the routines along the comments and answers I've received:</p>
<pre><code>#########################################
#---PROBABILITY DISTRIBUTION FUNCTION---#
#########################################
debinom <- function(k, n, p) {
if (k <=floor(n)) {
return( choose(n, k) * p^k * (1-p)^(n-k) )
} else if(k == (floor(n)+1)) {
cumProb = 0.0
for(i in 0 : floor(n)) {
cumProb = cumProb + debinom(i, n, p)
}
return (1.0 - cumProb)
} else {
return(0.0)
}
}#END: pebinom
########################################
#---CUMULATIVE DISTRIBUTION FUNCTION---#
########################################
pebinom <- function(x, N, P) {
cumProb = 0
for(i in 0 : (floor(x)) ) {
cumProb = cumProb + debinom(i, N, P)
}
return(cumProb)
}
</code></pre>
|
g73326
|
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] |
<p>I want to programatically calculate at which particular hours of a day the probability of a webpage hits(accessed) are high.</p>
<p>Which statistic formula should I use to calculate the peak hours of the web page, if I have already the below data about a page .</p>
<p>e.g. for page xyz, at left I have hours and at right I have hits , For different pages the hits are different.</p>
<p>Page xyz hits count data:</p>
<pre><code>hr=hits
1=0
2=0
3=0
4=0
5=14
6=0
7=0
8=5
9=5
10=8
11=10
12=10
13=12
14=7
15=5
16=5
17=3
18=0
19=0
20=0
21=0
22=0
23=0
24=0
</code></pre>
|
g73327
|
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] |
<p>I have data on a repeat length polymorphism. For each subject, I have two values, giving the (discrete) number of repeats on each allele. I want to test whether the length of the repeat on one allele and that on the other are independent of each other.</p>
<p>My problem is that there is no natural order in the repeat lengths of one subject. If I wanted to do say a chi-squared test, there would be no justification for assigning one repeat length to the row variable and the other to the column variable of the contingency table I apply the test to, or vice versa.</p>
<p>How do you test for independence of two-dimensional categorical data when, for each sampling unit, the two values are interchangeable?</p>
|
g73328
|
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<p>I'm currently working on a self study worksheet. I understand most parts of the solution for part III, but I can't seem to make out how this comes about:</p>
<p><img src="http://i.stack.imgur.com/emSUF.jpg" alt="enter image description here"></p>
<p><strong>QUESTION:</strong></p>
<p><img src="http://i.stack.imgur.com/6g1QI.jpg" alt="enter image description here"></p>
<p><strong>ANSWER:</strong></p>
<p><img src="http://i.stack.imgur.com/ESOp2.jpg" alt="enter image description here"></p>
|
g73329
|
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] |
<p>I have run the Fisher Exact test for several larger than 2x2 matrices. I got a Value number and a P value instead of just a P value. Does this mean the test ran out of memory and is invalid? or...Why did I get a Value?</p>
|
g73330
|
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<p>I am reading the book "<a href="http://rads.stackoverflow.com/amzn/click/0470539399">how to measure everything</a>", there is a chapter when the author encourages the usage of Monte Carlo simulation in simulating the future events in order to get a better understanding of the risk/ uncertainty involved. The theory sounds great in paper, and I am tempted to apply <a href="http://stats.stackexchange.com/questions/30801/run-a-monte-carlo-simulation-of-a-startup-while-conceiving-it-has-it-been-done">Monte Carlo techniques to startup analysis</a>, to study the performance of employees, sales campaign, markets... everything!</p>
<p>But in practice, I doubt whether Monte Carlo simulation is useful when the distribution of the variables involved in an equation is unknown. Think of the stock price return distribution-- it doesn't fit into a Gaussian Distribution, but what distribution we can use? And when the variable distribution is unknown, how useful is Monte Carlo simulation? My guess is not very useful, but I am right?</p>
<p>A relevant, but probably narrower question is, is there any research done along the line of sensitivity analysis? By "sensitivity analysis" I mean we assume known distributions for the variables, but we perturb them a little by slightly changing the distribution shape or slightly changing some of the constants, will the outcome of the simulation results remain roughly the same, or completely different?</p>
|
g73331
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] |
<p>Here is a simple test I've run on MATLAB to check the validity of a single pass (online) algorithm for computing $3$rd moment and $4$th moment.</p>
<pre><code>randn('state',0);
num2 = 0;
num1 = 0;
delta = 0;
M1 = 0;
M2 = 0;
M3 = 0;
M4 = 0;
Xvec = zeros(1, 100000);
for j = 1:length(Xvec)
X = 3*randn(1);
% Single pass algorithm
num2 = num1;
num1 = num1 + 1;
delta = X - M1;
delta_n = delta / num1;
delta_n2 = delta_n * delta_n;
term1 = delta *delta_n * num2;
M1 = M1 + delta_n;
M4 = M4 + term1 * delta_n2 * (num1 * num1 - 3.0*num1 + 3.0) + ...
6.0 * delta_n2 * M2 - 4.0 * delta_n * M3;
M3 = M3 + term1 * delta_n * (num1 - 2.0) - 3.0 * delta_n * M2;
M2 = M2 + term1;
Xvec(j) = X;
end
% Quantities obtained from Single Pass
avg = M1;
variance = M2 / (num1 - 1.0);
kurtosis = (num1 * M4)/(M2 * M2) - 3.0;
skewness = sqrt(num1) * M3 / (M2^1.5);
% Reference Quantities
avg1 = sum /length(Xvec);
moment_2 = moment(Xvec, 2);
moment_3 = moment(Xvec, 3);
moment_4 = moment(Xvec, 4);
</code></pre>
<p>The online algorithm provides a correct mean (avg = avg1) and variance (variance = moment_2). However, the values for kurtosis and skewness obtained from the online algorithm are way off from the actual $3$rd and $4$th moments.</p>
<p>What might be going wrong? </p>
<p><a href="http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance" rel="nofollow">Source</a></p>
|
g35643
|
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<p>Let's consider the example of whether a person's weight is correlated with their height (simple linear regression). What is the difference between running this correlation on the following two data sets?</p>
<p><strong>Measurements independent of time</strong>
Randomly sample 100 people and record their weight and height.</p>
<p><strong>Measurements with time dependence</strong>
Randomly sample 10 people, but record their weight and heights at 10 different times.</p>
|
g35644
|
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] |
<p>I need to plot an interaction between two continuous factors for interpretation. I am using the wireframe function in the lattice package and plotting the predicted values from the model with the best fit. The model looks somewhat like this:</p>
<pre><code>out<-lmer(response~apples+pears+strawberry+mangoes+(mangoes)^2+strawberry:mangoes+
(1|id),family="poisson")
</code></pre>
<p>However, if I use the predicted values from the whole model the wireframe's surface is different than if I only use the predicted values from a model that only contains the variables that interact (omitting also the quadratic term):</p>
<pre><code>out<-lmer(response~strawberry+mangoes+strawberry:mangoes+(1|id),family="poisson")
</code></pre>
<p>The difference is big enough to cause concern, and I would like to ask which method gives the best interpretation of the data, and why are the surfaces so different?</p>
|
g73332
|
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<p>In the research that I am carrying out I have a moderation in which predictor, moderator and outcome variable are on the different levels: predictor and moderator on within level (the data were collected longitudinally over 6 months, every participant has 10 results) and outcome variable on between level (the data were collected just one time in the end of the study). I work with R.</p>
<p>Is it possible to use Growth Modeling in this case?</p>
<p>If not, is it possible to analyze this data using any different method? </p>
|
g73333
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] |
<p>Suppose that $X$ is a random variable with any distribution that takes only positive values. Can the following inequality hold for constants $c_2 >c_1 >0$?</p>
<p>$$\text{Var}(Z^{c_2})/\text{E}[Z^{c_2}]^2 > \text{Var}(Z^{c_1})/\text{E}[Z^{c_1}]^2$$</p>
<p>In other words:</p>
<p>$$\text{E}[Z^{2c_2}]/\text{E}[Z^{c_2}]^2 > \text{E}[Z^{2c_1}]/\text{E}[Z^{c_1}]^2$$</p>
<p>where $Z=X+1$.</p>
<p>With many thanks for your answer.</p>
|
g73334
|
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0.04336601868271828,
0.01506753172725439
] |
<p>When splitting attributes while constructing a random tree, I use information gain in order to determine the best value to split the tree on. I add nodes to the tree until a stopping criterion is met. What is the minimum value of information gain, to be used as a stopping criterion?</p>
|
g35652
|
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<p>I’m trying to make a Liquid State Machine, I have a spiking neural network as the liquid, and a feedforward neural network that should learn to map the reservoir’s states to the output.</p>
<p>I’ve read many articles, but I didn’t find much about how I give the reservoir’s states to the feedforward network’s inputs. One of my sources said that I should sum all the reservoir’s values and give it to all input units, but that would result in the inputs having all the same value.</p>
<p>Other articles said that the input units should be sensitive towards different features, but my project is recognizing handwriting and I have no idea what features I could extract from that. It only consists of values between 0 and 1, according to whether the pixel is filled or not.</p>
<p>I tried to map the liquid’s different layers to different input units of the feedforward network, but it also didn’t work. I didn’t really think it was a good idea, but I tried it just in case.</p>
<p>My question is: how do I give the reservoir's states to the feedforward network, so it could learn anything at all?</p>
<p>I also might have problems with the liquid itself too, since it doesn’t do anything, only fires its data randomly. Should it also change its structure according to the input data? (The articles usually say that it doesn’t have to react to the input, but I think it’s strange.)</p>
|
g35653
|
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<p>Like the title says, I've got two time series, one is stationary to begin with and thus has no unit root, the other time serie is stationary after one-time differencing. </p>
<p>I want to create a model out of this and I know that when unit roots are present, I should test for cointegration. But I've read in <a href="http://www.ntuzov.com/Nik_Site/Niks_files/Research/papers/stat_arb/EG_1987.pdf" rel="nofollow">Engle & Granger</a> (1987) that cointegration tests are only to be done when you have two or more I(1) variables, is that correct?</p>
<p>So I cannot find in literature if I should now use a VAR model on differences or test for cointegration and perhaps do a Vector Error Correction model.</p>
<p>Can anyone help me? I would be very thankful!</p>
|
g73335
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<p>For a university project I wrote a SVM classifier and during the benchmark phase I'm getting some results I'd like to better understand from the theoretical side.</p>
<p>My original dataset contains a multi-labeled examples but I'm buiding a binary classifier so I pick a feature <code>A</code> and I replace all the labels with +1 if <code>A</code> is present or -1 if it isn't. For instance:</p>
<pre><code>label1 label2 label3 label4 = feature1 feature2 feature3 feature4
label2 label4 = feature1 feature2 feature3 feature4
label3 label4 = feature1 feature2 feature3 feature4
</code></pre>
<p>If choose <code>label3</code> the dataset becomes:</p>
<pre><code> 1 = feature1 feature2 feature3 feature4
-1 = feature1 feature2 feature3 feature4
1 = feature1 feature2 feature3 feature4
</code></pre>
<p>If choose <code>label2</code> the dataset becomes:</p>
<pre><code> 1 = feature1 feature2 feature3 feature4
1 = feature1 feature2 feature3 feature4
-1 = feature1 feature2 feature3 feature4
</code></pre>
<p>Now, my original dataset contains 20k rows and:</p>
<ol>
<li>If I choose a label which is in 9k rows I get a average test error of 13%</li>
<li>If I choose a label which is in 5k rows I get a average test error of 7% </li>
</ol>
<p>I was wondering why this is happening. My guesses are:</p>
<ul>
<li>In the second case the separating hyperplane has a larger margin </li>
<li>In this the first case the is overfitting </li>
</ul>
|
g35654
|
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<p>Following on my question <a href="http://stats.stackexchange.com/questions/19227/possible-extensions-to-the-default-diagnostic-plots-for-lm-in-r-and-in-general">for OLS</a>, I wonder: what diagnostic plots exists for quantile regression? (and are there R implementation of them?)</p>
<p>A quick google search already came up with the <a href="http://smj.sagepub.com/content/7/4/363.short">worm plot</a> (which I have never heard about before), and I'd be happy to know of more methods you might know about. (are any of them one from OLS ported for quantile-regression?)</p>
<p>Thanks</p>
|
g35656
|
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<p>I've some numerical sequence of data monitored over time $v(i)$, which belongs to one of two classes, 0 or 1. I monitor the variable several times, obtaining a sequence associated to 0 or 1.
I use part of the cases in which $v(i)$ belongs to class 0 to have a profile/baseline (training data/cases).
I then use the cases in which $v(i)$ belongs to 1 to see if there is some difference from the baseline (test data/cases). I end then in computing a metric, based on the information showed by $v(i)$, namely if it showed some "difference" when the case was a 1, or a 0 (error), and the viceversa considering the class 0.</p>
<p>So from the whole cases $N$ I get just one value $M(v(i),N)$.
But this value is just a statistic.</p>
<p>My question is: How to guess the distribution of this metric? I thought to partition the "test data/cases" in $k$ groups (keeping the proportions), and then estimate the distribution of $M(v(i),N/k)$ through a $T$-test, or something similar.
But does it make really sense? Is it a valid way to infer the distribution of $M$?</p>
<p>Thanks in advance for the tips and discussion I will (in case) receive :)</p>
|
g73336
|
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] |
<p>Is it a good or a bad practice to use R packages from CRAN for research? I'm talking about the common packages like: simple models for regression, estimation, econometrics
Most of them use function that can be written easily on your own.</p>
<p>My yes arguments:</p>
<ul>
<li>Time to focus on the main part of the research</li>
<li>The community is a good quality control</li>
<li>R offers a lot of modern methods</li>
<li>Some models are too complicated to write them on your own</li>
</ul>
<p>My con arguments:</p>
<ul>
<li>Not every package of R has been created in an academic environment</li>
<li>There could be bugs that influence the outcome and I do not know it</li>
<li>Most models can be written in a short time period from scratch</li>
</ul>
<p>How can we use open source without risking failures in the outcome? Are there certain quality indicators for packages in general and for R?</p>
|
g49919
|
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<p>I have physiological data (electodermal activity) from several subjects recorded continuously during a task with multiple components. I'm interested in comparing whether the response within each component is different (for example: is the response in part D greater/different than in part A). Visually, there is a trend toward increased EDA as we get deeper into the task.</p>
<p>I'm teaching myself time-series analysis as I go (reading Brockwell and Davis). My advisor suggested running a repeated-measures ANOVA on the mean EDA in each component with participant as the repeat so that we get a sense of main effect of component. </p>
<p>My question is this: Would it be prudent to do anything in particular to the data (i.e. detrend it, etc) prior to calculating means within components? Additionally, (and I suppose more overarchingly) does my advisor's suggestion for comparing the components make functional sense (RM ANOVA). If this were anything but time-series I would think so but I'm new to TS so any advice would be helpful.</p>
<p>I'm doing this primarily in R but have access to SAS as well.</p>
<p>Thanks for any help anyone can be.</p>
|
g73337
|
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] |
<p>When analysing many real datasets, I have noticed that the most of correlations is positive. For example, here is a visualization of Pearson's correlation matrix for my current data. Is there any reason for this?</p>
<p><img src="http://i.stack.imgur.com/Yec8K.jpg" alt="enter image description here"></p>
<p><strong>EDIT:</strong> Matrix is computed from 500*140 dataset, where the most of variables are Likert items. Here is the distribution of correlations.</p>
<p><img src="http://i.stack.imgur.com/UOvod.png" alt="enter image description here"></p>
<p>And here is example from another area. Vitamin and mineral contents were measured in different food samples (of the same weight).</p>
<p><img src="http://i.stack.imgur.com/cEd4i.png" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/oZX8t.png" alt="enter image description here"></p>
|
g1006
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<p>In the book of Witten and Frank on <em>Data Mining algorithms</em>, I read:</p>
<p><em>"If boosting succeeds in reducing the error on fresh test data, it often does so
in a spectacular way. One very surprising finding is that performing more
boosting iterations can reduce the error on new data long after the error of
the combined classifier on the training data has dropped to zero. Researchers
were puzzled by this result because it seems to contradict Occam’s razor, which
declares that of two hypotheses that explain the empirical evidence equally
well the simpler one is to be preferred. Performing more boosting iterations
without reducing training error does not explain the training data any better,
and it certainly adds complexity to the combined classifier. Fortunately, the contradiction can be resolved by considering the classifier’s confidence in its predictions."</em></p>
<p>If I understand correctly, boosting can reduce the test error after the training error has dropped to zero. Does it mean that the classifier does overfit? Can you clear me this point?</p>
|
g73338
|
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] |
<p>Suppose $X$ and $Y$ are both normally distributed, with $X \sim \mathcal{N}(0,1)$ and $Y \sim \mathcal{N}(c,1),$ where $c > 0$. Consider $n$ independent draws of both $X$ and $Y$. As $n \rightarrow \infty,$ what is the probability that the sample maximum of the draws of $Y$ is greater than the maximum for $X$?</p>
|
g35662
|
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] |
<p>I'm looking for someone who is familiar with the ITSM software. I have some data that needs to be fit with an ARIMA/SARIMA model and then forecast using Holt-Winters/Seasonal method. I then need to compare them using RMSE and MAPE.</p>
<p>I'm completely unfamiliar with ITSM and just need some help on the commands required to perform each of the above functions. The ITSM manual that comes with the download was not very helpful.</p>
<p>If ITSM is not your forte, is there another easily available program that would perform all of these functions for me?</p>
|
g73339
|
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] |
<p>I am running the below mixing model using the <code>rjags</code> package in R, but I keep getting the error message <code>RUNTIME ERROR:Cannot insert node into p[1,1]. Dimension mismatch</code>. I have clearly specified the Dirichlet prior incorrectly but I am unsure what needs changing.</p>
<pre><code>model
{
# Likelihood
for(i in 1:N) {
Y[i,1:J] ~ dmnorm(mu[i,],Sigma.inv)
mu[i,1:J] <- p[i,1:K]%*%s[1:K,1:J,i]
}
# Priors on s
for(i in 1:N) {
for(k in 1:K) {
s[k,1:J,i] ~ dmnorm(mu.s[,k],Sigma.s.inv[,,k])
}
}
# Prior on p
for(i in 1:N) {
for(k in 1:K) {
p[k,i] ~ ddirch(alpha)
}
}
}
# alpha is specified as alpha<-c(1,1) in R
</code></pre>
<p>Any help will be much appreciated.</p>
<p>As requested, here is the R code to run the model:</p>
<pre><code>#Data for rjags mixing model
# Y values
Y<-matrix(c(5.8565, 18.5979, 5.7579, 1.1401, 0.4945, 0.2122, 0.3984,
14.0696, 10.6925, 8.5126, 2.1779, 1.1406, 0.4051, 0.5971,
13.7417, 10.0652, 8.2977, 2.2172, 1.1204, 0.3929, 0.6143,
11.7867, 15.1036, 8.3222, 1.9592, 0.9697, 0.3454, 0.5695), byrow=TRUE,ncol=7)
colnames(Y)<-c("Al","Ca","Fe","K","Mg","Na","Ti")
# mu.s values
mu.s<-matrix(c(6.9746333, 6.6574444, 10.5605000, 13.9441083,
35.4727333, 13.2216667, 6.7945000, 4.1493958,
5.0452333, 7.1281111, 6.1497083, 6.9320042,
1.1962000, 1.1212222, 2.0860833, 2.4469958,
0.6191000, 0.4853333, 1.0108333, 0.8803833,
0.1965333, 0.1992222, 0.4911250, 0.4069042,
0.4584000, 0.3072222, 0.6167083, 0.6584167),
byrow=TRUE, ncol=4)
rownames(mu.s)<-c("Al","Ca","Fe","K","Mg","Na","Ti")
colnames(mu.s)<-c("CB","FD","RV","TS")
# Sigma.inv values - a precision matrix
Sigma.inv<-structure(c(1291.8709, 6061.281, 698.1364, -5510.728, -690.3269, -3010.418, 641.0724,
6061.2809, 171684.070, 2179.5785, -36806.221, 10430.4946, -13140.215, -93994.2303,
698.1364, 2179.578, 1705.0527, -3500.690, 559.1736, -3054.477, -11664.9575,
-5510.7282, -36806.221, -3500.6902, 30963.025, -5429.0766, 18493.588, -10856.3964,
-690.3269, 10430.495, 559.1736, -5429.077, 41562.2004, -38633.413, -18496.1137,
-3010.4185, -13140.215, -3054.4766, 18493.588, -38633.4135, 116805.134, 21412.5527,
641.0724, -93994.230, -11664.9575, -10856.396, -18496.1137, 21412.553, 291117.7431), dim=c(7,7))
Sigma.inv<-as.positive.definite(Sigma.inv)
# Sigma.s.inv values - a precision matrix
Sigma.s.inv<-structure(c(17.1162359691711, 4.27333154820829, 0.799319413122213,
67.8990020405825, -181.19674061241, 240.147200630862, -235.997112580624,
4.27333154820829, 1.30433955546833, 0.346955743724074, 23.1902684301427,
-49.6382239122873, 59.017476611683, -63.7180758402929, 0.799319413122213,
0.346955743724074, 1.31697237634114, 5.28599480618941, -13.9928477614376,
-1.89552256841994, -9.54585305537158, 67.8990020405825, 23.1902684301427,
5.28599480618941, 577.794716546282, -1005.75939032625, 1125.51717030183,
-1523.09284200498, -181.19674061241, -49.6382239122873, -13.9928477614376,
-1005.75939032625, 2530.24588028147, -3264.56488630485, 2931.08069507173,
240.147200630862, 59.017476611683, -1.89552256841994, 1125.51717030183,
-3264.56488630485, 5517.74069570005, -4010.71091461381, -235.997112580624,
-63.7180758402929, -9.54585305537158, -1523.09284200498, 2931.08069507173,
-4010.71091461381, 5348.51616374144, 856.390529266247, -23.7499072549466,
30.8155799569968, -3121.79812866305, -6697.97335697594, 201.209069779657,
1119.41488802919, -23.7499072549466, 1.16945366195659, -0.680279236072279,
92.6596468824124, 185.589336069471, 8.55556473205667, -50.7878188653177,
30.8155799569968, -0.680279236072279, 1.33309308251978, -109.66739253505,
-247.377133710695, 20.475196391213, 35.4240283157601, -3121.79812866305,
92.6596468824124, -109.66739253505, 11599.9856016394, 24300.5608779793,
-610.557137045431, -4613.78940593557, -6697.97335697594, 185.589336069471,
-247.377133710695, 24300.5608779793, 52721.3237164215, -1907.99103757817,
-8706.61402757383, 201.209069779657, 8.55556473205667, 20.475196391213,
-610.557137045431, -1907.99103757817, 1924.48807974801, -150.765001020582,
1119.41488802919, -50.7878188653177, 35.4240283157601, -4613.78940593557,
-8706.61402757383, -150.765001020582, 3107.68558872587, 49.0622143602674,
8.44130661570893, -68.6376288719083, -256.909898229718, 45.2409921131372,
-122.516603322888, 505.474492036306, 8.44130661570893, 5.04250385971496,
-17.8396095728346, 0.998493378138782, -23.6324766148321, -21.9783007018327,
11.6566702138881, -68.6376288719083, -17.8396095728346, 122.63962551017,
281.428831916314, -9.59515390867994, 284.182865766167, -811.53358800718,
-256.909898229718, 0.998493378138782, 281.428831916314, 2315.44570687734,
-688.357300654226, 693.150782011221, -4275.03644110308, 45.2409921131372,
-23.6324766148321, -9.59515390867994, -688.357300654226, 1005.15772657742,
-887.017891953989, 937.328239057861, -122.516603322888, -21.9783007018327,
284.182865766167, 693.150782011221, -887.017891953989, 2701.25571899862,
-3519.5533300646, 505.474492036306, 11.6566702138881, -811.53358800718,
-4275.03644110308, 937.328239057861, -3519.5533300646, 13930.3108880326,
7.66040736195613, 1.14566743309344, 2.21528817899981, 12.2202312499515,
-75.5047038963214, 15.8162629586147, -144.642630413016, 1.14566743309344,
0.80708707189904, -0.219335995078617, 0.00356901053686257, -5.58097800246653,
10.9900105678523, 5.78098900706769, 2.21528817899981, -0.219335995078617,
4.25455776136105, 1.87986945691396, -11.0086131453236, 12.770373667221,
-71.2240549969279, 12.2202312499515, 0.00356901053686257, 1.87986945691396,
73.8970279130133, -192.535629882285, 38.158382504518, -564.560539731276,
-75.5047038963214, -5.58097800246653, -11.0086131453236, -192.535629882285,
1332.63815286144, 369.902304528778, 1013.5952607372, 15.8162629586147,
10.9900105678523, 12.770373667221, 38.158382504518, 369.902304528778,
1566.66721031925, -1476.55006583692, -144.642630413016, 5.78098900706769,
-71.2240549969279, -564.560539731276, 1013.5952607372, -1476.55006583692,
8509.10242328047), .Dim = c(7L, 7L, 4L))
#N
N<-nrow(Y)
#K
K<-4
#J
J<-7
#alpha
alpha<-c(1,1)
myjagsfile<-"JAGSmodel2.txt" # the above jags model
mydata <-list(N=N, J=J, K=K, Y=Y, mu.s=mu.s, Sigma.s.inv=Sigma.s.inv, Sigma.inv=Sigma.inv, alpha=alpha)
mypars <-c("p", "s")
myiterations<-10000
myburnin<-5000
mythin<-125
set.seed(1000)
run.mcmc <- jags(data=mydata, inits=NULL, parameters.to.save=mypars, model.file=myjagsfile, n.chains=2,
n.iter=myiterations, n.burnin=myburnin, n.thin=mythin, DIC=TRUE)
</code></pre>
|
g35664
|
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] |
<p>What is the best technique to calculate a confidence interval of a binomial experiment, if your estimate is that p=0 (or similarly p=1) and sample size is relatively small, for example n=25?</p>
|
g73340
|
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] |
<p>There is a question about testing whether the interquartile ranges(IQR) from the two non-normal distributions are significantly different.
Now I am looking for a test of significance testing interquartile ranges.
I found some approaches for comparison of IQR, ie.
Westenberg-Mood test
permutation test
boostrap + z test
from <a href="http://r.789695.n4.nabble.com/significance-test-interquartile-ranges-td4636456.html" rel="nofollow">http://r.789695.n4.nabble.com/significance-test-interquartile-ranges-td4636456.html</a>
Which test is appropriate for significance test interquartile ranges?
(Data information:ratio data, the sample size is unequal in five groups,the least is less than 10, the most is about 300)</p>
|
g35666
|
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<p>I have recently discovered <a href="http://www.iro.umontreal.ca/~kegl/research/pcurves/" rel="nofollow">Principal Curves</a> while trying to solve the problem I will describe below.</p>
<p>The principle of Principal Curves is to fit a cloud point to find the "path" running along that points.</p>
<p>My goal is to use something like this to fit a set of GPS tracklogs running along a road, so that the result would be a statistical aproximation of the "real" road (or, more precisely, the region of the road where people - bikers in this case - ACTUALLY ride, which most probably would be side lanes and road shoulders).</p>
<p>The problem is: while classical Principal Curves Analysis consider the point set to have independent <em>points</em>, I believe it would be more appropriate to consider each <em>track</em> to be composed of <em>dependent vectors</em>.</p>
<p>When using points, for example, a track segment with high sampling rate might cause a bias when compared to another with lower sampling rate, although each of them describe only ONE trajectory each, and I am more interested in weighting the trajectories with one another instead of the individual points. (by the way, does that rationale of mine make sense?)</p>
<p>I posted a question on the same topic, but with different formulation, in the Gis.StackExchange site, with some representative pictures:</p>
<p><a href="http://gis.stackexchange.com/questions/70623/how-can-i-statistically-calculate-the-real-road-from-a-set-of-gps-tracks">http://gis.stackexchange.com/questions/70623/how-can-i-statistically-calculate-the-real-road-from-a-set-of-gps-tracks</a></p>
<p>Thanks for reading!</p>
|
g73341
|
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<p>I was reading some notes and it says that PCA can "sphere the data". What they define to me as "sphering the data" is dividing each dimension by the square root of the corresponding eigenvalue. </p>
<p>I am assuming that by "dimension" they mean each basis vector into which we are projecting (i.e. the eigenvectors we are projecting to). Thus I guess they are doing:</p>
<p>$$ u^{'}_i= \frac{u_i}{\sqrt{eigenValue(u_i)}}$$</p>
<p>where $u_i$ is one of the eigenvectors (i.e. one of the principal components). Then with that new vector, I am assuming they are projecting the raw data we have, say $x^{(i)}$ to $z^{(i)}$. So the projected points would now be: </p>
<p>$$ z'^{(i)} = u^{'}_i \cdot x^{(i)}$$</p>
<p>They claim that doing this ensures that all the features have the same variance.</p>
<p>However, I am not even sure if my interpretation of what they mean by sphering is correct and wanted to check if it was. Also, even if it was correct, what is the point of doing something like this? I know they claim it makes sure everyone has the same variance but, why would we want to do this and how does it achieve this?</p>
|
g73342
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] |
<p>I am reviewing the R package OpenMx for a genetic epidemiology analysis in order to learn how to specify and fit SEM models. I am new to this so bear with me. I am following the example on page 59 of the <a href="http://openmx.psyc.virginia.edu/docs/OpenMx/1.0.0-1448/OpenMxUserGuide.pdf">OpenMx User Guide</a>.</p>
<p>Here they draw the following conceptual model</p>
<p><img src="http://i.stack.imgur.com/3jOmk.png" alt="enter image description here"></p>
<p>And in specifying the paths, they set the weight of the latent "one"
node to the manifested bmi nodes "T1" and "T2" to be 0.6 because:</p>
<blockquote>
<p>The main paths of interest are those from each of the latent variables
to the respective observed variable. These are also estimated (thus
all are set free), get a start value of 0.6 and appropriate labels.</p>
</blockquote>
<pre><code># path coefficients for twin 1
mxPath(
from=c("A1","C1","E1"),
to="bmi1",
arrows=1,
free=TRUE,
values=0.6,
label=c("a","c","e")
),
# path coefficients for twin 2
mxPath(
from=c("A2","C2","E2"),
to="bmi2",
arrows=1,
free=TRUE,
values=0.6,
label=c("a","c","e")
),
</code></pre>
<p>The value of 0.6 comes from the estimated covariance of bmi1 and bmi2 (of strictly *mono*zygotic twin pairs). I have two questions:</p>
<p>1) When they say that the path is given a "starting" value of 0.6 is this like setting a numerical integration routine with initial values, like in estimation of GLMs?</p>
<p>2) Why is this value estimated strictly from the monozygotic twins?</p>
|
g73343
|
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<p>I am trying to apply R depmixS4 package in order to cluster time series with model based clustering. The model consists of K components, each being a first order Markov models. The Expectation-Maximization algorithm is then used to estimate model parameters. </p>
<p>My time series are multivariate and of arbitrary length ( i.e. can be 400, can be 1). </p>
<p>Now, there are 2 problems:</p>
<ol>
<li>depmixS4 is oriented towards Hidden Markov Models, not the basic first order ones. </li>
<li>I do not completely understand the E and M-steps of model based clustering when applied to first-order Markov model components. Overwhelmingly, scientific literature talks about Hidden Markov Models. </li>
</ol>
<p>However, it seems to me that simple first-order Markov models can be seen as a particular case of hidden ones (where the response probability distribution is just identity, response equals state - thus the states are actually visible). So the clustering process does not have to decode the hidden states. However, the E-M process itself is still unclear, and I am not sure if I can apply the depmixS4 package methods by adjusting them or should I develop my own algorithm in R. </p>
<p>The mixture Markov model used in my research, is the following:</p>
<p>$$p(v | \Theta) = \sum_{t=1\ldots K}p(c_k)p_k(v | \Theta_k),$$
where $v=v_1,\ldots,v_L$ - vector of arbitrarily length, and
$$p_k(v |\Theta_k)=p(v_1| \Theta_{k_i})\prod_{i=2\ldots L} p(v_i |v_{i-1}, \Theta_{k_T}).$$
Given are also vector of initial state prior distribution and transition probability matrix $T_p$. </p>
|
g73344
|
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] |
<p>I want to include sample weights to my quantile regression model, but I'm not sure how to do this. </p>
<p>I've already define my weight, which are replicated weights already given in survey dataset (computed in survey package): </p>
<pre><code>w<-svrepdesign(variables=data[,1:10],repweights=data[,11:30],type="BRR",
combined.weights=TRUE, weights=r.weights, rho=0.5,dbname="")
</code></pre>
<p>and my rq model is:</p>
<pre><code>rq(y~x,tau=c(.1,.2,.3,.4,.5,.6,.7,.8,.9),data=my.data))
</code></pre>
<p>I tried to use <code>withReplicates</code> function, but with no success. Any suggestions? </p>
|
g35670
|
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<p>I apologize if this is too simple a question for this forum but...</p>
<p>If I'm trying to build a neural network or other machine learning based prediction of who will win a football game and by how many points given such and such inputs do I use the actual score of past games as the correct answer for my neural network for training purposes.</p>
<p>For example if I'm using winning percentage of each team to predict winners. I might have the following:</p>
<pre><code>[Home Team Win Pct] [VisitingvTeam Win Pct] [Home Team Win Margin (points)]
50% 45% +2
50% 75% -6
.... ..... ....
</code></pre>
<p>...and so on from past games - I might have 10 years of game data let's say.</p>
<p>Can I use the actual outcome point differential ([Home Team Win Margin]) as the "correct answer" for training purposes? Since I have no way of knowing if these two teams played 100 times under the same exact conditions if the average winning margin would be +2 or some other number since for a given game result I only have a sample size of one. Or is there some other measure of "correct answer" that I should use instead? I certainly can't think of one.</p>
<p>Thanks for your help.</p>
|
g73345
|
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<p>Currently iam working on my master thesis which is about risk adjusted returns in the Asia Pacific REIT market. The goal of the paper is to determine/find variables that conceive explanatory power over the IV. </p>
<p>To determine this I also performed a FE regression based on countries. The result are more or less in line with FE for the whole sample (with firmID as dummy) and OLS regression.
The suprising thing actually is that for the whole sample period (so still with country dummies) some of the variables seem to be insignificant, while on the contrary, if the sample is split up in 2 sub-periods, they show to have a significant effect in both the periods. </p>
<p>I find this rather strange that a variable is significant for both the sub-periods, but fail to do so for the whole sample period. What could be the reason the reason for this? Is this a statistical problem or more should I be looking more in the finance direction?
For those with an finance background, the variables which show this pattern are market capitalization, price-to-book ratio and dividend yield. </p>
<p>I've uploaded the FE regression result for the Australian market. Hopefully this works clarifying.</p>
<p>Help is highly appreciated!</p>
<p>PS. Lagrange and Hausman test favored FE model.</p>
<p>Whole sample regression;
<img src="http://www.freeimagehosting.net/newuploads/pyjot.png" alt=""></p>
<p>Sub period 1;
<img src="http://www.freeimagehosting.net/newuploads/d3ull.png" alt=""></p>
<p>Sub perdiod 2;
<img src="http://www.freeimagehosting.net/newuploads/betwt.png" alt=""></p>
|
g73346
|
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] |
<p>I am working on sample size of 70 . My observed and expected values are different
(Observed 586,
648,
526,
662,
658,
502,
..... so on for 70 samples and expected 570
634,
513,
647,
644,
490,
.....so on for 70 samples). I used Chi-sq test to check the null that there is no difference in observed and expected value. And I got a p-value of 0.99 which means I can't reject null. Can I use any other test for this kind of problem since I can see that for all the 70 samples observed is higher than expected but I cant show this result statistically. </p>
|
g73347
|
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<p>I have two sets of data that hypothesis tests have shown to be normal and from the same distribution. I'm using MATLAB and for the way they give p-values, higher p-values suggest a better goodness-of-fit, as I understand it. I want to combine the two data sets to get the parameters for the combined data set. However, when I run a hypothesis test on the combined data set, hypothesis tests either reject the null assumption of Normality or come very close as seen by the test statistics. I've been looking for an explanation but have no idea where to start. Could anyone shed some light into this?</p>
|
g26916
|
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<p>I was wondering if somebody could help with trying to visualise some data. </p>
<p>I have 11 groups of organisms and have related them to levels of a specific bacteria in water samples. I have a strong positive relationship between the proportion of one of the groups and some non-significant relationships in others, some positive, some negative. My idea was to show on one plot how the proportion of this positively related group increases as the level of bacteria increases and others stay similar or decline.</p>
<p>I was trying to do this using the geom_area plot on ggplot <a href="http://docs.ggplot2.org/current/geom_area.html" rel="nofollow">http://docs.ggplot2.org/current/geom_area.html</a>.</p>
<p>Using the raw proportional data is a bad idea as the relationship is only really seen when including random effects in a mixed effects model. I considered using the fitted model values, however I am not sure if this is the best idea if I want to compare model results?</p>
<p>Many thanks for any help with this.</p>
|
g73348
|
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] |
<p><img src="http://i.stack.imgur.com/4dw9Z.jpg" alt="The Conjugate Beta Prior"></p>
<p>Hello.
I'm having a problem with trying to figure out this proof that shows the beta
distribution is conjugate to the binomial distribution (picture attached).
I understand it until the third row, but I got confused with this step from the third to the fourth row.
I would appreciate a simple explanation.
Thank you in advance.</p>
|
g73349
|
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] |
<p>I'm trying to analyse the performance of my server by collecting performance data using standard tools such as Windows Performance Monitor, and then putting this data on Excel for analysis.</p>
<p>When I set up the data collector (as it's called), I can chose different intervals for collection, such as every 1 second, every 10 seconds and so on.</p>
<p>My first thought was that data collected every 1 second was going to be a "population", and greater intervals turned this data into "sample", but I soon realized that I could break it further into milliseconds and whatnot.</p>
<p>Is the data I collect at any given interval going to be considered "population" or "sample"?</p>
|
g73350
|
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<p>Is it possible to add standard error or confidence interval to a plot of a predicted vs observed values derived from a multiple regression model? I believe that I have seen such plots as an output in Statistica, but am unsure how to create them in R.</p>
<p>I believe I have a solution (below), but am unsure that I have done this correctly. Basically, I have created a new <code>dataframe</code> with predictor variable in the range of their possible values. My worry with such an approach is that the prediction is based on the rows of data, and does not really address situations where the variables are randomly selected. </p>
<p>Many thanks for your help.</p>
<p><strong>Example:</strong></p>
<pre><code>set.seed(1)
n <- 200
x1 <- rnorm(n, mean=10, sd=3)
x2 <- rnorm(n, mean=20, sd=5)
e <- rnorm(n, mean=10, sd=3)
y <- 5 + 2*x1 + 0.5*x2 + e
fit <- lm(y ~ x1 + x2)
summary(fit)
#plot of predicted vs observed
pred1 <- predict(fit, se.fit=TRUE)
plot(pred1$fit ~ y)
abline(0,1, col=8, lwd=2)
#new dataframe sequence of each predictor variable in their range
df.new <- data.frame(x1=seq(min(x1), max(x1),,100), x2=seq(min(x2), max(x2),,100))
pred2 <- predict(fit, df.new, se.fit=TRUE)
#plot of predicted vs observed w/ standard error interval?
png("pred_vs_obs.png", width=6, height=6, units="in", res=200)
plot(pred1$fit ~ y)
abline(0,1, col=8, lwd=2)
lines(pred2$fit+1.96*pred2$se.fit ~ pred2$fit, col=2, lty=2, lwd=2)
lines(pred2$fit-1.96*pred2$se.fit ~ pred2$fit, col=2, lty=2, lwd=2)
dev.off()
</code></pre>
<p><img src="http://i.stack.imgur.com/AgUkO.png" alt="enter image description here"></p>
<p><strong>Edit:</strong> </p>
<p>The following code elaborates on my hesitation with the method that I used. The relationship between Standard Error (SE) and y is not a precise; i.e. various values of y that are relatively close together, have widely differing SE (black symbols in figure below, <code>pred1</code>), while the above method predicts a single SE for each predicted y (red symbols, <code>pred2</code>). Furthermore, using several different combinations of x1 and x2 that always result in the same y-value, I get a single (but different!) SE (green symbol, <code>pred3</code>). What is going on here? Is there a more correct way of doing this with some sort of permutation method?</p>
<pre><code>#? Do different solutions to a given predicted value always give the same standard error?
y.tmp <- rep(40,20)
x1.tmp <- seq(0,10, length(y.tmp))
x2.tmp <- (y.tmp - fit$coeff[1] - fit$coeff[2]*x1.tmp) / fit$coeff[3]
df3 <- data.frame(x1=x1.tmp, x2=x2.tmp)
pred3 <- predict(fit, df3, se.fit=TRUE)
YLIM <- range(pred1$se.fit, pred2$se.fit, pred3$se.fit)
png("fit.se_vs_fit.png", width=6, height=6, units="in", res=200)
plot(pred1$se.fit ~ pred1$fit, ylim=YLIM, lwd=2)
points(pred2$se.fit ~ pred2$fit, col=2, lwd=2)
points(pred3$se.fit ~ pred3$fit, col=3, lwd=2)
legend("topright", legend=c("orig. data", "range of x1 & x2", "various comb. of x1 & x2 \nto acheive y=40"), col=1:3, pch=1, lwd=2, lty=0)
dev.off()
</code></pre>
<p><img src="http://i.stack.imgur.com/4TcVs.png" alt="enter image description here"></p>
|
g35680
|
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<p>I have made a factor analysis of one construct (i.e. difference between two countries) and got two distinct factors (1=cultural differences, 2=economical environment). I extracted the scores as I want to check if the score of cultural differences is bigger than economical. How do I do that? I have tried making a simple T test but it does not return any good result, as the factor scores are standardized and the factor means are 0 (S.Dev=1). What approach do I have to do?</p>
|
g35682
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] |
<p>I'm reading this chapter
<a href="https://www.otexts.org/fpp/4/1" rel="nofollow">forecasting principles and practise</a> from a forecasting book.</p>
<p>The author has explained a linear regression model. Now this linear regression model will definitely have some errors in fit. For these errors, the author has listen certain characteristics, which should be taken into account. He assumes that these errors:</p>
<ol>
<li>Have mean zero; otherwise the forecasts will be systematically biased.</li>
<li>Are not autocorrelated; otherwise the forecasts will be inefficient as there is more information to be exploited in the data.</li>
<li>Are unrelated to the predictor variable; otherwise there would be more information that should be included in the systematic part of the model.</li>
</ol>
<p>The problem is that I'm not able to comprehend these and come up with an example to get a hang of these points. Could somebody point out some examples / situations from daily life so as to understand these points. For example the author wrote in point 2.] ..."there is more information to be exploited in the data"... </p>
<p>What is this information? How does it come into being? If I don't even know how this information comes into existence, then how will I be able to understand its existence or effects for that matter?</p>
<p>Is there a simple explanation with example for my question? I have been trying to understand this since quite some time, please help.</p>
|
g49560
|
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<p>I'm attempting a project where I need to statistically rank available cars based on several variables such as cost, mpg, seating, milage, etc.. I wish to rank these cars in order decide which car would be the best choice (highest "worth") to buy (or best several cars if I was informing multiple people of the best cars to get). As the list of available cars changes from day to day, I will also need to re-run the code every day to allow the rankings to give me the best decision for this new day. </p>
<p>What statistical methods should I use to go about this ranking system? I plan on determining which factors I find most important so the variables used will be subjective in choice. I thought about trying MDS or clustering but I didn't know if that would be relevant since I'm already subjectively determining what variables are to be used. I don't see how regression can be used since I can't get a handle on the "worth" of previous cars as that is what I'm trying to rank by. Also, I will be attempting this in R so any helpful packages/functions would be great to know as well.</p>
<p>Any help with how to go about this ranking scheme would be helpful as I'm at a loss.</p>
<p>Thanks so much</p>
|
g73351
|
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<p>I have two variables <em>Distance</em> and <em>Slope</em>. These go into a model resulting in a <em>cost</em> variable. I like to figure out the influence of the variables Distance and Slope on the Cost variable. I have several hundred test numbers for the variables. What programs or steps could I use to see the impact of the two variables on the cost?
In the end I would like to know for example <em>Distance</em> influences the <em>Cost</em> variable too 70 %. <em>Slope</em> influence <em>Cost</em> too 30 %.</p>
|
g73352
|
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] |
<p>I would like to compare the means of the same group on two continuous scales. I want to see if the scores are significantly different on the scales. Which statistical test do I use for this? </p>
|
g35685
|
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<p>I have a problem that seems tractable, which I will attempt to describe with classic balls and buckets probability nomenclature.</p>
<p>Imagine someone brings you a bag of colored balls. This sample was selected at random from one of many large buckets of balls. Each bucket contains 1,000,000 balls, and each ball is one of 1,000 colors. For any bucket, the proportion of balls for each color is fixed, and we know what it is. For example, Bucket A always has 0.02 Red, 0.013 Green, 0.009 Blue, etc.</p>
<p>So--how would I go about estimating which bucket the sample of balls came from? I know that if I have a bag (sample) of 1,000,000 balls, I can say unambiguously which bucket that came from, as the proportions are defined. However, what do I do if I have only 2000 balls in the sample? It seems to me I should be able to calculate quite specifically the likelihood that the sample came from a particular bucket.</p>
<p>Any help would be greatly appreciated! I'll be doing this in code (likely Python).</p>
<p>Best regards,
Dan</p>
|
g73353
|
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<p>Can someone explain the intuition behind the split plot. From what I understand, its is essentially restricted randomization. But I still quite understand it. Is there a resource or example anyone can give me to make it clearer?</p>
|
g43656
|
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0.025564027950167656
] |
<p>I use <code>cpgram</code> function in R to produce a cumulative periodogram of a monthly time series. Its horizental axis is a number between 0 and 6 labeled as frequency: what does these numbers mean, since the frequency in cumulative periodogram should be between 0 and 0.5 like the ones shown below (upper ones)?</p>
<p><img src="http://i.stack.imgur.com/Gs4O2.jpg" alt="enter image description here"></p>
<p>Also, do you know how can I create cumulative periodograms like these plots?</p>
|
g73354
|
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<p>Can someone provide a work flow about this? For instance, suppose I am doing binary classification,</p>
<p>For each iteration of the algorithm:</p>
<p>Randomly sample k*N rows, where k is the bag.fraction, and N is nrow(dataset).</p>
<p>Build a classifier using this training sample, suppose we use classification tree here.</p>
<p>Predict the terminal node class label.</p>
<p>This how boosting is done without a CV. If I want to do a 3-fold CV, where exactly do I apply it? Between step 1 and 2 or after step 3? </p>
<p>Thanks!</p>
|
g35687
|
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<p>I know about the following tests:</p>
<ul>
<li>Mantel-Haenszel for categorial stratified data</li>
<li>Kruskal-Wallis for nonparametric ANOVA for more than two treatments</li>
<li>Friedman for a repeated measures version of Kruskal-Wallis</li>
<li>van Elteren for nonparametric comparisons of stratified data between two treatments</li>
</ul>
<p>But is there something that combines the features of these? In other words, I'm looking for a test that takes data for $g$ experimental treatments, collected across $q$ strata, where the response cannot be assumed to follow any parametric distribution, and I want to test for a difference in treatment effect while controlling for the confounder(s) that I stratified across. The sample size is small.</p>
<p>If there isn't such a test (I could not find any references in the literature), then can we resort to some kind of nonparametric bootstrap, or a Monte Carlo method? How could we design such a procedure?</p>
|
g73355
|
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] |
<p>I wish to measure the "diversity" of a group of objects. Right now I'm using Euclidean distance to compute the similarity matrix between all the objects in the group.</p>
<p>I'm searching for a measure of this diversity to decide if replacing an element of this matrix with a new one will make the group more or less homogeneous. I wish to end up the most heterogeneous group.</p>
<p>Of course, I'm open to another approaches if I'm looking at this from the wrong angle.</p>
<p>Bonus points if it's computationally efficient.</p>
|
g73356
|
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<p>Following the <a href="http://en.wikipedia.org/wiki/Tobit_model" rel="nofollow">wiki page</a> and the form of the likelihood function for a generalized Tobit model presented <a href="http://support.sas.com/documentation/cdl/en/etsug/63348/HTML/default/viewer.htm#etsug_qlim_sect022.htm" rel="nofollow">here</a>, I am thinking about applying a model of this type to a problem I'm facing but need some help in the interpretation. </p>
<p>I have a variable $Y$ which I assume to linearly depend on $X$ via a parameter $\beta$. My model is</p>
<p>\begin{equation}
Y = X\beta + \epsilon_i
\end{equation}</p>
<p>The problem is that some observed values I have for $Y$, the $y_i$'s, are upper limits. Can I extend the concept of "censored data" to this case and use the Tobit model to perform the linear regression? </p>
<p>Do you have any thoughts on the possibility of further inclunding a categorical moderator variable in the regression? Is this possible?</p>
<p>Thanks.</p>
|
g73357
|
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<p>I am going through this paper <a href="http://prac.im.pwr.wroc.pl/~mbogdan/TE/materials/Efromovich_Wiley_interdisciplinary_reviews_2010_orthogonal_series.pdf" rel="nofollow">Orthogonal series density estimation</a>. I have a doubt in following</p>
<p>Assume that the random variable X is supported on [0, 1], that is, P(X ∈ [0, 1]) = 1, and that the probability density f of X is square integrable. Then the density may be approximated with any wished accuracy by a partial sum</p>
<p>$f_J(x) :=\sum_{j=0}^J \theta_j \varphi_j(x), 0\le x\le1$</p>
<p>Here $\{\varphi_j\} $ is the cosine basis</p>
<p>$ \varphi_0(x)=1, \varphi_j(x)=\sqrt 2 cos(\pi j x), j=\{1,2,\cdots\}$</p>
<p>$\theta_j$ is the $j_{th}$ coefficient and $J$ is the cut-off</p>
<p>Note that $\theta_0=\int_0^1f(x) dx=1$</p>
<p>Also $\theta_j=\int_0^1 \varphi_j(x) f(x) dx= E\{\varphi_j(x)\}$</p>
<p>This implies that $\theta_j$ can be estimated by sample mean estimator.</p>
<p>$\hat{\theta}=n^{-1}\sum_{l=1}^n \varphi(X_l)$</p>
<p>$Var(\hat{\theta_j})=E(\hat{\theta}-\theta)^2$</p>
<p>$=n^{-1}[1+2^{-1/2}\theta_{2j}-\theta_j^2]=n^{-1}d$ Using $cos^2(\alpha)=(1+cos(2\alpha))/2$</p>
<p>Here d is defined as coefficient of difficulty.</p>
<p>My doubt is in last step $E(\hat{\theta}-\theta)^2=n^{-1}[1+2^{-1/2}\theta_{2j}-\theta_j^2]$</p>
<p>I think $E({\hat{\theta_j}^2}-2\hat{\theta_j}{\theta}+{\theta}^2)=E({\hat{\theta_j}^2}-{\theta}^2)$</p>
<p>If we assume the points are drawn iid $E(\varphi(x_l),\varphi(x_m))=E(\varphi(x_l))E(\varphi(x_m))$</p>
<p>So $E((\sum_{l=1}^n\varphi(x_l))^2)=E(\sum_{l=1}^n\varphi(x_l)^2+2*\sum_{l,m=0}^n\varphi(x_l)\varphi(x_m))$</p>
<p>$=E(\sum_{l=1}^n\varphi(x_l)^2)+2*E(\sum_{l,m=0}^n\varphi(x_l)\varphi(x_m))$</p>
<p>$E({\hat{\theta_j}^2})=n^{-2}[n(1+2^{-1/2}\theta_{2j})+\big(n(n-1)/2\big)2*{\theta_j}^2]$</p>
<p>$E({\hat{\theta_j}^2})=n^{-1}[1+2^{-1/2}\theta_{2j}+(n-1){\theta_j}^2]$</p>
<p>Please let me know if my understanding is correct</p>
|
g73358
|
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] |
<p>According to some articles (e.g. <a href="http://brenocon.com/blog/2012/03/cosine-similarity-pearson-correlation-and-ols-coefficients/" rel="nofollow">here</a>) correlation is just a centered version of cosine similarity. I use the following code to calculate the cosine similarity matrix of the column vectors of a matrix <code>X</code> (slightly modified from <a href="http://stats.stackexchange.com/questions/31565/is-there-an-r-function-that-will-compute-the-cosine-dissimilarity-matrix">here</a>):</p>
<pre><code>cos.sim <- function(ix)
{
A = X[,ix[1]]
B = X[,ix[2]]
return(t(A)%*%B/sqrt(sum(A^2)*sum(B^2)))
}
n <- ncol(X)
cmb <- expand.grid(i=1:n, j=1:n)
C <- matrix(apply(cmb,1,cos.sim),n,n)
</code></pre>
<p><strong>My question</strong> <br>
Which modifications of the code above are needed to get the correlation matrix <code>cor(X)</code> instead of the cosine similarity matrix. I guess the changes are minimal but I can't see them at the moment.</p>
|
g73359
|
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] |
<p>There are a set of ("artifical") not Minkovski (triangle inequality is not guaranteed) metrics defined on set of objects.</p>
<p>There are one etalon ("natural") metric, which estimation is known only for some objects (a finite learning subset).</p>
<p>How can I get some combination of "artifical" metrics (new metric essencually) that would be the best (for proposed class of combinations) approximation of the "natural" metric? I mean the type of appropriate methods or something specifying the area of further googling.</p>
<p>May be it's just two dimensional function approximation where both dimensions present the same discrete space as a distance matrix and function is an etalon metric.</p>
<p>Specific realization of distances combination is not the point (though lower computational complexity is better), so it may be simple linear combination. And kind of objects is not important too, but in my case it's some data sets for which I define several similarity measures that must be combined into one corresponding to the expert estimation.</p>
|
g73360
|
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<p>I'm trying to make a model to forecast the electricity price, a time series model with R and i have some questions</p>
<p>Our data are daily price of the past 3 years from north pool countries, and we are trying to do a model to forecast the daily prices too. </p>
<p>We don't know how to descompose the seasonality of our data, because all the test and studies need to be made at the data without seasonality. </p>
<p>In the other hand, we have some problems to understand the ARIMA or ARMA model, because is the one we want to apply, and we don't know how to do it in R.</p>
<p>Thanks and sorry for my bad english.</p>
|
g73361
|
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<p>I have been wanting to get away from using power calculation tools (JMP, Lenth) in favor of Monte Carlo techniques to determine the a-priori power to observe factor level effects in a DOE. I am really new to this and have a few questions. Lets start with what I have:</p>
<ol>
<li>A binomial response which I plan to perform a logistic regression to</li>
<li>List of factors that I think are relevant</li>
<li>A model (Main Effects + interaction + quadratic terms)</li>
<li>An experimental design (Taken from JMP or the DoE.wrapper package)</li>
<li>A threshold requirement (0.6)</li>
<li>An effect size (ES = 0.1)</li>
</ol>
<p>I would like to determine the power to observe an effect in the response for each one of the model terms. I have read the excellent <a href="http://stats.stackexchange.com/questions/35940/simulation-of-logistic-regression-power-analysis-designed-experiments">response by user gung</a> which I wanted to use to help tailor my own approach. After reading, I had a few specific questions.</p>
<ol>
<li>The example uses prior knowledge of the system performance (the rates) that I do not have. How do I continue without this knowledge? </li>
<li>The solution does not factor in effect size in any way (at least as far as I can tell). How do I factor in effect size to this process?</li>
<li>The power for each of the terms is coming from the significance of the model term to be non-zero. Is this the same as the power to observe an effect size in the response?</li>
</ol>
<p>For question 2, I would assume that you would just need to run the model assuming the null performance (p = 0.6) and then re-run the fit assuming the performance of Null + Effect Size (p = 0.6 + ES). I know this last part might be a bit jumbled up. Any help would be greatly appreciated.</p>
|
g73362
|
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<p>Good evening everyone, </p>
<p>I am working on the following self-test question for regressions, but my answer 26.901 seemed really different from the model answer 27.2155.</p>
<p><strong><em>Question</em></strong></p>
<blockquote>
<p>A hotel derives its gross income from its hotel and restaurant operations.
The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant . Below are a sample of 25 days (Monday through Thursday) from last year showing the restaurant income Y in thousand dollars and number of rooms occupied X</p>
<p><img src="http://i.stack.imgur.com/NvVcQ.jpg" alt="enter image description here"></p>
</blockquote>
<p><strong><em>My Attempt</em></strong></p>
<blockquote>
<p><img src="http://i.stack.imgur.com/pjueE.jpg" alt="enter image description here"></p>
</blockquote>
<p>Appreciate any advice please.</p>
|
g26981
|
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] |
<p>I am looking for the word/phrase that is used to say that a (potential) erroneous conclusion has been drawn from data without having a correlation to other supporting data points.</p>
<p>For example, if someone has the dataset of the number of red cars sold in the US per month as <code>Jan: 10, Feb: 10, Mar: 9, Apr: 8, May: 7, etc.</code> and draws the conclusion of <code>"Red cars are going out of style"</code> without correlating this data to total car sales for the same time period, or the number of other color cars sold, etc.</p>
<p>This conclusion might be correct if there was data showing that car sales as a whole have not declined, but this conclusion could be false if car sales as a whole have declined, etc, etc.</p>
<p>Is this called "Sampling Bias" or something else?</p>
|
g73363
|
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<p>A gaussian random vector $X$ can be represented using a graph where two nodes $a$ and $b$ are connected $\Leftrightarrow X_a$ is dependent on $X_b$ given all the remaining random variables. I have two questions - </p>
<p>1) It is stated that the neighborhood of $a$ is the smallest subset such that given this subset, $X_a$ is conditionally independent of all the remaining variables. Is this easy to prove or does the proof depend on proving a series of theorems? I'm wondering whether to find and read the proof or just assume this fact.</p>
<p>2) It is generally assumed that the neighborhood of any node is small in size i.e. a node is not connected to all other nodes. Why is this a reasonable assumption in practice?</p>
<p>Thanks!</p>
|
g1007
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<p>P-value is defined the probability of obtaining a test-statistic at least as extreme as what is observed, assuming null-hypothesis is true. In other words,</p>
<p>$$P( X \ge t | H_0 )$$
But what if the test-statistic is bimodal in distribution? does p-value mean anything in this context? For example, I am going to simulate some bimodal data in R:</p>
<pre><code>set.seed(0)
# Generate bi-modal distribution
bimodal <- c(rnorm(n=100,mean=25,sd=3),rnorm(n=100,mean=100,sd=5))
hist(bimodal, breaks=100)
</code></pre>
<p><img src="http://i.stack.imgur.com/spCCE.png" alt="enter image description here"></p>
<p>And let's assume we observe a test statistic value of 60. And here we know from the picture <em>this value is very unlikely</em>. So ideally, I would want a statistic procedure that I use(say, pvalue) to reveal this. But if we compute for the p-value as defined, we get a pretty high-p value</p>
<pre><code>observed <- 60
# Get Pvalue
sum(bimodal[bimodal >= 60])/sum(bimodal)
[1] 0.7991993
</code></pre>
<p>If I did not know the distribution, I would conclude that what I observed is simply by random chance. But we know this is not true. </p>
<p>I guess the question I have is Why, when computing p-value, do we compute the probability for the values "at least as extreme as" the observed?
And if I encounter a situation like the one I simulated above, what is the alternative solution?</p>
|
g35695
|
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<p>This is not homework. Just practicing for an upcoming exam. Question is taken from a web pdf : <a href="http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf" rel="nofollow">http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf</a></p>
<p>Consider the following process. We have two coins, one of which is fair, and the
other of which has heads on both sides. We give these two coins to our friend,
who chooses one of them at random (each with probability 1/2). During the
rest of the process, she uses only the coin that she chose. She now proceeds
to toss the coin many times, reporting the results. We consider this process
to consist solely of what she reports to us.</p>
<p>(a) Given that she reports a head on the nth toss, what is the probability
that a head is thrown on the (n + 1)st toss?</p>
<p>(b) Consider this process as having two states, heads and tails. By computing
the other three transition probabilities analogous to the one in part (a),
write down a \transition matrix" for this process.</p>
<p>(c) Now assume that the process is in state "heads" on both the (n - 1)st
and the nth toss. Find the probability that a head comes up on the
(n + 1)st toss.</p>
<p>(d) Is this process a Markov chain?</p>
<p>Solution is given here: Chapter 11 question 19 :<a href="http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Answersodd-10-14-08.pdf" rel="nofollow">http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Answersodd-10-14-08.pdf</a></p>
<p>Also, what is the best approach in assigning state i a state? "state 1=..."?
Also, what is the difference between the Markov process and Markov chain?</p>
|
g73364
|
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] |
<p>The beta distribution is conjugate prior for the binomial distribution.</p>
<p>Is the beta-binomial distribution a conjugate prior for some sampling distribution?</p>
|
g35697
|
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] |
<p>Panel estimators such the one implemented in the R package <code>plm</code> allow to estimate <code>"individual"</code>, <code>"time"</code> or <code>"twoways"</code> effects.</p>
<p>See <a href="http://cran.r-project.org/web/packages/plm/vignettes/plm.pdf" rel="nofollow">http://cran.r-project.org/web/packages/plm/vignettes/plm.pdf</a> (page 5).</p>
<p>When do I use which of the three possible specifications?</p>
|
g73365
|
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<p>There have been threads here before which posted links of the media attributing causality to correlational studies, and links to those studies have been posted. It seems as if we are always focusing on showing students how to identify correlations and not to confuse it with causality.</p>
<p>We are missing something important in the process though: Some students assume afterwards that causality can never be inferred, and absolutely everything is a correlation!</p>
<p>Does anyone have any links to studies in the media which actually DO show causal links? </p>
<p>Student understanding of the difference between correlation/causation in studies reported by journalists, can only be inferred when "causal relationship" sometimes is actually the correct answer. </p>
|
g73366
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] |
<p>I'd like to measure the duration of a function call. The function call has one parameter, <code>n</code>. If I were to graph an average of the function call's duration, with <code>n</code> on the x axis, I would also provide the standard error for each <code>n</code>.</p>
<p>The function call duration is, however, extremely short. It seems more appropriate to time, say, 100 calls. Is this approach completely orthogonal to the earlier use of the standard error? Does an average of the 100 calls now count as 1 measurement? Does <em>it</em> have a standard error?</p>
|
g73367
|
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<ol>
<li>Using either percent error or percent difference, I want to compare one of my measured values from a set to the mean of the set. By reading the Wikipedia article on <a href="http://en.wikipedia.org/wiki/Percent_difference" rel="nofollow">percent difference</a>, it's still not quite clear which I should choose.</li>
<li>What if I wanted to compare an instantaneous slope to the slope of a linear regression, do I use percent error or percent difference?</li>
</ol>
<p>If it isn't clear yet, my misunderstanding lies in the comparison of one value from a set to some computed aggregated value from that set.</p>
<p>Thanks in advance.</p>
<p>-JP</p>
|
g35699
|
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] |
<p>The data for my variable is in the form of Z-scores only. I'd like to log transform the scores, but I don't know the mean or standard deviation in order to covert to raw scores. Can I assign an arbitrary mean and standard deviation, use that to convert to raw scores, then log transform the raw scores? Or is there some other way to log transform Z-scores? Thanks.</p>
|
g73368
|
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] |
<p>I wonder why gene expression data are very frequently modeled by multivariate normal distributions. What is the reason for those strong assumptions that the genes follow multivariate gaussian? Are there any reasons specific for genetics other than the reasons for general gaussian assumptions (mathematical convenience, etc.)?</p>
|
g73369
|
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] |
<p>I understand how differential calculus is useful for basic Maximum Likelihood estimation techniques. However, my question is: what broad types of statistics require an understanding of integral calculus?</p>
|
g73370
|
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<p>I was recently told that it was not possible to incorporate time-varying covariates in longitudinal mixed models without introducing a time lag for these covariates. Can you confirm / deny this? Do you have any references on this situation ?</p>
<p>I propose a simple situation to clarify. Suppose that I have repeated measures (say over 30 occasions) of quantitative variables (y, x1, x2, x3) in 40 subjects. Each variable is measured 30 times in each subject by a questionnaire. Here the final data would be 4 800 observations (4 variables X 30 occasions X 40 subjects) nested in 40 subjects.</p>
<p>I would like to test separately (not for model comparison) for :</p>
<ul>
<li>simultaneous (synchronous) effects : the influence of x1, x2, and x3 at time t on y at time t.</li>
<li>lagged effects : the influence of x1, x2, and x3 at time t-1 on y at time t.</li>
</ul>
<p>I hope everything is clear (I'm not a native English speaker !).</p>
<p>For instance, in R lmer{lme4}, the formula with lagged-effects is : </p>
<pre><code>lmer(y ~ lag1.x1 + lag1.x2 + lag1.x3 + (1|subject))
</code></pre>
<p>where <code>y</code> is the dependent variable at time t, <code>lag1.x1</code> is the lagged independent variable x1 at the individual level, etc. </p>
<p>For simultaneous effects, the formula is : </p>
<pre><code>lmer(y ~ x1 + x2 + x3 + (1|subject))
</code></pre>
<p>Everything is running well and it gives me interesting results. But is it correct to specify a lmer model with synchronous time-varying covariates or have I missed something ?</p>
<p><em><strong>Edit:</em></strong>
Moreover, is it possible to test both simultaneous and lagged effects at the same time ? , For instance :</p>
<pre><code>lmer(y ~ x1 + x2 + x3 + lag1.x1 + lag1.x2 + lag1.x3 + (1|subject))
</code></pre>
<p>Theoretically, it makes sense to test competition between concurrent vs. lagged effects. But is it possible with <code>lmer{lme4}</code> in R, for example ?</p>
|
g27014
|
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] |
<p>I am working with the two step cluster process in SPSS Modeler (Clementine) and trying to get a sense for the distance function used. It is a log-likelihood function (as stated in docs) but I am unsure for even the continuous variables (the function handles continuous and nominal variable) how this is a log likelihood (it is missing most of the elements of a Gaussian). Below is a screen shot of the documentation describing the distance formula.</p>
<p>Has anyone seen the derivation of this distance function?</p>
<p><img src="http://i.stack.imgur.com/LlSix.jpg" alt="enter image description here"></p>
|
g73371
|
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<p>Usually, we can test difference of two groups of data by adding the dummy variable. But my question is, if these two groups of data in the same line, but they concentrate at the different part of this line. Is there any way we can test difference?
For example,in group one, our data set is $(x_{1i},y_{1i})$, in group two, our data set is $(x_{2j},y_{2j})$. Both of the groups can regress to the same line $y=a+bx$,where $a$ and $b$ are constant. But in group one $x_{1i}\in(1,3)$, in group two $x_{2j}\in(6,7)$. Thus if we plot group one and group two together, we can see they centralize to different part of line $y=a+bx$. Apparently, dummy variable does not work well here. So is there test can show the difference?
Thanks. </p>
|
g35706
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] |
<p>Can I use a chi-squared test to compare two empirical distributions?</p>
<p>Signs point to "yes." <a href="http://stat.ethz.ch/R-manual/R-patched/library/stats/html/chisq.test.html" rel="nofollow">R's chisq.test</a> allows two vectors x and y. It says:</p>
<blockquote>
<p>cases with missing values are removed, the objects are coerced to factors, and the contingency table is computed from these. Then Pearson's chi-squared test is performed of the null hypothesis that the joint distribution of the cell counts in a 2-dimensional contingency table is the product of the row and column marginals.</p>
</blockquote>
<p>See also: <a href="http://stats.stackexchange.com/questions/13326">same question about KS test</a>.</p>
|
g35707
|
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<p>I have a bunch of points that belong to one of population P1, P2, ... Pn AND to class A or B.</p>
<p>Within each population I'll be doing classification between A and B, and I want to select features that discriminates the best between A and B. Now, my features are also correlated with population membership, but I don't care about that, I only want to know how well the measures discriminate within a population.</p>
<p>So, is there a "proper" way to measure that? Within a population, I can just check how much the metric is correlated with class membership (biserial correlation), but if I get the correlation on the whole population, Simpson's paradox gets in the way and I may end up measuring the wrong thing.</p>
<p>I could just calculate correlations for each population, and average those or something, but that sounds ugly to me (this is for proramming real-world applications, not for publishing in a paper, so I don't mind if my method isn't <em>that</em> rigorous as long as the result is OK).</p>
<p>So, what's the proper way to control for population membership?</p>
|
g73372
|
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<p>Is there a simple example for a pair of hypotheses for which a uniformly most powerful (UMP) test does not exist? How does one go about proving this? Is it true that for tests with double-sided hypotheses, a UMP test does not exist? Is it true that for multivariate parameters, a UMP tests does not exist?</p>
|
g73373
|
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<p>Suppose that $x$ takes the following values: 0 feet from start, 10 feet from start, and 15 feet from start. Let the outcome variable be $y$. How would you interpret the regression coefficient of $x$ ($\beta_1$) in a linear regression? Would it be: a unit increase in $x$ is associated with an expected increase of $\beta_1$ in $y$? It seems that this would be a problem because a unit could be an increase from $x=0$ to $x=10$ or an increase from $x=10$ to $x=15$.</p>
|
g73374
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] |
<p>Folks, pardon my noobness but I have not touch maths for some time and need a refresher into statistics:</p>
<p>I read that in Bayes rule, the denominator of <code>P(params|data) = L(params)P(params)/P(data)</code> is called a normalizing constant. Can anyone explain why does integrating f(data|params)f(params) as in the case of the denominator, does not depend on the parameters?</p>
|
g73375
|
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] |
<p>What is v-fold cross validation in relation to k-fold cross validation?</p>
<p>Also is there a more common way in which v-fold cross validation is referenced?</p>
<p>I'm struggling to find resources on this method.</p>
|
g73376
|
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] |
<p>The definition for the $k$-th lag auto correlation is $Cov(y_t,y_{t-k})/Var(y_t)$.<br>
My question is why should not it be $Cov(y_t,y_{t-k})/[Var(y_t)\cdot Var(y_{t-k})]^{0.5}$.<br>
In another words, what is it different from the correlation coefficient between $y_t$ and $y_{t-k}$?</p>
|
g73377
|
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<p>I have a set of data with an ordinal response ranging from <code>1-5</code> (worst to best) and a categorical predictor with five unordered levels. The experiment is a language experiment whereby subjects are asked to rate different sentence types. In the literature it seems that people fit <code>lmer()</code> most of the time by scaling the ordinal response per subject (i.e. taking the mean response and standard deviation of that subject and dividing the every single response by it.). On the other hand, it seems a reasonable approach to use ordered linear mixed effects probit models or ordered linear mixed effects logit models as implemented in e.g. <code>MCMCglmm()</code> or <code>clmm()</code>.</p>
<p>(1) I find myself asking what the best method would be. When is one method to be prefered over the other in an experiment as I have sketched above?</p>
<p>(2) Why do people prefer fitting an <code>lmer()</code> model with a scaled response? What is the advantage?</p>
<p>(3) If it is advisable to use an ordered probit or logit model, how do I decide between an ordered probit or ordered logit model?</p>
<p>Thanks for any help!</p>
|
g73378
|
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] |
<p>Following the design and data described in <a href="http://stats.stackexchange.com/questions/11887/is-this-design-a-one-way-repeated-measures-anova-or-not">this question</a>, I did a simple one-way within-subjects repeated-measures (RM) ANOVA and found some significant p-values. I then applied non-orthogonal post-hoc Tukey's HSD tests, and when I got significant results I applied Holm-Bonferroni (1979) correction. Whenever some p-values survived the FWER correction, I calculated 95% CIs and mean for the associated pairwise comparisons.</p>
<p>My question is: If I don't observe a significant result at any of the above steps, do I have to carry out a power analysis for the RM ANOVA, apply <a href="http://en.wikipedia.org/wiki/Tukey%27s_range_test" rel="nofollow">Tukey's HSD test</a> or <a href="http://en.wikipedia.org/wiki/Holm%E2%80%93Bonferroni_method" rel="nofollow">Holm-Bonferroni</a> adjustments, or do I simply report results from the RM ANOVA without doing the power analysis?</p>
<p>The problem is that I'm starting to immerse in biostatistics only after my experiments, and unfortunately I didn't run a power analysis beforehand. </p>
|
g73379
|
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] |
<p>I want to estimate the parameters of a function of general form $y = a \cdot x^b$. I applied a log-log transformation to obtain a linear function of the form $\log y = \log a + b \times \log x$. I have fitted the linear model in MATLAB.</p>
<p>MATLAB computes the goodness of a fit in terms of sum of squares error (SSE) and (adjusted) R bar. I want to report these numbers but they are probably meaningless given that in fact $\log a$ and not $a$ has been estimated. How do I fix this?</p>
|
g73380
|
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] |
<p>I have a set of points which is a count of links that users have clicked on : </p>
<pre><code> link1,link2,link3,link4
user1, 0 ,2 ,3 ,2
user2, 1 ,4 ,0 ,5
</code></pre>
<p>I am not sure which distance function I should use to calculate the distance between users. I think Euclidean distance is a good fit (reading <a href="http://en.wikipedia.org/wiki/Euclidean_distance" rel="nofollow">http://en.wikipedia.org/wiki/Euclidean_distance</a>) ? </p>
|
g73381
|
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] |
<p>Suppose that I have a linear model with autocorrelated errors. Is there any results telling me that if I assume iid errors I overestimate or underestimate my standard errors ? </p>
|
g361
|
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<p>I have a question on coding a Likert scale in SPSS.</p>
<p>Assuming we have a 7-point Likert scale, a "well-being" score may rank from 1 through 7.</p>
<p>While doing some reading on multi-variate analysis, I've come across a reference that suggests a "deviation score". That is, it's ranging from [-3, -2, -1, 0, 1, 2, 3].</p>
<p>For later analysis of survey results, which method ("well-being score" vs. "deviation score") will serve me best? Or are these "apples and oranges"?</p>
<p>Thanks,
EEH</p>
|
g35715
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<p>I have a dataset containing values representing monthly sales in hypothetical e-commerce website. First columns contains order of particular month (eplanatory variable) and the second column (dependent variable) is value of sales in this month.</p>
<pre><code>month_order value
1 2591
2 2262
3 2531
4 2379
5 2106
6 2500
7 2345
8 2200
9 2385
10 2991
11 2219
12 2600
13 3000
</code></pre>
<p>Equation of linear regression for this data set is:</p>
<pre><code>f(x) = 27,42x + 2278
</code></pre>
<p><strong>Question:</strong> Because I would like to make a very simple prediction of sales value in next month and I have no another more suitable eplanatory variable, may I use month_order and predict linear trend? In my case it would be:</p>
<pre><code>f(14) = 27,42 * 15 + 2278 = 2689
</code></pre>
<p>is this correct in a theory of a linear regression and can I count it in this way?</p>
|
g18512
|
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<p>This is somewhat of a beginner's question, but how does one interpret an exp(B) result of 6.012 in a multinomial logistic regression model?</p>
<p>1) is it 6.012-1.0 = 5.012 = 5012% increase in risk?</p>
<p>or</p>
<p>2) 6.012/(1+6.012) = 0.857 = 85.7% increase in risk?</p>
<p>In case both alternatives are incorrect, can someone please mention the correct way?</p>
<p>Ive searched many resources on the internet and I get to these two alternatives, and I am not entirely sure which one is correct.</p>
|
g38182
|
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] |
<p>The z-test to compare two proportions is $\newcommand{\p}{\hat{p}}\newcommand{\v}{\mathrm{Var}} z=\frac{\p_1-\p_2}{\sqrt{\v(\p_1-\p_2)}}$. Usually it is defined that </p>
<p>$$\v(\p_1-\p_2)=\p(1-\hat{p})(1/n_1+1/n_2),$$ </p>
<p>where </p>
<p>$$\p=\frac{n_1 \p_1+n_2 \p_2}{n_1+n_2}.$$</p>
<p>Is there any written reference that legitimizes me instead to use the unpooled variance, that is </p>
<p>$$\v(\p_1-\p_2)=\frac{\p_1(1-\p_1)}{n_1}+\frac{\p_2(1-\p_2)}{n_2}?$$ </p>
|
g73382
|
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<p>My data-set consists of points in globe. Suppose a User visits locations $l_1,l_2,\dots l_n$ (each location in $(lat, long)$ in the city with probability $p_1,p_2,\dots,p_n$ and I want to calculate the expected location visited by the user. How should I go about calculating that? If I use geodesic distance between points then do we have a formula or recipe to calculate geodesic expectation? What possibly can go wrong if I convert the individual $(lat,long)$ values to cartesian co-ordinates and calculate their expectation?</p>
|
g73383
|
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<p>I have done an experiment of how different animal species affect nutrient fluxes in sediments. I had a number of experimental units (sediment boxes) to which different animal species were added. I then measured nutrient fluxes in these units. Each unit was measured five times. I have used the ezANOVA package for R to do a repeated measures ANOVA with two factors (between subjects factor “Species” and within subject factor “Time”).
Here's an example of my input:</p>
<pre><code>> ezANOVA(data=NoP_3_5,dv=.(AcPO4),wid=.(Subject),within=.(Time),between=.(Species),return_aov=T)
$ANOVA
Effect DFn DFd F p p<.05 ges
2 Species 2 6 10.60384830 1.072453e-02 * 0.50875722
3 Time 2 12 27.88590570 3.081718e-05 * 0.76667542
4 Species:Time 4 12 0.08093179 9.867291e-01 0.01871588
$`Mauchly's Test for Sphericity`
Effect W p p<.05
3 Time 0.1439855 0.007866779 *
4 Species:Time 0.1439855 0.007866779 *
$`Sphericity Corrections`
Effect GGe p[GG] p[GG]<.05 HFe p[HF] p[HF]<.05
3 Time 0.5387889 0.001349263 * 0.5630403 0.001103048 *
4 Species:Time 0.5387889 0.933492515 0.5630403 0.939138882
$aov
Call:
aov(formula = formula(aov_formula), data = data)
Grand Mean: -0.004276663
Stratum 1: Subject
Terms:
Species Residuals
Sum of Squares 0.0004410742 0.0001247870
Deg. of Freedom 2 6
Residual standard error: 0.004560464
Estimated effects may be unbalanced
Stratum 2: Subject:Time
Terms:
Time Species:Time Residuals
Sum of Squares 0.0013994206 0.0000081229 0.0003011028
Deg. of Freedom 2 4 12
Residual standard error: 0.005009181
Estimated effects may be unbalanced
</code></pre>
<p>I want to use the $aov output to do a Tukey HSD post hoc test of the between factor ("Species"). However, it does not work:</p>
<pre><code>mod <- ezANOVA(data=NoP_3_5,dv=.(AcPO4),wid=.(Subject),within=.(Time),between=.(Species),return_aov=T)
> TukeyHSD(mod$aov)
Error in UseMethod("TukeyHSD") :
no applicable method for 'TukeyHSD' applied to an object of class "c('aovlist', 'listof')"
</code></pre>
<p>I have also tried to use the aov-command directly:</p>
<pre><code>> mod2 <- aov(AcPO4~(Species)+Error(Subject/Time)+(Species),data=NoP_3_5)
> TukeyHSD(mod2)
Error in UseMethod("TukeyHSD") :
no applicable method for 'TukeyHSD' applied to an object of class "c('aovlist', 'listof')"
</code></pre>
<p>I have tried to use lme() to specify the anova-model with the aim to produce something that TukeyHSD() will accept without success.</p>
<p>Any help would be greatly appreciated!</p>
|
g27063
|
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