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<p>Suppose I have two dependent categorical attributes A, B. I have a dataframe X that lists probabilities (or expected counts) for all combinations of all categories of A and B. Let's assume two categories in each attribute, the dataframe could then look like this:</p>
<pre><code>X <- data.frame(A = c(1,1,2,2), B = 1:2, PROB = c(0.1,0.3,0.2,0.4))
X
</code></pre>
<p>Output:</p>
<pre><code> A B PROB
1 1 1 .1
2 1 2 .3
3 2 1 .2
4 2 2 .4
</code></pre>
<p>Now I would like to add a B column to another dataframe Y that has only an A column. Y exists and has many more rows than X, and also additional columns. A synthetic Y could look like this:</p>
<pre><code>Y <- data.frame(A=sample(2, size=10000, replace=TRUE),
B=NA,
C=sample(5, size=10000, replace=TRUE),
D=sample(3, size=10000, replace=TRUE))
</code></pre>
<p>The contents of the new B column should be sampled at random using the conditional probabilities for B given the value of the A column.</p>
<p>I am new to R, and I was wondering whether this operation can be handled more elegantly than writing a loop that iterates over all A categories. Perhaps a dedicated model class for which <code>predict</code> could be applied? Also, I lack the knowledge of statistical terminology -- I would appreciate any hint on how this kind of imputation (?) is referred to in the literature.</p>
|
g73090
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] |
<p><a href="http://en.wikipedia.org/wiki/Blum_Blum_Shub" rel="nofollow">Wikipedia says</a> that Blum Blum Shub is a pseudorandom generator whose ith value can be computed directly for a given seed. Wikipedia also says that this generator is too slow to be practical for simulation applications.</p>
<p>Is there any standard generator with the direct computation property that is fast enough for Monte Carlo? Is there a reason this cannot exist?</p>
|
g39992
|
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<p>What should I look for when putting together a computer specifically for runnig R and similar programs. A lot of CPU power and RAM are given, but what about such things as an SSD and can R run on the graphics card? (like OpenCL..)</p>
<p>Thanks in advance.</p>
|
g73091
|
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] |
<p>So I'm trying to derive the covariance between $z_t$ and $z_{t-1}$ in the $AR(1)$ model:
$z_t =\phi z_{t-1} + a_t$. Can anyone give me some advice on where to start?</p>
|
g49913
|
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] |
<p>The concentration of impurities in a semiconducter in the production of microprocessors for computer is a normally distributed random variable with mean 127 parts per million and standard deviation 22 parts per million. A semiconducter is acceptable only if its concentration of impurities is below 150 parts per million.</p>
<p>What is the proportion of semiconducters that are acceptable for use?(the area under normal curve for the value of $Z=1.5$ is $0.668$).</p>
|
g73092
|
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] |
<p>Suppose I have a non-linear model, say probit/logit, how can I understand the significance of a coefficient as opposed to the significance of it's marginal effect? Say, I just need to know the <em>importance</em> of a variable, would the former suffice?</p>
|
g73093
|
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] |
<p>What is the difference between knowledge based annotation and corpus based annotation in the context of training a Machine Learning algorithm?</p>
|
g73094
|
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<p>I am designing a study for my project. I wanted to test if music affects reading comprehension. This study will be a between group design. The independent variable is type of music and the dependent variable is the score on a reading comprehension task.</p>
<p>Half of participants will be randomly assigned to a room with classical (soft) music, and the remaining half of participants will be assigned to the room with rock (hard) music.</p>
<p>Would this be a t-test? Then what kind of t-test should I need to use?</p>
<p>Or is this a one way ANOVA?</p>
<ul>
<li>Someone answered my question as to use independent t test and since i have two independent sample, i would need to conduct unpaired test.... I am still a basic statistic student and i am not aware of this unpaired test...</li>
</ul>
<p>Then how could i make simple design? Could anyone explain why do i need to use unpaired t test? and what will happen if i don't?</p>
|
g49914
|
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] |
<p>I have to evaluate a test paper which contains both dichotomous and polytomous items. I am currently using R. But in R IRT models for scoring of dichotomous and polytomous items are different and I have not found any way of combining both type of items so how can I mix both dichotomous and polytomous items into one. Specifically - </p>
<ol>
<li>Is there any programme/function in R that handles both dichotomous and polytomous items </li>
<li>If no direct function can combine both dichotomous and polytomous items in R then is there any indirect way of doing it </li>
<li>If not 1 and 2 then any other open source IRT software which can handle dichotomous and polytomous items together</li>
</ol>
|
g73095
|
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<p>I am trying to build a model for auto rejection of crowd-sourced task (eg: human name transcription of census data). My data set has 5 predictors, and dependent variable is either correct or incorrect. However, there are few issues I have had.</p>
<ol>
<li><p>Data set is unbalanced with ~5% (up to 10% sometimes) of incorrect instances and 95% of correct instances.</p></li>
<li><p>Also, the patterns in predictors for incorrect and correct tasks are similar.</p></li>
</ol>
<p>I tried logistic regression, but it didn't work.
But, it is very important for me to be able to predict those 5% of incorrect tasks since it is very critical.</p>
<p>In such situation what should be the direction to move forward? I would appreciate your help.</p>
<p>Thanks.</p>
|
g73096
|
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] |
<p>Suppose there exists a simple linear equation, where the dependent variable y(time series; measurements available) depends on x1 and x2. If the parameter multiplier of x2 is time dependent and the multiplier of x1 is a deterministic variable. How to find the pdf of the parameter multiplier of x2. Given the time series observations of y, x1 and x2.
Please tell me how to solve this. Kalman/particle filter?</p>
|
g73097
|
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] |
<p>They are both regression methods for discrete dependent variables. </p>
<p>I have a discrete dependent variables like $\{A, B, C, D, E\}$, and $A$, $B$, $C$, $D$, $E$ can be cardinal data(10, 20, 30...) or non-cardinal data(like car, train, and ship).</p>
<p>Which model is proper for each case?</p>
|
g35298
|
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] |
<p>I am attempting to estimate the following model in Stata (the only statistics package I'm familiar with):</p>
<p>$$
Y_{t}=\alpha_{t} + \beta_{t}X_{t}+\varepsilon_{t}
$$
where $X$ and $Y$ are series and $\alpha_{t}$ and $\beta_{t}$ are time-varying parameters defined in state equations:
$$
\alpha_{t}=\alpha_{t-1}+\eta_{1t}
\\
\beta_{t}=\beta_{t-1}+\eta_{2t}
$$
which are assumed to follow a random walk. $\varepsilon$, $\eta_{1t}$, $\eta_{2t}$ are assumed to be gaussian independent white noise.</p>
<p>I am interested in finding the value of $\beta$ over time. The paper from which I am working suggests estimation by the Kalman filter.</p>
<p>I have attempted to understand and implement the <code>sspace</code> function here, but I believe it is incapable of handling the time variation. </p>
<p>Is any of this achievable in Stata 11?</p>
|
g38072
|
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<p>My original model is:
$Y=\alpha(\delta*X_1^{-\rho}+(1-\delta)*X_2^{-\rho})^{-\eta/\rho}exp(e_t)$</p>
<p>Which I partially linearize to:
$ln(Y)=ln(\alpha)-(\eta/\rho)*ln(\delta*X_1^{-\rho}+(1-\delta)*X_2^{-\rho})+e_t$</p>
<p>I've used a nonlinear least squares algorithm to estimate the parameters.</p>
<p>Now, I am trying to determine if the "intercept" in this partly linearized model (in this case $ln(\alpha)$) is different for the different years of data that I have. I have 3 years of data, with about 24 observations in each year.</p>
<p>My first thought is to just add a dummy variable for each year as $ln(\beta*Year)$ and just test if the two coefficients that would result (three years minus one comparison years) are jointly statistically different from zero using an F-test. But I doubt that this would be legit since I am trying to test if one parameter ($ln(\alpha)$) varies over years rather than if all the parameters vary over the years.</p>
<p>My second thought is to just split up the sample by year, run three different regressions, and somehow test if all the $ln(\alpha)$ parameters are different. I don't what test I would use or how I would use it, though, to do this. I'm thinking maybe a t-test with unequal variance on each pair of the coefficients, but I feel like pairwise tests on each parameter does not get me a legitimate "joint" test. I have also read about the Chow test, but again I want to test if just one parameter is different across the subpopulations, not all the parameters, which is what the Chow test does.</p>
<p>Any thoughts on what the right procedure is?</p>
<p>Thanks!</p>
|
g73098
|
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<p>I had just conducted a test where the customer wants to see a 20% improvement in perforation length from a baseline perforator. The baseline perforator has not been tested in the customer's specific conditions in which he will eventually perforate in. </p>
<p>The customer plans to shoot 40,000 perforations in the future. I'm not sure if that bit of information is important but I wanted to be sure that it is understood that the true population mean of perforation length does not exist yet.</p>
<p>Under the specific conditions tailored for the customer the baseline perforator was shot 3 times with the following results: [7.68, 8.72, 8.08] inches.</p>
<p>Three new perforator designs were constructed in hopes to out perform the baseline perforator and each design was shot 3 times with the following results:</p>
<ul>
<li>D1 [8.04, 8.93, 10.05] inches</li>
<li>D2 [11.15, 6.91, 9.21] inches</li>
<li>D3 [7.1, 7.6, 7.02] inches</li>
</ul>
<p>As I am relatively new to statistics I was wondering if some of you professionals can help me out with what information can be gained from these tests results. If you can point me in the right direction as in what methods I should refer to in gaining these insights you suggest would be of much help.</p>
<p>I know that effort is encouraged on my part so I would like to include some of my initial attempts at inferential statistics and maybe you can correct me where I am wrong or include what more I should/can do.</p>
<p>Estimating Sample Size Requirements: Solving for the sample size requires the population standard deviation, $\sigma$. Most often we do not know it so we have to use an estimate or “planning value” in its place. Here are a few options:</p>
<ol>
<li>Estimate σ from previous studies using the same population of interest</li>
<li>Conduct a pilot study to select a preliminary sample. Use the sample standard deviation from the pilot study</li>
<li>Use a judgment or “best guess” for $\sigma$. A common “guess” is the data range (high value – low value) divided by 4</li>
</ol>
<p>The question I asked is: “What minimum sample size is necessary to produce 95% confidence (assuming a normal distribution) that the sample mean is $\pm$ 1 inch of the true population mean, $\mu$?”</p>
<p>Since we do not have an estimate of $\sigma$ from previous studies we will go with option 2 and consider our information as pilot studies.</p>
<p>Test charge Design 2 perforation length data is as follows: [11.15, 9.21, 6.91] inches. The sample mean is 9.09 inches and sample standard deviation is 2.12 inches. How large a sample should be shot to provide a 95% confidence interval with a margin of error (E) of 1 inch, assuming the population standard deviation is equal to the sample standard deviation?</p>
<p>$$n = \frac{(z_{\alpha /2})^2 (\sigma)^2}{E^2}$$</p>
<p>$$n = \frac{(1.96)^2 (2.12)^2}{(1)^2}$$</p>
<p>$$n = 17$$ </p>
<p>Interpretation: To have 95% of our sample means contain the true population mean, $\mu$, we need a sample size of 17 shots. Or, 95 out of 100 tests made up of 17 perforation shots will contain within its average length $\pm$ 1 inch the perforation design’s true average perforation length. </p>
<p>It is not clear to me, however, how to move forward with this result. Does it mean I need to make an additional 17 shots as it's own sample or do I need to make 14 more shots to add to the original 3 shots? How do I handle the new information? I would suspect that the standard error of the mean would narrow with more measurements and would thus adjust the required sample size?</p>
<p>If we do not assume that the population standard deviation is equal to the sample standard deviation we can set the planning value for the population standard deviation as the Range of the perforation lengths we observed divided by 4 (option 3). From there we can estimate the minimum number of shots that should be taken with the margin of error of 1 inch to contain the true population mean 95% of the time.</p>
<p>Test charge Design 2 perforation length data is as follows: [11.15, 9.21, 6.91] inches.</p>
<p>$$\text{Planning Value for Std. Dev.} = \frac{\text{Range}}{4}$$</p>
<p>$$\text{PV} = \frac{(11.15-6.91)}{4} = 1.06$$</p>
<p>$$n = \frac{(z_{\alpha /2})^2 (\sigma)^2}{E^2}$$</p>
<p>$$n = \frac{(1.96)^2 (1.06)^2}{(1)^2}$$</p>
<p>$$n = 4.3$$</p>
<p>Interpretation: To have 95% of our sample means contain the true population mean, $\mu$, we need a sample size of 4 shots. Or, 95 out of 100 tests made up of 4 perforation shots will contain within its average length $\pm$ 1 inch the perforation design’s true average perforation length. </p>
<p>So which would be the more appropriate method (option 2 or 3)? And how should that information be used? In both cases more shots were required. But what does it tell me if the opposite occurs? e.g. for charge Design 3, using both option 2 and 3 method, I got n = 0.37 shots and n = 0.08 shots respectively.</p>
<p>Lastly, I tried to estimate what the %chance that the new charge design's true-population-mean-perforation-length will meet the required improvement. Taking the mean of the baseline shots to be 8.16 inches and adding 20% to it I found the goal length to be $\approx 9.792$ inches. By taking the sample means of each design we see that none of them averaged to meet the required length. However, I found the 95% confidence interval using a t-distribution for Design 2 to be [3.81 to 14.36] inches. Using excel Goal Seek I believe there is a 31% chance that Design 2's true perforation mean length will meet the 9.792 inch requirement. I'm not sure if my method was correct but maybe you can tell me if I am wrong or right or if interested, I will spell out how I went about that estimation.</p>
|
g73099
|
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] |
<p>I would like to generate pairs of random numbers with certain correlation. However, the usual approach of using a linear combination of two normal variables is not valid here, because a linear combination of uniform variables is not any more an uniformly distributed variable. I need the two variables to be uniform.</p>
<p>Any idea on how to generate pairs of uniform variables with a given correlation?</p>
|
g73100
|
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<p>I believe I have quite a simple problem, but want clarification on whether it is the best method to use.</p>
<p>Say I have have insurance line, and the net income (£) from this business for 2011, 2012, 2013 is 1,000,000; 4,500,000; and 5,000,000 respectively.</p>
<p>Hence, the percentage increase from 11-12 is 350%, and from 12-13 is 11.1%.</p>
<p>Now, the average of these is 180.5%, which is a representation of the average percentage increase across all years, but it has been suggested to me to instead represent the data by a “weighted” average.</p>
<p>I am curious… would the weights be the difference in income from each year?</p>
<p>i.e. Weighted Avg. = $((3.5)*350\% + (0.5)*11.1\%)/4 = 307\%$</p>
<p>or would the weights possibly the values themselves? Or maybe there is another option? Maybe a standard average is sufficient?</p>
<p>Thanks very much for your inputs.</p>
|
g35303
|
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<p>In order to verify the assumption of proportional hazards, I plotted the following:
$$\log(-\log(S(t))) = \log(\Lambda(t))$$</p>
<p>If the hazards are indeed proportional for two groups, these curves should be parallel with the vertical distance being the log hazard ratio (which is constant if the proportional hazards assumption holds).</p>
<p>I used the following R code to make such a plot (using the <code>survival</code> and <code>rms</code> packages):</p>
<pre><code>foo <- survfit(Surv(TIME, HADEVENT)~CASE, data=bar)
survplot(foo, loglog=T, xlim=c(0,5*365.25), ylim=c(-10,-2), col=c("red","blue"))
</code></pre>
<p>I obtained the figure shown below for the groups in my study, and I am unsure what to make of it. For small values of $t$ ($t \leq 120$ days), the proportional hazards assumption does not hold at all based on visual inspection. For larger values ($ \gt 1$ year), it seems to be very reasonable. </p>
<p><img src="http://i.stack.imgur.com/RT54b.png" alt="bla"></p>
<p>I also fitted a Cox PH model and used <code>cox.zph</code> to assess the proportionality assumption, with the following results:</p>
<pre><code>foocox <- coxph(Surv(TIME, HADEVENT)~CASE, data=bar)
print(cox.zph(foocox))
rho chisq p
CASE -0.0372 46 1.18e-11
</code></pre>
<p>Based on the $p$-value, I conclude that the null hypothesis of proportionality is strongly rejected. Here is the <code>cox.zph</code> plot, which also doesn't look too promising (e.g. it should be constant):</p>
<p><img src="http://i.stack.imgur.com/Nnm5e.png" alt="coxzph"></p>
<p>Here's a frequency table for my data (<code>CASE=0</code> is a 1:1 matched sample for case <code>CASE=1</code>):</p>
<pre><code>CASE event no event n
0 10.464 93.832 104.296
1 22.903 81.393 104.296
</code></pre>
<p><strong>Edit</strong>: after filtering out very large times -- which were inaccurate -- I obtain a highly significant $p$-value via <code>cox.zph</code>, indicating the proportionality assumption is violated.</p>
<p>What are my options given this situation? Is it justified to continue working with proportional hazards models based on the graph of <code>cox.zph</code> for larger values of $t$? Should I somehow refrain from using them for $t \lt 1$ year based on the visual inspection?</p>
|
g35305
|
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<p>I am writing an algorithm where, given a model, I compute likelihoods for a list of datasets and then need to normalize (to probability) each one of the likelihood. So something like [0.00043, 0.00004, 0.00321] might be converted to may be like [0.2, 0.03, 0.77]. </p>
<p>My problem is that the log likelihoods, I am working with, are quite small (for instance, in log space, the values are like -269647.432, -231444.981 etc). In my C++ code, when I try to add two of them (by taking their exponent) I get an answer of "Inf". I tried to add them in log-space <a href="http://en.wikipedia.org/wiki/List_of_logarithmic_identities#Summation.2Fsubtraction">(Summation/Subtraction of log)</a>, but again stumbled upon the same problem.</p>
<p>Can anybody share his/her expert opinion on this? </p>
|
g35307
|
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] |
<p>I am analysing a diagnostic test (against a gold standard, using a 2x2 table). I want to calculate likelihood ratios (sensitivity / (1-specificity) etc) however I have several sets of data with 0 false positives therefore a specificity of 1....</p>
<p>I have come across other <a href="http://www.aaos.org/research/guidelines/PJIguideline.pdf" rel="nofollow">data</a> (e.g. in evidence bases for clinical guidelines for investigation of periprosthetic infection of hip or knee by AAOS) where I know that the authors had 0 false positives but have still presented confidence intervals for the likelihood ratios.</p>
<p>Does anyone know how they have adjusted their calculations to allow this?</p>
<p>Thanks</p>
|
g73101
|
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] |
<p>I have skewness of -0.5 in the residuals which does not seem to be improve much after using logs/root.
Is this a major concern? Tests relating to homoskedasticity, multicollinearity, outliers all seem fine. Perhaps interpreting the regression using robust standard errors would help..</p>
|
g73102
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<p>I need a closed-form expression for the probability that 2 values drawn at random from a normal distribution are separated by at most T, as a function of T and the variance of the distribution. I can formulate the problem as an integration, but can't solve it. I'd be happy with a well-motivated approximation. I'd be amenable to making some simplifying assumptions about the distribution, if that would help.</p>
|
g73103
|
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] |
<p>A random sample of size <code>n = 40</code> is taken. Conduct a goodness of fit test to see whether this sample appears to have been selected from a normal distribution. The number of intervals for the sample data is equal to:</p>
<pre><code>4
5
8
10
20
</code></pre>
<p>How do you calculate this?</p>
|
g73104
|
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] |
<p>For the following model:</p>
<p>$$T = A_0 + A_1M+ A_2M^2 + A_3\ln(P) + A_4\ln(P)^2+A_5M\ln(P)$$</p>
<p>where:</p>
<blockquote>
<p>$T$ = Dependent variable </p>
<p>$P$ = Independent variable </p>
<p>$M$ = Independent variable</p>
<p>$A_0 \dots A_5$ = Coefficients of the regression.</p>
</blockquote>
<p>I would like to know which class of regression model this equation corresponds to, when you use this kind of model, and how you find the parameters $A_0 \dots A_n$.</p>
|
g35312
|
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<p><strong>Background:</strong> Although <a href="http://en.wikipedia.org/wiki/Correspondence_analysis" rel="nofollow">correspondence analysis</a> is used mainly for <a href="http://www.datavis.ca/courses/grcat/grc5.html#H2_82%3aExample%3a" rel="nofollow">visualizing similarities of categories of two or more nominal variables</a>, I tried following: 39 students (from the same survey as in <a href="http://stats.stackexchange.com/questions/61215/how-to-correctly-interpret-group-differences-with-this-pca-plot">this question</a>) were asked to ask their friends about smoking habits with four possible responses (I do smoke; I used to, but I do not anymore; I have tried and I have not even tried).</p>
<p>Then I created matrix with two columns: First is nominal variable with 39 categories (my students, in further labeled by numbers) and second one is also nominal with 4 categories (smoking levels). This data were used as an input into correspondence analysis and resulting plot can be seen below.</p>
<p><strong>Questions:</strong> I am not sure about some interpretations of the plot.</p>
<ul>
<li>Can we say something about frequencies of categories of second (smoking) variable? It looks for example that there is higher number of respondents near the category "I have tried". Does it mean that most of participants have only tried smoking?</li>
<li>If two respondents are close together (for example 6 and 18), does it mean that their friends have similar smoking "behavior"?</li>
<li>Where in the map are for example those respondents whose friends mostly used to smoke, but they do not anymore? Are they those who are near the label "I used to, but I do not anymore" (respondents 3, 22, ...) or those whose label has similar angle with x -axis as label "I used to, but I do not anymore" (respondents 3, 22, 30, 29, 10, 21, ...) or those whose projection to any axis is similar as projection of label "I used to, but I do not anymore" (respondents 5, 8, 2, 25 when projected to x - axis)?</li>
<li>Does the plot below say something about the degree of dependence between two variables? How should plot below look like if variables were independent?</li>
</ul>
<p><img src="http://i.stack.imgur.com/zpFUe.jpg" alt="Correspondence analysis"></p>
|
g73105
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<p>Some adapative test systems (e.g. school assessment tools) use the 1pl IRT model, while others use the 2pl or the 3pl. When developing an adaptive IQ test, is there a rule of thumb about which model to choose in calibrating the item difficulty and test takers ability? </p>
<p>I can't find any research that gives some insights in fit between IQ test items and different kinds of IRT models.</p>
<p>Many thanks in advance!</p>
|
g35315
|
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<p>So I have data that has been quantized by an analogue to digital converter. (continuous data has been turned into discrete data and the values range from 0 to the saturation value , which is 127 in this case). </p>
<p>This particular instrument I used to gather the data is quite noisy, let's say there is added Gaussian noise to the real value. Luckily, when taking single measurements, I have enough time to take multiple measurements and average them to reduce the noise. Note that sampling rate is not an issue here since the thing that I'm taking measurements of is completely stable. </p>
<p>Obviously , taking the simple mean will produce a biased result because values cannot exceed 0 or 127 (for example, if you attempt to use a plain old averaging on something with a "real" value of 126, you will get an estimated value that is less than 126. This is because the added Gaussian noise will not give you any value higher than 127 because of the truncation). So how do I take the average so the result will give me an unbiased estimator of the real value? </p>
|
g46638
|
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] |
<p>In a paper by <a href="http://www.ncbi.nlm.nih.gov/pubmed/23628224" rel="nofollow">Faraklas et al</a>, the researchers create a Necrotizing Soft-Tissue Infection Mortality Risk Calculator. They use logistic regression to create a model with mortality from necrotizing soft-tissue infection as the main outcome and then calculate the area under the curve (AUC). They use the bootstrap method to find the "bootstrap optimism-corrected ROC area."</p>
<p>If I were to do this in <code>R</code>, how would it look like? The code I have been toying with looks something like below:</p>
<pre><code>library(boot)
library(ROCR)
auc_calc <- function(data, indices, outcomes) {
d <- data[indices,]
# Using glm for logistic regression
# Do I recreate the glm model for each dataset?
fit <- glm(outcomes[indices,] ~ X1 + X2 + X3, data=d, family=binomial)
fit.predict <- predict(fit, type="response")
# Using ROCR to calculate AUC
pred <- prediction(fit.predict, outcomes[indices,])
perf <- performance(pred, "auc")
# Returning the AUC
return([email protected][[1]])
}
boot.results <- boot(data=my.data, statistic=auc_calc, R=10000, outcomes=my.outcomes)
</code></pre>
<p>Is this correct? Or am I doing something wrong - namely should I be passing in a glm model rather than recalculating it each time? As always thanks for the help.</p>
|
g35318
|
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] |
<p>This question is kind of a follow up of another question I had: <a href="http://stats.stackexchange.com/questions/73830/asymptotic-normal-distribution-via-the-central-limit-theorem">Asymptotic normal distribution via the central limit theorem</a></p>
<p>There I had to calculate the estimator for $p$ (meaning $p$ for success) and approximate it's distribution by approximation with a normal distribution.</p>
<p>Now I would like to get the exact distribution of $p$.</p>
<p>I got already the following hint: "You have the functional form of $\hat{p}$. Look up how we derive the distribution of a function of a discrete random variable." Unfortunately that did not lead me to a solution...</p>
|
g73106
|
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<p>I would like to compare 2 different classifiers for a multiclass text classification problem that use large training datasets. I am doubting whether I should use ROC curves or learning curves to compare the 2 classifiers.</p>
<p>On one hand, learning curves are useful for deciding the size of the training dataset, since you can find the size of the dataset at which the classifier stops learning (and maybe degrades). So the best classifier in this case might be the one reaching the highest accuracy with the smallest dataset size.</p>
<p>On the other hand, ROC curves let you find a point with the right trade-off between between sensitivity/specificity. The best classifier in this case is just the one closer to the top-left part, with the highest TPR for any FPR. </p>
<p>Should I use both evaluation methods? Is it possible for a method with a better learning curve to have a worse ROC curve, and vice-versa?</p>
|
g73107
|
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<p>I am looking for a robust version of Hotelling's $T^2$ test for the mean of a vector. As data, I have a $m\ \times\ n$ matrix, $X$, each row an i.i.d. sample of an $n$-dimensional RV, $x$. The null hypothesis I wish to test is $E[x] = \mu$, where $\mu$ is a fixed $n$-dimensional vector. The classical Hotelling test appears to be susceptible to non-normality in the distribution of $x$ (just as the 1-d analogue, the Student t-test is susceptible to skew and kurtosis). </p>
<p>what is the state of the art robust version of this test? I am looking for something relatively fast and conceptually simple. There was a paper in COMPSTAT 2008 on the topic, but I do not have access to the proceedings. Any help? </p>
|
g73108
|
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<p>I have a dataset that contains ~7,500 blood tests from ~2,500 individuals. I'm trying to find out if variability in the blood tests increases or decreases with the time between two tests. For example - I draw your blood for the baseline test, then immediately draw a second sample. Six months later, I draw another sample. One might expect the difference between the baseline and the immediate repeat tests to be smaller than the difference between the baseline and the six-month test.</p>
<p>Each point on the plot below reflects the difference between two tests. X is the number of days between two tests; Y is the size of the difference between the two tests. As you can see, tests aren't evenly distributed along X - the study wasn't designed to address this question, really. Because the points are so heavily stacked at the mean, I've included 95% (blue) and 99% (red) quantile lines, based on 28-day windows. These are obviously pulled around by the more extreme points, but you get the idea.</p>
<p><img src="http://a.imageshack.us/img175/6595/diffsbydays.png" alt="alt text"></p>
<p>It looks to me like the variability is fairly stable. If anything, it's higher when the test is repeated within a short period - that's terribly counterintuitive. How can I address this in a systematic way, accounting for varying n at each time point (and some periods with no tests at all)? Your ideas are greatly appreciated.</p>
<p>Just for reference, this is the distribution of the number of days between test and retest:</p>
<p><img src="http://a.imageshack.us/img697/6572/testsateachtimepoint.png" alt="alt text"></p>
|
g73109
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] |
<p>I am having some problems figuring out what distribution my data best fits into.</p>
<p>My data is from a 100 mm visual analogue scale, so data points range from 0 to 100.</p>
<p>Participants were asked to score an animal's 'lameness' using these scales. There were 4 animals, all with varying severity of lameness. </p>
<p>Am I correct in assuming my data could be considered:
1. Continuous - as it's measured on a continuous scale
OR
2. Binomial (with 100 binomial totals) as something either did or did not happen at each point on the scale</p>
<p>I am using a GLMM to make my model. I have run the data through using gamma (had to recode my zero values), Poisson, and binomial. And bar eye balling the results on a bar chart of the data, I have no idea which is correct.</p>
|
g73110
|
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<p>I'm using a genetic algorithm (GA) to estimate the minimum value of a likelihood function $L[x]$ which is too complicated to evaluate mathematically. This likelihood function quantifies the goodness of fit between a model (which depends on the $x$ parameter) and a set of $M$ observations $O=\{a_1, a_2, ..., a_M\}$.</p>
<p>After enough iterations (when the optimal value found by the GA hasn't changed for a while) I stop the GA and assume the value $x_0$ for the model parameter $x$ it settled on, is one that satisfies:</p>
<p>$$L[x_0] \sim min(L[x])$$</p>
<p>which identifies the "best" model/observation fit. </p>
<p>Now, I want to assign an uncertainty to this $x_0$ value for which I apply a bootstrap process with replacement. This means I run the GA again a number $N$ of times (each time using a random sample of $M$ observations taken from $O$) which results in $N$ values for the $x$ parameter: $(x_1, x_2, ..., x_N)$. </p>
<p>Finally I assign the standard deviation of the $N$ values returned by the GA as the uncertainty (error) of $x_0$:</p>
<p>$$e_{x_0} = std(x_1, x_2, ..., x_N)$$</p>
<p>This process works fine, but since I am forced to run the GA a large $N$ number of times, this can quickly become unmanageable in computational time.</p>
<p>The question is: is there a faster/computationally cheaper way of assigning uncertainty to a parameter value estimated through a genetic algorithm?</p>
|
g3415
|
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<p>I am trying to compare readings from an old flowmeter and a new digital flowmeter to find out if they are significantly different. With the new meter I did readings under different conditions eg. calibrated at 30 seconds, calibrated at 60 seconds, uncalibrated at 30 seconds and uncalibrated at 60 seconds. I want to compare my old flowmeter (first column on dataset) to the other readings (columns 2:5 on dataset). I used anova to compare the groups and found some differences but I am stuck with TukeyHSD...My question is: Is this the correct way to do the comparisons...I would appreciate some advice on how to accomplish this task...Here is my dataset and code....</p>
<pre><code> meter <- structure(list(SiteNumber = structure(c(1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L), .Label = c("site1",
"site2", "site3", "site4"), class = "factor"), old_dev = c(2.09,
1.927, 2.11, 2.114, 2.11, 1.995, 2.605, 2.563, 2.393, 2.286,
2.529, 2.371, 2.214, 2.128, 2.302, 2.204, 2.274, 3.513, 2.61,
3.502, 3.155, 3.131, 3.55, 3.656, 3.666, 3.618, 3.023, 3.226,
3.649, 3.519, 3.322, 3.352, 3.323, 3.144, 2.869, 3.383, 3.076,
2.978, 3.189, 2.934, 2.813, 3.015, 3.014, 3.056, 2.952, 2.988,
2.976, 3.049, 2.869, 2.965, 2.895, 2.064, 1.333, 1.432, 1.599,
1.52, 1.51, 2.734, 2.182, 2.71, 2.488, 2.242, 1.998, 1.175, 1.791,
2.152, 3.414, 3.278), new_dev_unc30 = c(2.6, 2.6, 2.7, 2.6, 2.3,
2.6, 3.2, 2.9, 2.1, 2.8, 1.8, 2.6, 2.5, 1.4, 2.7, 2.6, 2.2, 4.1,
3.4, 3.7, 4, 4, 4.5, 4.5, 1.7, 2.9, 2.4, 2.9, 3.7, 3.3, 4, 1.7,
3.5, 1.9, 3.3, 4.1, 3.7, 4, 3.6, 2, 2.4, 3.7, 2, 2.8, 3, 1.8,
1.8, 3, 1.9, 3.1, 1.1, 2.2, 1.6, 1.2, 1.4, 1.3, 1.4, 2, 1.9,
1.4, 0.7, 2.1, 1.2, 1.8, 1.3, 1.2, 0.8, 2.5), new_dev_unc60 = c(2.7,
2.2, 2.6, 2.3, 2.7, 2.4, 3.1, 2.8, 2.3, 2.9, 1.8, 2.4, 2.6, 1.3,
2.7, 2.6, 2.2, 4.1, 3.8, 3.9, 4.5, 4, 4.2, 4.6, 2, 2.6, 2.6,
3, 3.4, 3.5, 3.9, 2, 3.4, 2.3, 3.3, 4.2, 3.7, 3.9, 3.5, 2.1,
2.4, 3.1, 2.1, 3, 3.2, 1.9, 1.9, 3, 2.1, 3.1, 1.3, 1.5, 1.6,
1.2, 1.8, 1.1, 1.2, 2.1, 2, 1.4, 0.8, 1.9, 1.1, 0.9, 1.4, 1.5,
0.8, 2), new_dev_cal30 = c(2.4, 2.5, 2.5, 2.8, 2.4, 2.3, 3.1,
2.6, 2, 3.5, 1.6, 2.5, 2.5, 1.7, 2.9, 2.5, 2.4, 4.5, 3.3, 4.3,
4.3, 4.3, 4.4, 4.5, 1.1, 1.9, 4, 3.5, 3.1, 3.8, 3.5, 2.2, 3.5,
2, 3.6, 3.7, 4, 3.5, 3.8, 2.4, 2.7, 3.3, 2.7, 2.3, 3.2, 2.3,
0.9, 3.2, 2.9, 3.1, 0.9, 2.3, 1.3, 1.4, 1.5, 1.1, 1.3, 2.7, 1.7,
2.1, 0.7, 1.9, 1.2, 1, 1.6, 1.1, 1.4, 1.6), new_dev_cal60 = c(2.6,
2.5, 2.4, 2.3, 2.5, 2.3, 3.2, 2.8, 1.9, 3.1, 2.1, 2.7, 2.4, 1.8,
2.7, 2.6, 2.3, 4.3, 3.5, 4.3, 4.3, 4.3, 3.8, 4.4, 1.4, 2, 4.2,
3.3, 3.2, 3.3, 3.4, 2.1, 3.4, 2.5, 3.8, 3.8, 3.9, 3.6, 3.5, 2.4,
2.9, 3.1, 2.3, 2.6, 3.1, 2.2, 0.8, 3.2, 2.6, 3.1, 0.9, 1.7, 1.2,
1.5, 1.2, 1, 1.1, 2.6, 1.6, 1.9, 0.6, 2.3, 1.4, 1.2, 1.5, 1.2,
1.4, 1.4)), .Names = c("SiteNumber", "old_dev", "new_dev_unc30",
"new_dev_unc60", "new_dev_cal30", "new_dev_cal60"), class = "data.frame", row.names = c(NA,
-68L))
</code></pre>
<p>Here is what I did:</p>
<pre><code>str(meter)
attach(meter)
boxplot(list(old_dev,new_dev_unc30,new_dev_unc60,new_dev_cal30,new_dev_cal60))
summary(firsttest <- aov(old_dev ~ new_dev_unc30 + new_dev_unc60 + new_dev_cal30 + new_dev_cal60 ))
plot(firsttest)
TukeyHSD(??????)
</code></pre>
|
g73111
|
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<p>Just a simple question on parameter selection for SVMs. If I use a minimum finding algorithm to find the optimal parameters for a set of data, how do I "average" the parameters over a set of cross validation runs to come up with the best parameters for my test set run? When doing X-fold cross validation, I can see simply averaging the fit of the model for each parameters set, but not sure how to do it with a minimum finding algo.</p>
<p>Thanks</p>
|
g35331
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<p><em>(ignore the R code if needed, as my main question is language-independent)</em></p>
<p>If I want to look at the variability of a simple statistic (ex: mean), I know I can do it via theory like:</p>
<pre><code>x = rnorm(50)
# Estimate standard error from theory
summary(lm(x~1))
# same as...
sd(x) / sqrt(length(x))
</code></pre>
<p>or with the bootstrap like:</p>
<pre><code>library(boot)
# Estimate standard error from bootstrap
(x.bs = boot(x, function(x, inds) mean(x[inds]), 1000))
# which is simply the standard *deviation* of the bootstrap distribution...
sd(x.bs$t)
</code></pre>
<hr>
<p>However, what I'm wondering is, <strong>can it be useful/valid(?) to look to the standard <em>error</em> of a bootstrap distribution in certain situations?</strong> The situation I'm dealing with is a relatively noisy nonlinear function, such as:</p>
<pre><code># Simulate dataset
set.seed(12345)
n = 100
x = runif(n, 0, 20)
y = SSasymp(x, 5, 1, -1) + rnorm(n, sd=2)
dat = data.frame(x, y)
</code></pre>
<p>Here the model doesn't even converge using the original data set, </p>
<pre><code>> (fit = nls(y ~ SSasymp(x, Asym, R0, lrc), dat))
Error in numericDeriv(form[[3L]], names(ind), env) :
Missing value or an infinity produced when evaluating the model
</code></pre>
<p>so the statistics I'm interested in instead are more <em>stabilized</em> estimates of these nls parameters - perhaps their means across a number of bootstrap replications.</p>
<pre><code># Obtain mean bootstrap nls parameter estimates
fit.bs = boot(dat, function(dat, inds)
tryCatch(coef(nls(y ~ SSasymp(x, Asym, R0, lrc), dat[inds, ])),
error=function(e) c(NA, NA, NA)), 100)
pars = colMeans(fit.bs$t, na.rm=T)
</code></pre>
<p>Here these are, indeed, in the ball park of what I used to simulate the original data:</p>
<pre><code>> pars
[1] 5.606190 1.859591 -1.390816
</code></pre>
<p>A plotted version looks like:</p>
<pre><code># Plot
with(dat, plot(x, y))
newx = seq(min(x), max(x), len=100)
lines(newx, SSasymp(newx, pars[1], pars[2], pars[3]))
lines(newx, SSasymp(newx, 5, 1, -1), col='red')
legend('bottomright', c('Actual', 'Predicted'), bty='n', lty=1, col=2:1)
</code></pre>
<p><img src="http://i.stack.imgur.com/xHyqE.png" alt="enter image description here"></p>
<p>Now, if I want the variability of these <em>stabilized</em> parameter estimates, I think I can, assuming normality of this bootstrap distribution, just calculate their standard errors:</p>
<pre><code>> apply(fit.bs$t, 2, function(x) sd(x, na.rm=T) / sqrt(length(na.omit(x))))
[1] 0.08369921 0.17230957 0.08386824
</code></pre>
<p><strong>Is this a sensible approach? Is there a better general approach to inference on the parameters of unstable nonlinear models like this?</strong> (I suppose I could instead do a second layer of resampling here, instead of relying on theory for the last bit, but that might take a lot of time depending on the model. Even still, I'm not sure if these standard errors would be useful for anything, since they would approach 0 if I just increase the number of bootstrap replications.)</p>
<p>Many thanks, and, by the way, I'm an engineer so please forgive me being a relative novice around here.</p>
|
g46656
|
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<p>I'm trying to solve this problem out loud. I'm not great at statistics but I try sometimes to understand where things are and where they're going.</p>
<p>I'm trying to figure out the best method to compare the two following datasets. The first is the actual observation and the second is of what my sensor determined the value was. Basically an object travels across the sensor that with properties. Each object can have anywhere from 2 to 5 components. We know the exact value of each one of those components. </p>
<p>The big table below shows the data results from running those objects on the sensor. Observations are independent so observation 5 has no affect on observation 26. The dataset has 31 objects in it, and each object was measure using the sensor. We know the exact properties of the object and I put it under "Actual"</p>
<p><strong>Note:</strong></p>
<p>Total = 1 + 2 + 3 + 4 + 5</p>
<p>All what I'm trying to figure out is if the sensor was adequate or does it need further calibration? The old way of doing things was to get an average difference less than 5% to be acceptable. I don't agree with that methodology as I believe it's prone to error and does not capture the essence of measurements. So therefore, I'm investigating better data analysis tools for the problem.</p>
<p><strong>Hypotheses:</strong></p>
<ol>
<li>"Is the sensor performing adequately?"</li>
<li>Is there an overall statistical difference between Actual and Sensor values?</li>
<li>Is there a statistical difference between each observed pair?</li>
<li>At which point is the significance broken? i.e. at which confidence interval do the two datasets become different?</li>
</ol>
<p><strong>Analysis:</strong></p>
<p>The first thing I did was to compare the average differences for each column. I also did the mean of the absolute differences and here are the results:</p>
<pre><code> Difference between Actual and Sensor (%)
Total 1 2 3 4 5
Mean of Diff 1.06 2.80 -4.00 7.12 -10.86 17.01
Mean of abs diff 7.31 6.96 7.56 8.52 0.70 1.10
</code></pre>
<p>These numbers don't tell me much really but they show somewhat of a relevant comparison. I then proceeded to do a two paired t-test using alpha = 0.05 with the following results:</p>
<pre><code> df Mean Actual Mean Sensor Var Actual Var Sensor pearson t stat P 1 tail t Crit 1 tail P 2 tail t Crit 2 tail
Total 30 37,858 89,829,589 89,829,589 77,766,451 0.9463 1.4871 0.0737 1.6973 0.1474 2.0423
1 30 5,411.61 5,261 254,000 407,118 0.7829 2.1076 0.0218 1.6973 0.0435 2.0423
2 30 15,246 15,719 4,762,169 3,878,279 0.7845 -1.9103 0.0328 1.6973 0.0657 2.0423
3 27 17,943 15,396 40,196,438 33,216,653 0.4268 2.0742 0.0239 1.7033 0.0477 2.0518
4 1 6,770.00 7,600 14,257,800 20,480,000 1.0000 -1.5661 0.1809 6.3138 0.3618 12.7062
5 1 5,910.00 4,900 64,800 0.00 N/A 5.6108 0.0561 6.3138 0.1123 12.7062
</code></pre>
<p>I basically concluded that the means are not significantly different for "Total", "", "4", and "5". Am I correct on the analysis? </p>
<p>I then did an F test analysis for two means to compare those results. Note that I wasn't sure if I needed to do the F-test but I did it to compare the variance. I concluded that according to the F test, it appears that my variance is high on all accounts that the results are statistically significant.</p>
<pre><code> F P 1 tail F Crit 1 tail
Total 1.1551 0.3477 1.8409
1 0.6239 0.1011 0.5432
2 1.2279 0.2887 1.8409
3 1.0299 0.4698 1.9048
4 0.6962 0.4427 0.0062
5 65,535 N/A 161.4476
</code></pre>
<p><strong>Data Table</strong></p>
<pre><code> Actual Sensor
Observation Total 1 2 3 4 5 Total 1 2 3 4 5
1 36820 5860 14840 16120 36200 5500 15900 14800
2 42530 5160 12000 9840 9440 6090 43300 5200 13100 9200 10800 4900
3 48650 4770 18260 25620 52000 4700 18300 29000
4 42290 5020 16080 21190 48800 5600 18400 24800
5 40530 5350 15670 19510 37800 4800 15300 17700
6 41610 5140 16000 20470 41500 5700 17100 18700
7 35210 5310 15150 14750 34000 5100 15600 13300
8 36150 5430 15520 15200 33600 4900 15400 13300
9 17600 6770 10830 19300 6600 12800
10 35920 5280 15540 15100 28700 4700 13000 11000
11 37900 5740 15440 16720 35100 5500 14700 14900
12 41530 5590 16560 19380 39300 5400 16600 17200
13 33580 5330 14870 13380 33400 5100 14800 13500
14 25550 4990 13450 7110 24600 4800 13000 6800
15 45920 5420 16200 24300 43300 5100 15800 22400
16 17750 5740 12010 21700 6500 15200
17 29570 5230 14140 10200 28800 4600 14600 9600
18 44870 5150 16990 22730 47500 5600 18900 23000
19 35500 5780 14930 14790 32200 5600 14200 12500
20 54070 5310 17170 31590 50100 5000 16700 28300
21 35440 4590 13920 16930 35000 3900 14400 16600
22 40680 5330 12840 12680 4100 5730 40000 5400 13400 11900 4400 4900
23 16540 7160 9380 20200 6900 13300
24 47820 4960 17480 25380 47100 4700 18100 24300
25 39410 5350 18070 15990 42100 5900 20700 15500
26 40790 5470 16480 18840 36400 5000 15700 15700
27 31760 5480 14570 11710 33700 5900 16200 11600
28 33000 5090 14760 13150 30900 4800 14600 11500
29 49390 5350 18110 25930 45500 4900 18100 22400
30 54290 5110 17540 31640 48800 4800 16700 27300 20900
31 40930 5500 17850 17580 37300 4900 16700 15700
</code></pre>
|
g73112
|
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] |
<p>I've been reading some materials on Spatial data analysis, and I've a good background in GLMs. Right now I'm looking to find an example in spatial generalized linear models, but so far I've not found any. I'm aware of some packages in R such as GeoR. etc. but couldn't find a concrete example that includes codes, data, and analysis. </p>
<p>I was wondering if anyone can help. Please share links or papers.</p>
<p>Thanks!</p>
|
g73113
|
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<p>Its an interview question..</p>
<p>Initially there are n white balls. Each day you are allowed to take a ball. If the ball in hand is white, replace it by red ball. If it is red in color, put that ball into bag without doing anything. The question is to find the probability to have k red balls after d days.Give the general solution</p>
<p>I started with making a binary tree.. initially on 1st day we have n white balls, when we pick 1 ball and apply the rule we get 1 red ball and (n-1) white balls on second day pick 1 ball, it could be white or red. if we pick white we are left with 2red and (n-2) white balls otherwise 1 red and (n-1) white balls. these two nodes again will each have two children each for the 3rd day.. 1 with 3 red balls and (n-3) white balls , other with 2 red balls and (n-2)white balls and so on</p>
<p>But this is a direct recursive formula, is there a better solution? I think it can be solved with dynamic programming, but I am unable to connect dynamic programming with probability. any idea how to do this ?</p>
<p>Also can someone help me with how the probability will be calculated in this question?</p>
<p>Last, Can someone give me a good resource to study probability based programming questions?</p>
|
g73114
|
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<p>I'm trying to use an inverse hyperbolic sine transformation to reduce the effect of outliers in my target variable. Unfortunately, I don't appear to have access to the basic papers on it. I've found the formulation but am not sure how to estimate the theta parameter for it. Does anyone know?</p>
<p>Thanks</p>
|
g73115
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] |
<p>Then I fit linear models to the <code>plot(n_clust, error)</code> aiming to identify the best combination of I'm trying to perform a k-means cluster on my data (matrix with 2000 cases and 10 variables). I don't know how many clusters should I choose. To solve this problem, I adopted a strategy in which different values of K are setted. Error results and the number of used clusters are stored in two vectors.</p>
<p>Then I fitted linear models that gives me the highest sum R-squared.
I used this strategy to choose de best K value. The point is that I have performed this process several times, noting that error vector varied between each run. This gave me different values of best K. An alternative to make k-means results "stable" is the use of <code>set.seed()</code> function prior <code>kmean()</code>. However I'm afraid that the result, despite fixed, have no consistency.
Somebody could give me some "clues"? <code>set.seed()</code> will not just hind a variability? Is there another strategy for choosing the best K?</p>
<p>Thanks!</p>
<pre><code>n_clust=NULL
error=NULL
for(i in 1:200){
cl <- kmeans(scores, i, iter.max=100)
erro <- c(error,cl$tot.withinss)
n_clust <- c(n_clust,i)
}
r2=NULL
for(i in 3:197){
a <- lm(error[1:i] ~ n_clust[1:i])
b <- lm(error[i+1:200] ~ n_clust[i+1:200])
rsqd <- as.numeric(summary.lm(a)[8]) + as.numeric(summary.lm(b)[8])
r2 <- c(r2, rsqd)}
id_n <- 3 + which(r2==max(r2))
</code></pre>
|
g35334
|
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] |
<p>I have created a linear model (which has multiple predictors) using the lm() function and I would like to interpret the "coefficients" that I get when I use the summary() function on the linear model. <br><br>Now I want to consider how the coefficients reflect on the predictors' influence in the model - am I right in thinking that a large value for the coefficient means that the corresponding predictor has a greater effect? I'm not sure what else I need to consider or if I'm even thinking along the right lines.<br><br>Also, am I correct in thinking these "coefficients" are in fact the Beta coefficients?</p>
|
g35336
|
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<p>I am working with an anaerobic treatment plant where I have got main 3 variables, gas production (l/d), flow rate (l/h) and COD influent (g/l). if I want to do multiple l.regression, is it necessary to standardize (gas ~ flow+ COD) the variables?</p>
|
g49325
|
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] |
<p>I am doing multiple regression with Gas production (l/d) as response variable, and flow rate (l/h) and COD influent (g/l) as explanatory variables in R. I made two models. </p>
<pre><code>mod1 <- gas ~ flow + COD
r^2 = 0.64
f stat= 56.62(2,64) with 0.0000.... p value.
mod2 <- gas ~ flow*COD
r^2 = 0.81
f stat = 89.14 (3,63) with also very low p value.
</code></pre>
<p>Now for both cases, what the r^2 says and the f stat says?
I did the anova test of the both models. how to interpret them? </p>
<pre><code>Model 1: Gas ~ Flow + CODin
Model 2: Gas ~ Flow * CODin
Res.Df RSS Df Sum of Sq F Pr(>F)
1 64 24307
2 63 12835 1 11472 56.311 2.631e-10 ***
</code></pre>
|
g35338
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<p>Let's say I'm using the <code>Sonar</code> data and I'd like to make a hold-out validation in R. I partitioned the data using the <code>createFolds</code> from <code>caret</code> package as <code>folds <- createFolds(mydata$Class, k=5)</code>.</p>
<p>I would like then to use exactly the fold <code>mydata[i]</code> as test data and train a classifier using <code>mydata[-i]</code> as train data. </p>
<p>My first thought was to use the <code>train</code> function, but I couldn't find any support for hold-out validation. I mean, I don't want to partition my data and then test all the combinations for estimating the mean accuracy, I want to train it only once. Am I missing something here?</p>
<p>Also, I'd like to be able to use exactly the pre-defined folds as parameter, instead of letting the function partition the data. Does anyone have any thoughts?</p>
<p>Thanks in advance</p>
|
g35339
|
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<p>I am trying to use the package ‘fitdistrplus’ in R to fit one non standard distribution to my data set. I am trying to copy the methods the package creators used in their tutorial for specifying a Gumbel distribution but unfortunately I am not able to do it. </p>
<p>(The package documentation can be found in this <a href="http://databaser.net/moniwiki/pds/_ed_99_95_eb_a5_a0_eb_b6_84_ed_8f_ac_ec_a0_81_ed_95_a9_ec_84_b1/fitdistrplus.pdf" rel="nofollow">pdf</a>.) </p>
<p>So my problem is that I have my CDF function and my density function which are not standard : </p>
<p>$ \begin{align*}
H_{G}(x)&=\frac{1}{P(1)}\left[ \frac{\Phi^{3}\left( \frac{x-\mu}{\sigma}\right)}{6}-\frac{\delta}{2} \Phi^{2}\left( \frac{x-\mu}{\sigma}\right)+\left( \frac{\delta^{2}}{2} + \beta\right) \Phi\left( \frac{x-\mu}{\sigma}\right)\right]\\
h_{G}(x)&= \frac{1}{\sigma P(1)}\left[ \frac{\left[ \Phi^{2}\left( \frac{x-\mu}{\sigma}\right)\right] }{2}-\delta \Phi\left( \frac{x-\mu}{\sigma}\right)+\left( \frac{\delta^{2}}{2} + \beta\right) \right] \phi\left( \frac{x-\mu}{\sigma}\right)
\end{align*}$ </p>
<p>with $ P(1)= \left[ \frac{1}{6}-\frac{\delta}{2}+\left( \frac{\delta^{2}}{2} + \beta\right) x\right] $ and
\begin{equation*}
\Phi(\dfrac{x-\mu}{\sigma}) =\frac{1}{\sqrt{2\pi}}\int^{x}_{-\infty}e^{-\frac{\left(t-\mu\right) ^{2}}{2\sigma^{2}}}dt
\qquad \text{and} \qquad
\phi(\dfrac{x-\mu}{\sigma}) =\frac{1}{\sqrt{2\pi}}e^{-\frac{\left(x-\mu\right) ^{2}}{2\sigma^{2}}}.
\end{equation*}</p>
<p>And here is some of my code:</p>
<pre><code>###### I define my density as in the gumbel ######
ds <- function(u,a,e,mu,sigma){
P = function(a,e){ (( (1/6)*(1^3) ) - ((a/2)*(1^2)) + (((((a)^2)/2) + e)*1)) }
D = function(u,mu,sigma){ (1/((sigma)*sqrt(2*pi)))*exp(-(((u-mu)^2)/(2*(sigma^2)))) }
K = function(u,a,e){ (((1/2)*(u^2))- (a*u) +(((a^2)/2)+e)) }
H = function(u,mu,sigma){ pnorm(u,mu,sigma) }
Fprim = function(u,a,e,mu,sigma){ (1/P(a,e))*(D(u,mu,sigma))*(K(H(u,mu,sigma),a,e)) }
return(Fprim)
}
###### I define my CDF function as in the gumbel ######
ps <- function(u,a,e,mu,sigma) {
S = function(u) (((1/6)*(u^3)) - ((a/2)*(u^2)) +
( ((((a)^2)/2)+e)*u))/(((1/6)*(1^3)) - ((a/2)*(1^2)) +
(((((a)^2)/2)+e)*1))
cdf = S(pnorm(u, mu, sigma))
return(cdf)
}
###### I define my quantile function as in the gumbel ######
qs <- function(u,a,e,mu,sigma) optimize(function(z) (ps(z)-u)^2, c(-10,10))$minimum
###### The MLE estimation using fitdist and mledist ######
fgu <- fitdist(X, "s", start=list(a=0.035, e=0.005, mu=-0.52, sigma=1))
mledist(X, "s", start=list(a=0.035, e=0.005, mu=-0.52, sigma=1))
</code></pre>
|
g73116
|
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] |
<p>I have two variables each of which have three levels (low, medium & high). I would like to be able to test whether there is a significant trend between the two variables i.e. as x goes up y goes up. The trend tests I've looked at all seem to have one variable with 2 levels and the other with n levels.</p>
<p>Here is an example of the frequency table of my data:</p>
<pre><code>mat <- structure(c(20, 19, 6, 10, 22, 4, 0, 12, 4), .Dim = c(3L, 3L), .Dimnames = list(
c("low_1", "medium_1", "high_1"), c("low_2", "medium_2", "high_2")))
</code></pre>
<p>If there was a function for it in R that would be useful.</p>
|
g44987
|
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] |
<p>After removing 25% (21 observations) of the sample as a holdout, model selection on the original 75% of the a sample led to a six variable multiple linear regression with R2 of 54%.</p>
<p>A simple regression of the holdout values on their predictions under the fitted model led to an R2 of 8% and and adjusted R2 of 2%. Regression slope parameter was non-significant.</p>
<p>Can anyone think of an interpretation other than that there is potentially a serious overfitting issue here, enough that the original six-variable model is in question? Was there a better way to use the holdout sample to validate the model?</p>
<p>Thanks</p>
|
g73117
|
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<p>I have a complete population consisting of 6587 individuals (genes) and for each individual I have a distance value. These distance values are not normally distributed.</p>
<p>I'm interested in determining if a sample of 348 individuals (which has a smaller mean distance value compared with the mean distance value from the complete population) is significantly different than expected.</p>
<p>I have limited statistics background and would appreciate advice on what statistical test to use.</p>
<p>Ideas include:</p>
<ol>
<li>two sample t-test (probably not right, since its not a normal distribution)</li>
<li>wilcoxon rank sum test (buddy suggested this)</li>
<li>some other test that's easy to implement in R</li>
<li>custom test - one idea I had was to randomly pick out 348 individuals (with replacement) and determine their mean distance. Then repeat this 1000 times (I think this is called bootstrapping). I did this, and I get a normal distribution of values with mean 32000 (same as population mean ) and sd = 2000. The mean distance value for the actual sample of 348 individuals was 18000. So by 1-tail p-value from normal distribution of mean 32000 and sd=2000 this appears significant.</li>
</ol>
<p>Thanks in advance for any advice! </p>
|
g73118
|
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<p>If I need to determine the value of a data point at each percentile of a distribution (such as lognormal, weibull, etc), can use its CDF and plug in %iles to get the value?
For e.g. finding the value at 95%ile by plugging in 0.95 in the CDF formula. Basically, I need to determine that if the distribution graph were drawn what data points do I obtain at each %ile. Does CDF tell me the same thing? Please advise urgently</p>
<p>Thanks,</p>
|
g45886
|
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<p>I am interested in learning more about testing for the bivariate probit model with an endogenous treatment regressor. I have figured some stuff out -- summary below, since I don't see much on this topic -- but other questions remain. </p>
<p>Here's the setup. Suppose I have a binary outcome $y_1$, which depends on $x_1$, the error $\varepsilon_1$ and binary treatment indicator $y_2$, which itself depends on $x_2$, and $z$ and error $\varepsilon_2$. The dependence is of the form $y_1=\mathbb{1}(\beta_1'x_1+\alpha y_2+\varepsilon_1>0)$ and $y_2=\mathbb{1}(\beta_2'x_2+\gamma z+\varepsilon_2>0).$ The errors int the two equations are correlated with $\rho$. </p>
<p>I am interesting in testing the assumptions of:</p>
<ol>
<li>normality of the two errors terms</li>
<li>$\rho=0$</li>
<li>homoskedasticity of the errors</li>
<li>exogeneity and weak instruments for the treatment equation</li>
</ol>
<p>Normality can be tested with goodness-of-fit Rao/Murphy score test described by <a href="http://hdl.handle.net/10986/3368" rel="nofollow">Chiburis et al. (2011)</a> and <a href="https://webspace.utexas.edu/rcc485/www/papers/murphycomment.pdf" rel="nofollow">Chiburis (2010)</a>, who provide Stata code do so (<code>scoregof</code>). This test embeds the bivariate normal distribution within a larger family of distributions by adding more parameters to the model and checks whether the additional parameters are all zeros using the score for the additional parameters at the biprobit estimate. It rejects when there is excess kurtosis or skewness in the error distributions. They do not recommend a variant of the Hosmer-Lemeshow test to do this based on simulations. </p>
<p>The correlation between the errors can be tested using a likelihood ratio test based on the idea that if $\rho=0$, the log-likelihood for the bivariate probit will be equal to the sum of the log-likelihoods from the 2 univariate probits. If you calculate Huber/White sandwich errors, this becomes a Wald test.</p>
<p>Some questions remain.</p>
<ol>
<li>Should I worry about heteroskedasticity if I use robust errors? How can I test for this?</li>
<li><p>Can I differentiate heteroskedasticity from heterogeneous treatments effects?</p></li>
<li><p>Can I use linear IV diagnostics (like weak instruments tests) to check the non-linear probit model? Is there anything better? This seems strange to me since they estimate different treatment effects.</p></li>
<li>Are there other things I should check that I am not aware of?</li>
</ol>
|
g73119
|
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] |
<p>Here is what I have :</p>
<p>A scaled training set, with labels.</p>
<p>Segmented images, from which I extract new vectors to classify.</p>
<p>My classifier is a KNN which would have obviously been trained using my training set.</p>
<p>Now, I wonder how I should scale those new vectors I just got. Is this correct to scale them on their own, or should I do something else ? I wonder for example if an outlier would have an effect on the scaling and subsequent classification...</p>
<p>[EDIT] adding an outlier (which I would like to detect using kNN algorithm) to the test datas does impact the scaling, so subsequent classification won't work properly. What should I do then ?</p>
<p>[EDIT 2] This is how I scale my data : </p>
<p><img src="http://i.stack.imgur.com/9tpnF.png" alt="enter image description here"></p>
<p>Which in Scilab I translate to :</p>
<pre><code>function dataout = scaledata(datain)
dataout = zeros(size(datain,1),size(datain,2));
for i=1:size(datain,2)
dataout(1:size(datain,1),i) = (datain(1:$,i) - min(datain(1:$,i))) / ...
(max(datain(1:$,i)) - min(datain(1:$,i)));
end
endfunction
</code></pre>
<p>Thank you</p>
|
g73120
|
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] |
<p>Suppose I need to run <code>ttest bhar12=0</code> and the output comes as:</p>
<pre><code>One-sample t test
------------------------------------------------------------------------------
Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
bhar12 | 124 -.0325875 .0751874 .8372516 -.1814163 .1162414
------------------------------------------------------------------------------
mean = mean(bhar12) t = -0.4334
Ho: mean = 0 degrees of freedom = 123
Ha: mean < 0 Ha: mean != 0 Ha: mean > 0
Pr(T < t) = 0.3327 **Pr(|T| > |t|) = 0.6655** Pr(T > t) = 0.6673
</code></pre>
<p>If I knew the distribution for <code>bhar12</code> is positively skewed, how can I perform a <code>ttest</code> to get the <strong>bootstrapped Pr(|T| > |t|) value</strong>?</p>
|
g47269
|
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<p>I am trying to fit a second order polynomial. I center and scale my predictors and fit the data using the <code>lm</code> function. I did <code>summary(fit)</code>. For 3 of my variables, I got NA in all columns including estimate, p-value etc.</p>
<p>So, I am using R</p>
<p>I used the function <code>lm</code> as follows</p>
<pre><code>fit1<- lm (y ~ x11+x22 + I(x11^2) +I(x22^2) +I(x11*x22) )
</code></pre>
<p>The output I got is:</p>
<pre><code>Call:
lm(formula = y ~ x11 + x22 + I(x11^2) + I(x22^2) + I(x11 * x22))
Residuals:
Min 1Q Median 3Q Max
-0.33889 -0.21371 0.01898 0.15166 0.47933
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.57956 0.05367 48.062 <2e-16 ***
x11 -0.13097 0.05329 -2.458 0.0194 *
x22 NA NA NA NA
I(x11^2) 0.08673 0.03559 2.437 0.0204 *
I(x22^2) NA NA NA NA
I(x11 * x22) NA NA NA NA
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
</code></pre>
<p>So, in short the variables x22, x22-square and interaction x1*x2 shows NA in all columns. </p>
<p>Is there an error to get NA or should I just be assuming that the predictors for which estimates are NA are just insignificant?</p>
<p>Thank you for your help</p>
|
g73121
|
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<p>Does it make sense to look at a scatterplot of means versus standard deviations in terms of looking for outliers or changepoints? So the mean is on the x-axis and the standard deviation is on the y-axis. We would get a clusters of data indicating similar data (relatively same mean and standard deviation). Note that I don't know the sample size or individual observations from which these means and standard deviations were computed from.</p>
|
g46674
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] |
<p>Let's say I have a vector of q-values, which allow for handling multiple hypothesis testing by controlling the false discovery rate. Usually, these q-values will be generated from a distribution of p-values.</p>
<p>However, what if I don't have the original p-value distribution, only the vector of q-values? Is there a way to convert from the q-values to the p-values?</p>
|
g73122
|
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<p>I have this daily time series of observed prices: $P_1,P_2,..., P_n$.</p>
<p>I want to works with returns: $ 0 , P_2-P_1,..., P_n - P_{n-1}$.</p>
<p>I have been told to "remove" the first term (P_1-P_0= P_1- ?) by setting it to 0. It appears that this 0 is very differents from others terms and not a good solution. (I even think it's not a solution at all). </p>
<p>Here are the solution I considered:</p>
<ul>
<li><p>0 as there is no returns on the first day</p></li>
<li><p>{P_1} to be consistent with the time series</p></li>
<li><p>nothing, just simply removing the problem</p></li>
</ul>
<p>what do you think about this problem ?</p>
<p>This remained be about a similar problem I had while doing moving average. There is similar missing terms at the begining of the time series. When doing a p - moving average I usually take the last p value before my date. </p>
<ul>
<li><p>I have the same problem than before: at the beggining of the time series there is not enough data to make a sum with p terms. Is there a trick to adress this problem ? </p></li>
<li><p>Would it change something to take the p values after my date ? the $[(p-1)/2] values before and after my date ? It won't change the general term of my moving average but only the values at the beggining and the end of my time series. does it matter ? How ? </p></li>
</ul>
|
g35348
|
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] |
<p>I have a large regression problem with a lot of cases, but relatively few independent variables. One of them is a categorical factor with thousands of levels. Robust regression runs forever. In some cases the large number of dummy variables becomes too sparse to calculate with even "normal" lm. </p>
<p>What would usually make sense is to somehow calculate the average for each level of the factor, then adjust the dependent variable accordingly, and do the regression without the big factor. A colleague of mine could remember there is a two-letter R function that does that automatically, but he cannot remember the two letter combination.</p>
<p>Any help would be greatly appreciated.</p>
|
g35350
|
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] |
<p>I try to understand and visualize myself covariance matrix. Supposing I have a matrix <code>A = [ 2 3 4; 5 5 6 ]</code>, how do I calculate its covariance matrix, and what is its practical meaning? (All I was able to understand by now is that on the diagonal of the covariance matrix, variances for particular variables are placed, and on the upper and lower fields correlations between those variables.)</p>
|
g73123
|
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<p>Consider $U_i \sim^{iid} Bernoulli(\pi)$. Also consider:</p>
<p>$$Y_i | U_i = 0 \sim exp(1/\gamma) \text{ and } Y_i | U_i = 1 \sim exp(1/2\gamma) $$</p>
<p>What are the method of moment estimators of $\pi \text{ and} \text{ }\gamma$ ?</p>
<p>Here is my solution:</p>
<p>$E(U_i) = \pi \Rightarrow \hat{\pi_{MOM}} = \bar{U} = \sum U_i / n$</p>
<p>$E(Y_i) = E(E(Y_i | U_i)) = \gamma (1 + \pi) \Rightarrow \hat{\gamma_{MOM}} = \frac{\sum Y_i / n}{1 + \hat{\pi_{MOM}}}$</p>
<p>Are the estimates above right?</p>
|
g73124
|
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<p>I am desperately looking for some statistical help with my data because I myself cannot transfer the theoretical stuff I lately read on residuals, chi square distributions, squared z-values ecetera to my problem. Therefore I would really appreciate somebody to help me on that:</p>
<p>I compared 2 distributions with 4 categories by using Fisher's exact test- the difference turned out to be significant. </p>
<p>Now I wanted to know which category is "responsible" for the difference. More specifically, I was interested in which of the 4 categories the observed values differed from the expected.</p>
<p>Therefore I calculated "standardized residuals" or "squared z-values" (if that is correct??), like this: (observed - expected) squared/ expected</p>
<p>category: 1; 2; 3;4</p>
<p>observed: 4; 7; 5; 56</p>
<p>expected: 1.4; 3.2; 4.6; 62.8</p>
<p>z-squared: 4.8; 4.5; 0.03; 0.73</p>
<p>Hence, from what I understand of this example the observed and expected values in category 3 and 4 are not "that" different, but well in category 1 and 2; But now what do the numbers exactly mean? Do they convey any information of contingency considering that the comparison deals with numbers of people in each category? </p>
<p>I would be very happy about any advice.
Kind regards,
Johanna</p>
|
g46677
|
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<p>I'm rolling a regular dodecahedron (12-side die) 1200 times. I need to find an interval, in which the total count of prime-number results will lie with the probability of 95%. I have to use the Central Limit Theorem (CLT).</p>
<p>I'm not sure, how to use the CLT, but I have developed some way, how it could work. I'd like you to check it and tell me whether it is right, or what is wrong and how it should be. And also there are some question, I would like to ask.</p>
<p>My solution:</p>
<p>$n = 1200$ ...count of the rolls</p>
<p>Prime numbers in dodecahedron are 2,3,5,7,11, therefor probability $q$ of the rolling one of the prime numbers is $\frac {5}{12}$.</p>
<p>For Alternative distribution the mean equals to $q$ and the variance is $q(1-q)$. So we got:</p>
<p>$\mu = \frac {5}{12}$</p>
<p>$\sigma^2 = \frac {35}{144}$</p>
<p>Then as the CLT says, we can obtain an approximation for the distribution of this random variable $X$ by a normal distribution ($X_n$). This random variable will have parameters:</p>
<p>$EX = n \cdot \mu = 1200 \cdot \frac {5}{12} = 500$</p>
<p>$DX=n \cdot \sigma^2 = 1200 \cdot \frac {35}{144} $</p>
<p>And the random variable we are looking for is:
$X_n = \frac {X-EX}{\sqrt{DX}}$</p>
<p>I know, that I need it for the probability of 95%, so I look up for it in statistical tables for the quantile function of the standardized normal distribution and I find $\Phi^{-1}(0.950) = 1.645$, which is $X_n$.</p>
<p>$\frac {X-EX}{\sqrt{DX}} = 1.645$</p>
<p>And I solve this for $X-EX$</p>
<p>$X-EX = 1.645 \cdot \sqrt{DX} = 1.645 \cdot \sqrt{1200 \cdot \frac {35}{144} } = 28.09$.</p>
<p>With the probability of 95% the count of values with the prime numbers in 1200 rolls of the regular dodecahedron will be in the interval $ \left[EX-28 ... EX+28\right] $. </p>
<p>This, I believe, is not correct result. There must be some inequality, right? Which one and why? I mean... the propability is 95% and more, or 95% and less? </p>
<p>And the second question is: How to round the distance between EX and X? I mean... all down, or .4 down, .5 up? In Chebyshev's inequality that is clear, because of the inequality in the formula. Here I'm confused. </p>
<p>And also I would like to know something more about the role of the standardization in here, if there is any. Because the tables are called "quantile function of the <b>standardized</b> normal distribution", $X_n$ should actually be standardized, whatever it means.</p>
|
g34216
|
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<p>I am studying the book "<a href="http://rads.stackoverflow.com/amzn/click/1461471370" rel="nofollow">An Introduction to Statistical Learning: with Applications in R</a>", on page 66</p>
<p>While the book explains how to calculate $\beta_0$ and $\beta_1$, it skips how the actual calculation happened and only displays the equations to calculate them and then the result in the next page. I got lost when
$\sigma^2$ is calculated. I don't know how it was calculated, as I quote the book:</p>
<blockquote>
<p>In general, $\sigma^2$ is not known, but can be estimated from the data. This esti-
mate is known as the residual standard error and is given by the formula $\text{RSE} = \sqrt\frac{RSS}{n-2}$</p>
</blockquote>
<p>so I calculated $\sigma^2$ as $\text{RSE} = \sqrt\frac{RSS}{n-2}$ which gives <code>3.258</code> but it doesn't add up when I try to use this value instead of $\sigma^2$ in the equations (3.8) in the same page.</p>
<p>P.S: This example belongs to the Advertising data set, and it is Sales (Y) as a function of TV (X) advertising. <a href="http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv" rel="nofollow">Available here</a></p>
|
g73125
|
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<p>I am working on fitting a GEE model to a multinomial logistic outcome using the R package <code>geepack</code>. My understanding is that the package uses <code>glm</code> to fit the formula. However, from what I can see, <code>glm</code> doesn't have a family for a multinomial outcome, just binomial. How do you go about fitting a multinomial logistic equation using <code>gee</code> in R?
Thanks.</p>
|
g73126
|
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<p>Hi i was wondering how to figure out the following</p>
<p>Suppose $y=x+e$ where e is an i.i.d error. Say $x \sim N(\mu,\sigma_1^2)$ and $e \sim N (0, \sigma_e^2)$ which means $y \sim N (\mu, \sigma_1^2+\sigma_e^2)$. I need to find the expected value of y, conditional on $y>\mu$. I know that the formula will be y multiplied by the normal pdf but what is the actual output. As in, i can set up the integral however i cannot calculate it. I know the answer will be ($\mu$+something) just dont know what that something is.</p>
<p>thanks </p>
|
g73127
|
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] |
<p>Suppose that we have 2 sets of data $X = x_1, \dots, x_n$ and $Y = y_1, \dots, y_m$ and a test $T$ that tests the null hypothesis that these data come from a distribution <strong>with the same median</strong>. $T$ can be for example the Mann-Whitney U test or the Wilcoxon signed rank test (if we have paired data). In programming terms $T$ is a function that takes two samples and <strong>returns a p-value</strong>
$$
p := T(X, Y)
$$
Now let us suppose that we want to compare $X$ and $Y$ <strong>quantitatively</strong>. That is we want to say for example:</p>
<blockquote>
<p>On the 5% significance level the median of $X$ is at least 5 times
bigger than that of $Y$ but not more than 7 times bigger.</p>
</blockquote>
<p>To do this we can test hypotheses for various multiples of $Y$:
$$
p(c) := T(X, cY)
$$</p>
<p>Then we plot the p-values and get something like this:</p>
<p><img src="http://i.stack.imgur.com/vMMqj.png" alt="enter image description here"></p>
<p>For very big and very small values of $c$ the p-value drops to a level determined by the sample size, while somewhere in the middle it will have one connected global maximum. If we select a certain significance level $s$ then the set $I_s$ defined by
$$
I_s := \{c\in \mathbb{R} \text{ such that } p(c) > s \}
$$
Is an interval $[a; b]$ and we can say that:</p>
<blockquote>
<p>On the 5% significance level the median of $X$ is at least $a$ times
bigger than that of $Y$ but not more than $b$ times bigger.</p>
</blockquote>
<p>But what did we just do? Did we find the confidence interval for the median of
$\frac{\textbf{x}}{\textbf{y}}$ where $\textbf{x, y}$ are the underlying random variables? Or is this methodology flawed? Is there such a method somewhere in literature? Is there some better way?</p>
|
g35353
|
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] |
<p>the question is quite general, but I am doing a research related to supervised machine learning to classify two set of characters into two categories.</p>
<p>in fact, I want to compute some measures of similarity between a train set and the test set based on the N-gram approach.</p>
<p>I am trying to find a resource explaining some common practice in the same domain in how to discover the best value of N when using N-gram based algorithms.</p>
<p>I know it is very general question, however, the main important thing I am looking for is how to automatically discover the best N based on the N-1 computation in order to decide if we increment N and loop again or to stop.</p>
<p>is there any well-know methods or common approach to do that other than using a development dataset (experiment and fix the N value)?</p>
<p>regards,</p>
|
g24882
|
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<p>I just got admitted to the MS program in statistics at Villanova University (top 1 regional university in the North of the U.S.) and at Temple University (a third tier national university). I was wondering if anyone can give me some guidance regarding which university I should choose. Villanova does not have PhD program in statistics, and only offers night classes to masters students, which means most of its students are working professionals. Its program is in the Department of Mathematics. Temple has a PhD program, and masters students can take PhD courses if they want. The program is run by the Department of Statistics which is in the School of Business. The program at Temple costs about $$45,000, while at Villanova the cost is around $25,000. My academic background is in economics and I have some research experience in economic data modeling and analysis. I am in my mid 40's. Any suggestions are appreciated.</p>
<p>Update: Since I am not able to leave a comment, so I will type some words here. I post the question here because I once read a related post here which is given a link below (Thank you, cardinal). Also, opinions from people with academic background in statistics (Masters or PhD) may be more relevant than those from people in totally different fields as far as my question is concerned.</p>
|
g73128
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<p>I'd like to estimate a 3 level model (years clustered in districts clustered in counties) on the Leyland data (Mortality in England and Wales, 1979-1992 An Introduction to Multilevel Modelling using <code>MlwiN</code>) using R.</p>
<p>I have 3 predictors (year79 (at level 1), year792 (at level 1), and family(at level 2)).
year792 is just the square of year79.</p>
<p>I'd like to vary the slope of year between units at the third level (county).</p>
<p>I used the following code but I'm not sure it is correct:</p>
<pre><code>fit7<-lmer(smr ~ year79 + year792 + family + (1 |county/district ) + (year79 |county), data=Imdp, REML=FALSE)
</code></pre>
|
g35355
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] |
<p>I made this linear regression that shows how well estimated animal locations (longitude) predict actual animal locations. </p>
<pre><code>estimate <- c(-1.514276, -1.513683, -1.514253, -1.514207, -1.513557, -1.513634, -1.513870, -1.511210, -1.511552, -1.511772, -1.511580, -1.511802, -1.509500, -1.510037, -1.510214)
actual <- c(-1.514255, -1.514053, -1.514527, -1.514223, -1.513672, -1.513729, -1.513934, -1.511118, -1.511567, -1.511658, -1.511585, -1.511830, -1.509438, -1.509843, -1.510080)
lm_longitude <- lm(actual ~ estimate)
summary(lm_longitude)
Call:
lm(formula = actual ~ estimate)
Residuals:
Min 1Q Median 3Q Max
-2.630e-04 -3.825e-05 8.945e-06 6.530e-05 1.645e-04
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.09325 0.02706 3.445 0.00435 **
estimate 1.06167 0.01790 59.325 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.000112 on 13 degrees of freedom
Multiple R-squared: 0.9963, Adjusted R-squared: 0.996
F-statistic: 3519 on 1 and 13 DF, p-value: < 2.2e-16
</code></pre>
<p>As you can see, estimated locations are very good predictors for actual locations. I was initially alarmed at the residuals vs fitted values plot. It appears to shows residuals that are correlated with the fitted values:</p>
<pre><code>library(ggplot2)
df_lm_longitude <- ggplot2::fortify(lm_longitude)
ggplot(df_lm_longitude, aes(.fitted, .resid)) + geom_point() + stat_smooth()
</code></pre>
<p><img src="http://i.stack.imgur.com/0c7Hk.jpg" alt="enter image description here"></p>
<p>But change the scale of the y axis, and residuals vs fitted values plot looks perfect:</p>
<pre><code>ggplot(df_lm_longitude, aes(.fitted, .resid)) + geom_point() + stat_smooth() + ylim(-0.01, 0.01)
</code></pre>
<p><img src="http://i.stack.imgur.com/NHres.jpg" alt="enter image description here"></p>
<p>So one of the assumptions of linear regression is that residuals should not be correlated with fitted values. In the model above, the residuals are correlated with the fitted values at a large scale. But zoom out to a small scale, and residuals are not correlated at all?</p>
<p>What resolution should I be using for y axis in residuals vs fitted values plot?</p>
|
g35356
|
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<p>I've been reading about Item Response Theory during the past few weeks and I'd like to use it to examine how my scales are functioning. The response categories are ordinal. If I understood well, the Graded Response Model is particularly appealing because it is more flexible than other alternatives such as the Partial Credit Model or the Rating Scale Model, providing different "difficulty" parameters per category within each item, and different "discrimination" parameters for each item. Moreover, I'm confident that the response categories are ordered (expressing different degrees of agreement with a statement) so cumulative logit rather than adjacent category models seem adequate. (I might be wrong in various parts of this reasoning though!).</p>
<p>1) Is there a way to fit Graded Response Models in Stata 13, maybe using the gsem command or gsem builder? If so, can anyone shed light on how to do it and how to process the outputs to draw Category Response Curves, Item Information Functions and Standard Error of Measurement function for the scale?</p>
<p>2) If it is not possible to do it with gsem, is it possible to do it with gllamm? In <a href="http://www.stata-journal.com/article.html?article=st0129" rel="nofollow">this article</a> it is explained how to fit PCM and RSM but not Graded Response Models. <a href="http://www.stata.com/statalist/archive/2007-09/msg00265.html" rel="nofollow">This post</a> suggests it is possible to do it with the thresh() option, in order to relax the proportional odds assumption/constraint, but I have no clue about what to put inside the thresh() option. It seems I have to define equations for the thresholds, and again I'm clueless here.</p>
<p>3) My final question is a conceptual one: If I understood well, the Graded Response Model gives a "discrimination" parameter for each item and C-1 "difficulty" parameters for the C response categories. Is there a model which provides different "discrimination" parameters for each response category as well? Would this be a nominal model? Why is it reasonable to constrain discrimination parameters to be equal for different response categories of an item? (maybe this is not really a "constraint"?)</p>
|
g35360
|
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<p>I'm trying to interpret some results here, and just want to make sure that my logic is sound.</p>
<p>I'm predicting a binary outcome with a categorical predictor (gene level coded as 0, 1, or 2 dependant on the number of risk alleles present). My hypothesis is that the gene's effect on the outcome is because of its effect on another variable (continous), say blood glucose level, which in turn affects CAD. </p>
<p>When I model the response as a function of the gene, all is fine, and it predicts very well (this is an established loci).</p>
<pre><code>glm(cad ~ gene, Mastersheet, family = binomial) %>% summary()
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.002729 0.041267 0.066 0.947
gene 0.354027 0.032885 10.766 <2e-16 ***
</code></pre>
<p>When I include my covariate in the model, all is still fine. The covariate is also an established predictor of cad.</p>
<pre><code>glm(cad ~ gene+glucose, Mastersheet, family = binomial) %>% summary()
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.66501 0.10820 24.630 <2e-16 ***
gene 0.33467 0.03813 8.778 <2e-16 ***
glucose -2.17507 0.07722 -28.168 <2e-16 ***
</code></pre>
<p>However, when an interaction term is included, the gene is no longer significant, though the model continues to be.</p>
<pre><code>glm(formula = cad ~ gene * glucose, family = binomial, data = Mastersheet)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.2845 0.1920 17.109 < 2e-16 ***
gene -0.2306 0.1449 -1.591 0.112
glucose -2.6674 0.1482 -18.004 < 2e-16 ***
gene:glucose 0.4471 0.1108 4.035 5.47e-05 ***
</code></pre>
<p>I'm looking for some help interpreting this meaningfully. Does this mean that because the gene becomes insignificant when the interaction is factored in, the effect of the gene on CAD is mediated entirely by it's interaction with glucose? </p>
<p>I couldn't find any other questions like this, sorry if it is a repeat. </p>
<p>Any and all help is appreciated! Thank you for your time! </p>
|
g73129
|
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] |
<p>When comparing variances, very often a F-test is used.</p>
<p>$$F=\frac{s_1^2}{s_2^2}$$</p>
<p>We then compare $F$ to an F-distribution. The assumption of this test is that the two samples (which variances are $s_1^2$ and $s_2^2$) are normally distributed.</p>
<p><strong>Can you please explain why (given that the two samples are normally distributed) $\frac{s_1^2}{s_2^2}$ is F-distributed?</strong></p>
<p>If I am not mistaken, if $U_1$ and $U_2$ are chi-squared distributed with degrees of freedom $df_1$ and $df_2$ respectively, then $\frac{U_1/df_1}{U_2/df_2}$ is F-distribution distributed. I would really appreciate an answer that also give some words between the link between the chi-squared distribution and the F-distribution.</p>
|
g35362
|
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] |
<p>I'm creating a scoring system for web pages based on their level of readability using <a href="http://en.wikipedia.org/wiki/LIX" rel="nofollow">LIX</a>. A selection of pages from a web site are crawled and given a score. </p>
<p>Besides average and median, what alternatives do I have in order to reflect the score for the entire web site, using the results from each page?</p>
|
g73130
|
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<p>As a work assignment, I've been asked to determine the optimal SKU count for a product group. I've decided to tackle this Q using a simple linear regression with sales as my dependent variable and the # of SKUs and the # of SKUs squared as my independent variables. My data set is a cross section of store sales and SKU counts for each store.</p>
<p>Trouble arises when I run the regression and get positive coefficients for both # of SKUs and # of SKUs squared (I think diminishing returns are identified by a negative coefficient for the squared variable). I suspect that sales for larger stores are proportionally higher than # of SKUs compared to smaller stores and maybe this is why my coefficient doesn't make sense.</p>
<p>I'm looking for suggestions on either model specification or ways to standardize stores (if that's the solution). My data set has about 600 stores and I thought about restricting the group by store size but similarly sized stores also generally have the same number of SKUs. </p>
<p>I also thought about using a time series, but my yearly data only goes back a decade or so. I'm also inexperienced in this area, and would be concerned I wouldn't model it properly.</p>
<p>Thanks for any advice.</p>
<p>Cheers,</p>
|
g35364
|
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] |
<p>As shown below, I'm trying to subtract TMin1array from Tarray. Does anyone know why the resulting array is returning all 0's? Tarray and TMin1array are of type double.</p>
<p><img src="http://i.stack.imgur.com/AJkCF.png" alt="enter image description here"></p>
|
g73131
|
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] |
<p>I am using LMM in lmer. To find the most optimal model, I compare models of three-level with two level using ANOVA function. If it turns out that no significant difference between these two, then I compare two-level model with one level model. My formulas are like this:</p>
<pre><code>lmer1 <- lmer(peak_Mid ~ (1|item) + (1+vowel|speaker) + sex*vowel*language, data=data.frame, REML=FALSE, na.action=na.omit)
lmer2 <- lmer(peak_Mid ~ (1|item) + (1+vowel|speaker) + sex + vowel + Language + language:vowel + Language:sex + vowel:sex, data=data.frame, REML=FALSE, na.action=na.omit)
anova(lmer1,lmer2)
lmer3 <- lmer(peak_Mid ~ (1|item) + (1+vowel|speaker) + sex + vowel + language, data=data.frame, REML=FALSE, na.action=na.omit)
anova(lmer2,lmer3)
</code></pre>
<p>Then suppose that the best model is two-level model which mean the interactions are significant. I will do the pairwise comparison using:</p>
<pre><code>lsmeans(lmer2, pairwise ~ language*vowel, adjust="tukey")
lsmeans(lmer2, pairwise ~ language*gender, adjust="tukey")
</code></pre>
<p>However, actually I would like to find out if each pair of language groups is different to one another in similar context, such as Indian and Chinese in high vowel spoken by female speakers. The results from lsmeans(lmer2, pairwise ~ language*vowel, adjust="tukey") will give me only comparison of language x vowel whereas the results from lsmeans(lmer2, pairwise ~ language*gender, adjust="tukey") will give me only comparison of language x gender. </p>
<p>My question is whether I can combine these two comparisons in the findings?</p>
|
g35367
|
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<p>Let $(\Omega,\mathcal B,P)$ be a probability space. I have two (related) questions. Assuming that $g:\mathbb{R}\to\mathbb{R}$ is Borel measurable, and understanding that</p>
<p>$$E(g(X)) = \int_{\Omega}g(X(\omega))dP(\omega),$$</p>
<p>how do I prove that these equalities hold for the two following circumstances?</p>
<p>First, $X$ is discrete, with range $\{x_{i}:i\in \mathbb N\}$. Then </p>
<p>$$E(g(X))=\sum_{i=0}^{\infty}g(x_{i})P(X=x_{i}),\ \ \text{ provided } \sum_{i=0}^{\infty}|g(x_{i})|P(X=x_{i})<\infty.$$</p>
<p>Second, $X $ is absolutely continuous with density $f.$ Then </p>
<p>$$E(g(X))=\int g(x)f(x)dx\ \ \text{ provided }\int |g(x)|f(x)dx<\infty.$$</p>
|
g73132
|
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] |
<p>When does one use the denominator $\sigma$ over the denominator $\sigma /\sqrt{n}$? Why are there two separate forms and why does one look exactly like the t-score? Do some authors just call both t and z scores z scores?</p>
|
g35369
|
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<p>A short question concerning the constructing of a 'missing-dummy', which I will consequently add to my logistic regression. This missing-dummy gives value '1' to the cases where data concerning a specific variable is missing and value '0' to the cases which have data.</p>
<p>I've used this command in SPSS, but in some way the missing values are not recognized.
( recode v204 (-2 -1=1)(else=0) into authomis ).</p>
<p>A cross-tabulation of v204 and authomis shows that the missing-dummy only has a '0'-category, regardless the fact that there are over 400 cases (on a total of 40.000) which have a missing on variable v204. Has this to do with how the missings are marked in variable v204?
I can't think of any other reason. Hopefully you can. Thanks in advance.</p>
|
g73133
|
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] |
<p>Statistical model for <em>Complete Randomized design</em></p>
<p>$y_{ij} = \mu + \tau_i + \epsilon_{ij}$</p>
<p>where, $i$ denotes treatment and $j$ denotes observation.</p>
<p>$i=1,2,...,k\quad and \quad j=1,2,..., n_i$</p>
<p>$y_{ij}$ be a random variable that represents the response obtained on the $jth$
observation of the $ith$ treatment.</p>
<p>$\mu$ is the overall mean of the response $y_{ij}$</p>
<p>$\tau_i$ is the effect on the response of $ith$ treatment.</p>
<p>$\mu_i = \mu + \tau_i$</p>
<p>here $\mu_i$ denotes the <em>true response</em> of the $ith$ treatment.</p>
<p>and $\epsilon_{ij}$ is the random error term represent the sources of nuisance variation that is, variation due to factors other than treatments.</p>
<p>the assumption is $\epsilon_{ij}\sim^{iid} N(0,\sigma^2)$</p>
<p>Why do we have to assume $\epsilon_{ij}\sim^{iid} N(0,\sigma^2)$ ?</p>
<p>that is <em>What is the importance of this assumption? If we do not assume it , what will be the effect?</em></p>
<p>Any help including reference will be appreciated.</p>
|
g73134
|
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<p>I have a collection (approximately 12,000) correlation values. Our correlation analysis does not allow for negative correlations (we correlate with sinusoidal waves, so instead of a negative correlation, we simply positively correlate with the opposite phase).</p>
<p>This produces a distribution of positive r values. Traditionally we have converted this distribution to z-scores using (in MATLAB):</p>
<pre><code>zVal = sqrt(degreesOfFreedom)/2 * log((1+rVal) ./ (1-rVal));
</code></pre>
<p>Where <code>sigma = sqrt(degreesOfFreedom)</code> and <code>z = 1/2 * log((1+rVal) ./ (1-rVal))</code></p>
<p>I'm pretty sure this is the "correct" calculation, although I am suspicious it is inappropriate because the r values are not normally distributed (fails the KS test, as well). Next, we convert to p-values using: </p>
<pre><code>pVal = 1 - normcdf(abs(zVal), 0, 1); # Assumes normal distribution w. mean = 0, sigma = 1
</code></pre>
<p>My question is, will the above calculation give you incorrect p values if your r values are not drawn from a normal distribution? I'm running into some resistance from higher-ups, but I'm pretty sure that this is wrong.</p>
<p>This is what the data looks like:</p>
<p><img src="http://i.stack.imgur.com/Umafg.jpg" alt="r, z, and p distributions from sample data set"></p>
<p>Would I be right to say that 'normcdf' is responsible for the enormous number of highly significant items? Is there a way to directly identify p values from an arbitrary distribution? Due to the incredible skew in the distribution of p values, most multiple-comparison correction procedures produce rather liberal p-thresholds. </p>
|
g73135
|
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<p>Suppose we have a test statistic designed for testing a null about two groups of samples.</p>
<p>If we apply permutation test to the groups of samples and the test statistic, will that change the null hypothesis? </p>
<p>What I heard of before is that permutation test is to test if the two groups of samples are coming from the same distribution, <a href="http://stats.stackexchange.com/questions/59638/how-to-choose-the-test-statistic-for-permutation-test/59642#comment114313_59642">"same" maybe in different sense</a>. So does it mean that after applying the permutation test, the original null will be changed?</p>
<p>An example, consider the case when the test statistic is to test if the locations of two groups of samples are the same.</p>
<ul>
<li><p>the t test statistic tests if the mean of two normally distributed groups of samples have the same mean. Will applying permutation change its null, for example, from equal mean to equal distribution?</p></li>
<li><p>the Wilcoxon rank-sum test test if two groups of samples have the mean ranks of the two groups are the same. Will applying permutation change its null, for example, from equal mean rank to equal distribution?</p></li>
</ul>
<p>What does permutation test bring to a location test?</p>
<p>Thanks and regards!</p>
|
g73136
|
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<p>I am working on a multinomial logistic regression problem which involves features from the dependent variable. It might be better to describe the problem by using the example in <em>mlogit</em> <a href="http://cran.r-project.org/web/packages/mlogit/vignettes/mlogit.pdf" rel="nofollow">mlogit manual</a></p>
<p>Here comes the training data,
<img src="http://i.stack.imgur.com/hbdtA.png" alt="enter image description here"></p>
<p>The goal is to predict the fishing mode based on three features, 1) price, 2) catch - both of which depend on the fishing modes chosen and 3) income - which is individual specific. </p>
<p>I am aware of glmnet does multinomial logistic regression, but it seems to me it does not apply directly to my problem. I also noticed that mlogit can handle dependent variable specific features but does not work for sparse feature. Does anyone know some package which can be used for my problem?</p>
<p>Thanks</p>
|
g28311
|
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] |
<p>Given a <em>partial sample</em> of values from a set (known size), how to extrapolate the lowest/highest value in the <em>entire set?</em></p>
|
g73137
|
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] |
<p>Hate asking such a general question, but I'm so unfamiliar with statistics in general that I don't know what to search or where to find the answer.</p>
<p>I'd like to learn how to manipulate errors. Like, if I had a function $f\left(x,y,z\right)$, and I knew $\sigma_x,\sigma_y,\sigma_z$, what the error of $\sigma_{f}$ is.</p>
|
g46697
|
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<p>Boosting algorithms, such as <a href="http://en.wikipedia.org/wiki/AdaBoost">AdaBoost</a>, combine multiple 'weak' classifiers to form a single stronger classifier. Although in theory boosting should be possible with any base classifier, in practice it seems that tree-based classifiers are the most common. </p>
<p>Why is this? What properties of tree classifiers make them best suited for this task? Are there any other base classifiers which also benefit a lot from boosting? I ask with classification problems in mind, but I would also be interested in answers concerning regression applications.</p>
|
g73138
|
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<p>I'm going to preface this all by saying that I'm pretty pedestrian when it comes to large statistical analysis.</p>
<p>I have approximately 11K discrete events and a corresponding score. I also have approximately 500 binary attributes. Each event is positive for one to six attributes. How do I go about trying to figure out the relationships between the variables and the score? What tool (open source preferred) should I use? Or is this really something I need to hire someone to do. I should note that I'm very good with Excel and do have a fair amount of programming experience.</p>
|
g73139
|
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<p>Imagine I organized a race between 2 types of ants. Type A and B.
At the end of the race, I have the ranking, which looks something like :</p>
<pre><code>1 A1
2 A3
3 B5
4 A4
5 B2
...
</code></pre>
<p>Where, in A1, A is the ant type and "1" the ant ID. Ants do not interfere between each other during the race. </p>
<p>If I plot the proportion of A or B every 10% of the ranking it gives this (fake data):</p>
<p><img src="http://i.stack.imgur.com/Ufi1g.png" alt="ants"></p>
<p>Maybe bar plot is better here. But one needs to read it as follow : </p>
<p>There are 1000 ants in the race, I arbitrary divide the ranking in 10.
When </p>
<ul>
<li>N = 1, that is the first 100, there are 54 Bs and 46 As. </li>
<li>N = 2, there are 50 As and Bs</li>
<li>N = 3, 55 As and 45 Bs </li>
<li>N = 4, 61 As and 39 Bs</li>
<li>etc..</li>
</ul>
<p>My question is :</p>
<p>I have just ranking results and I want to known whether there is some bias in the ranking as a function of the type. eg. For a given ant, can one predict where it will rank ?</p>
<p>For instance, how can we say whether A-ants are very good at arriving in first positions 10%), and B-ants are very good at arriving in the 30-50% of the ranking, or not, but both are equally good at performing bad. (I don't want to test for this, but how can I end up with results of that kind).</p>
<p>I have many replicate of this experiment.</p>
<p>I don't really know how to test for this. I was thinking of:</p>
<ul>
<li>dividing the ranking in N parts (how to choose N ?)</li>
<li><strike>Doing a $\chi^{2}$ test for each part, where I expect 50% of type A and B under null hypothesis.</strike> : No because parts are dependants.</li>
<li>I don't know.</li>
</ul>
<p>How would you do, and why ?</p>
<p>Note that the ranking doesn't include values (eg. time), so we only have ranking information.</p>
<p>In case we would have the time value, how would you do, if different ?</p>
<p>I would appreciate some re-wording of the problem, since I'm not a statistician and it prevents me to search in books (because I don't known where to search)</p>
<p>Thanks</p>
|
g73140
|
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<p>I have some data that span several years: 2006-2010. I have run logistic regression to model the data. For the whole dataset, I get a 95% confidence interval for the <strong>odds ratio</strong> of a parameter of interest of </p>
<pre><code>(0.34 - 0.47 )
</code></pre>
<p>indicating a very significant effect. However, for each individual year, with the same model specification, the confidence intervals are:</p>
<pre><code>2006: (0.78 - 1.94) (not significant)
2007: (0.61 - 0.93)
2008: (0.63 - 0.90)
2009: (0.92 - 1.30) (not significant)
2010: (0.88 - 1.33) (not significant)
</code></pre>
<p>How can I reconcile that the confidence interval for the whole dataset is below the confidence intervals for all the individual years ? I'm guessing that it is to do with the sample sizes - bigger sample sizes leading to lower p values: I think I get the maths behind this, but I can't get the intuition behind it.</p>
<p><strong>Update1</strong></p>
<p>In response to the answers by Michael and Peter, I am providing more information.</p>
<p>The model is:</p>
<pre><code>death~treatment+age+imd+smoking+clinicals+drugs+comorbidities
</code></pre>
<p>Notes:</p>
<ol>
<li>death is binary</li>
<li>treatment is binary - whether treatment A or treatment B was given. This is the parameter of interest that I have given confidence intervals for (which I obtained by exponentiating the CIs for the estimate +/- 1.96xSE )</li>
<li>age is age in years</li>
<li>imd is a socioeconomic status index for the patient</li>
<li>smoking is categorical and has several levels pertaining to the patients smoking status.</li>
<li>clinicals is a set of clinical measures such as heartrate, blood pressure</li>
<li>drugs is the a set of binary covariates indicating whether a particular drug was given</li>
<li>comorbidites is a set of binary covariates indicating whether the patient is suffering from certain conditions: eg asthma, diabetes</li>
</ol>
<p>In the overall model I have not included year as a covariate - the same model formula was used for the subsetted data and the whole data.</p>
<p>There is no problem with collinearity between the continuous variables but I am less sure about associations between the categorical variables. I think this could be a problem but I don't know how to tackle it - I tried some chi-square tests but nothing was independent from anything else (I thought that might be due to the sample size - according to my teacher it doesn't make sense that asthma would be collinear with diabetes for instance)</p>
<p><strong>Update2</strong></p>
<p>After further comments by Michael I am now giving some more info....The ratio of treatment A/B has changed a lot over the period - it was a new treatment in 2006 and hardly used, but is now the treatment of choice:</p>
<pre><code>2006: 555 out of 11,505
2007: 2,810 out of 12,307
2008: 5,669 out of 13,243
2009: 9,111 out of 14,654
2010: 12,368 out of 15,573
</code></pre>
<p>Overall: 30,643 out of 92,767</p>
<p>The death rate has not changed much (around 7% throughout)</p>
|
g35383
|
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] |
<p>Feel free to direct me to where an answer can be found, but I've banged my head against this for a while and turn to you good people:</p>
<p>Scenario:</p>
<p>I have a bunch of non-exclusive two-dimensional data (location data) for several thousand unique observations of independent subjects:</p>
<pre><code>Subject1, CategoryA, TypeB, two-dimensional_distribution
Subject2, CategoryB, TypeB, two-dimensional_distribution
Subject3, CategoryA, TypeA, two-dimensional_distribution
etc...
</code></pre>
<p>The two dimensional distribution is quite simple containing only three possible x and y coordinates with presence(1)/absence(0) for each. For example:</p>
<pre><code>C----0-----1-----1
B----1-----1-----0
A----1-----0-----0
-----X-----Y-----Z
</code></pre>
<p>If I combine all the obs, the fallout is something like</p>
<pre><code>C---15%---62%---25%
B---10%---35%---12%
A----9%---11%----7%
-----X-----Y-----Z
</code></pre>
<p>How can I go about performing an ANOVA/MANOVA to look at the influence of "category" and "type" on the distributions and determine whether there is a significant difference in distributions among groups.</p>
<p>Tricky bit:</p>
<ul>
<li>The frequency distributions don't equal to 100% (as you each observation can have presence in more than one location.)</li>
</ul>
<p>Ultimately I would like to run this through R - so if you have any ideas in that direction... </p>
<p>Apologies if this a totally pedestrian question. Thanks for your help.</p>
|
g24384
|
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] |
<p>I wonder between two performance metrics for classification models: accuracy and area under ROC curve (AUC), which one is to be preferred in which conditions? examples appreciated</p>
|
g35384
|
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<p>I posted this to the TraMineR user list and it was suggested that it would be appropriate to post it here as well.</p>
<p>Any suggestions as to how to determine the minimum dataset size and missingness characteristics to which TraMineR may be applied sensibly would be helpful. I looked for information in documentation but did not see anything that I could use as a heuristic.</p>
<p>I am using TraMineR to analyze 5 years of BMI observations, coded as a four-level ordinal categorical variable for 5046 elementary school children (grades K-5). Only 414 of these have 5 observations ( ~ 56% of the K, 1 students measured at time 1 who could have had been measured in years 1 to 5). Here are have two related, if not well-stated, questions:</p>
<ol>
<li><p>Is it legitimate to focus only on complete cases since I only have 5 data points and high cumulative natural attrition? Testing the complete cases against all cases reveals no substantive difference in values of predictors. The analyses from complete cases are informative, while including all cases, regardless of imputation choice, just makes things noisy. I tried admitting only sequences of 4 or 5, but results were still noisy.</p></li>
<li><p>Is five too short a sequence object to use with TraMineR, given the imputation patterns required by the full dataset, regardless of whether they are due to planned missingness or MAR?</p></li>
<li><p>Below is the number of cases with from 1 to 5 observations.</p>
<pre><code> 1 2 3 4 5
1846 1287 869 630 414
</code></pre></li>
</ol>
<p>TraMineR is a great tool. I want to make sure I am using it appropriately.</p>
|
g73141
|
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<p>I have a random sample $(X_1, X_2,...,X_n)$ and I have an estimator $\bar{X_n}=\sum_{i=1}^{n} X_i$</p>
<p>I need to compute the Fisher information of $\bar{X_n}$. The Fisher information is defined as $-E\left(\frac{d^2}{d\theta^2}logL\right)$, where $L$ is the likelihood function.</p>
<p>My question is: to compute the Fisher information <strong>of the estimator</strong> (NOT the random sample, but instead a function of the random sample), should we take the likelihood function of the random sample or the likelihood function of the distribution?</p>
|
g73142
|
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] |
<p>I have a number of distance matrices that I want to associate their members with a probability distribution. Is there a method which can affiliate each distance matrix with a distribution?</p>
<p>EDIT:
Lets say I have a distance matrix like:</p>
<pre><code> A1 A2 A3 A4 ...
A1 X 1 3 2
A2 1 X 4 3
A3 3 4 X 3
A4 2 3 3 X
.
.
.
</code></pre>
<p>Now I want to see what are the distribution parameters if members of this matrix were from a probability distribution. I only have the matrix and I do not know what is the distribution of the data.</p>
|
g73143
|
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<p>I have an experimental design with attitudes toward one positive and one negative stimulus nested within individuals. I also have a continuous predictor at the person level (a personality construct).<br>
My plan was now to build a multi-level model with valence as level-1 predictor, (centered) personality as level-2 predictor, and the cross-level interaction of these two variables. Since I wanted to use nested chi-square statistics to assess the individual effects, the code would be something like this:</p>
<pre><code> library(nlme)
mod0 <- lme(attitude~ 1, random = ~1|ID, data=dat, method="ML")
mod1 <- lme(attitude ~ valence, random = ~valence|ID, data=dat, method="ML")
mod2 <- lme(attitude ~ valence+z_personality, random = ~valence|ID, data=dat, method="ML")
mod3 <- lme(attitude ~ valence*z_personality, random = ~valence|ID, data=dat, method="ML")
</code></pre>
<p>My questions are the following: </p>
<p>1) Is it justified to use multi-level models, given that I have only two observations per participant? </p>
<p>2) The random variance for valence is exaclty defined (with only two data points per person, there are no degrees of freedom left; the standard error for the random variance estimate is 0). Should I include a random effect for valence in this case? </p>
<p>3) I am particularly interested in the cross-level interaction (dependeing on personality, some participants are hypothesized to have a more positve attitude toward the negative stimulus than toward the positive stimulus). If I do not include the random variance for valence (see 2), this - in my understanding - means that the difference between positive and negative stimuli is the same for all participants. However, this is explicitly not what I expect. To put the question simply: Do I need to specify random variance for a level-1 predictor if I am interested in the cross-level interaction of this predictor? </p>
<p>For all these points the question is not "Can R / SPSS do this?" (I have tried, both can do it), but rather if I can reasonably interpret the results, given my design. Also, if you had some references for me to back this up, this would be greatly appreciated.</p>
<p>Thanks for your help!</p>
|
g35387
|
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] |
<p>Does returning z-scores to a set mean and deviation result in a fair comparison? That is if I had 2 groups:</p>
<ul>
<li>group 1 mean = 76, stdev = 8</li>
<li>group 2 mean = 81, stdev = 11.</li>
</ul>
<p>Then to compare group 1 & 2 I return the groups scores using the z-scores against a set mean = 70 and stdev = 12.5. Will these values be fairly comparable?</p>
<p>is this a fair way of creating a standard ranking score out of 100 for each person?</p>
|
g73144
|
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] |
<p>Age pyramid looks like this:
<img src="http://i.stack.imgur.com/GtBSK.png" alt="alt text"><br>
I would like to make something similar, namely a 2 barplots (not histograms) with same categories, rotated vertically and extending to both sides as in pyramid.<br>
Is it a simple way to do this in R?<br>
It would be also nice to control the colour of each bar.</p>
|
g35388
|
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<p>I would just like someone to confirm my understanding or if I'm missing something.</p>
<p>The definition of a markov process says the next step depends on the current state only and no past states. So, let's say we had a state space of a,b,c,d and we go from a->b->c->d. That means that the transition to d could only depend on the fact that we were in c.</p>
<p>However, is it true that you could just make the model more complex and kind of "get around" this limitation? In other words, if your state space were now aa, ab, ac, ad, ba, bb, bc, bd, ca, cb, cc, cd, da, db, dc, dd, meaning that your new state space becomes the previous state combined with the current state, then the above transition would be *a->ab->bc->cd and so the transition to cd (equivalent in the previous model to d) is now "dependent" on a state which, if modeled differently, is a previous state (I refer to it as a sub-state below).</p>
<p>Am I correct in that one can make it "depend on previous states (sub-state)" (I know technically it doesn't in the new model since the sub-state is no longer a real state) maintain the markov property by expanding the state space as I did? So, one could in effect create a markov process that could depend on any number of previous sub-states.</p>
|
g49390
|
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