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<p>I'm a novice attempting to predict automobile sales using a combination of previous sales (seasonal AR model), macroeconomic indicators such as CPI, consumer sentiment index etc. and more significantly, I'm using weekly data from google search trends for the automobile and other variables from the category (automobile) in google trends. (code developed using Choi and Varian's 2009 paper). The model essentially looks at search trend indices for three weeks before the month in question</p>
<p>In addition to running spike and slab regression to determine attribute importance, I also ran a gradient boosted machine (R package GBM). as of now, the model seems to be performing fairly satisfactorily, with the Mean Average Error = 5.4 (monthly sales are in the range of 10000), however there are clear seasonal trends in the difference between predicted variables and actual sales that seem to coincide with sales promotions and other promotional events. My question, therefore is:</p>
<p>How do I account for these seasonal trends while using GBM? or for a linear model?</p>
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g73206
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] |
<p>Consider a new variable that is linear combination of original variables (e.g. one of the principal components). How can we find out which original variables "product" the new variable?</p>
|
g49514
|
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<p>My aim is to compare the forecast performance of several time series models. I have a bivariate dataset, and applied three different models to it:<br/><br>
<strong>1)</strong> A univariate <strong>Arima</strong> model (applied to the first variable) using the automatic order selection function 'auto.arima()'. The estimated model is <strong>Arima(1,1,1)</strong></p>
<p><strong>2)</strong> A Verctorautoregression using both variables. The recognized model (using the package 'vars') is VAR(1), and</p>
<p><strong>3)</strong> A univariate state space model (aggain applied to the first variable) using the package 'dlm'. I specified a state space form of Arima(1,1,1) model, as it was suggested by 'auto.arima()', namely I constructed a model consisting of a <strong>stochastic trend</strong> and of an <strong>arma</strong> model with one parameter <strong>ar</strong> and one <strong>ma</strong> (for details see the code). </p>
<p>I then generated forecasts compared the results graphically and was surprised to see, how poorly my state space model performs. The results of Arima are quite similar, only the VAR(2) model performs relatively well.</p>
<p>Is this poor result of state space model realistic or is my model specification wrong?</p>
<pre><code>data <- read.table(...)
library(vars)
library(forecast)
library("dlm", lib.loc="C:/Users/incognito/Documents/R/win-library/3.0")
# subsetting the data:
data.s<-data[1:528,1]
# Estimation of univariate Arima model and generating a forecast:
arima.m<-auto.arima(data.s.g)
arima.f<-forecast(arima.m,h=30)
# Estimation of a state space representation of Arima(1,1,1) model and forecast:
level0 <- data.s.g[1]
slope0 <- mean(diff(data.s.g))
buildGap <- function(u) {
trend <- dlmModPoly(dV = 1e-7, dW = exp(u[1 : 2]),
m0 = c(level0, slope0),
C0 = 2 * diag(2))
gap <- dlmModARMA(ar = ARtransPars(u[4]),ma=u[5], sigma2 = exp(u[3]))
return(trend + gap)}
init <- c(-3, -1, -3, .4, .4)
outMLE <- dlmMLE(data.s.g, init, buildGap)
dlmGap <- buildGap(outMLE$par)
filt<-dlmFilter(data.s.g,dlmGap)
forc<-dlmForecast(filt,nAhead=30)
# A bivariate VAR model and forecast:
var<-VAR(data.s)
var.f<-predict(var,n.ahead=30)
# Plotting the results:
plot(data.s.g,xlim=c(400,560),ylim=c(1.5,4),type="l")
lines(529:558,forc$f)
lines(529:558,var.f$fcst$gas[,1],col=3)
lines(529:558,data$gas[529:558],col=4)
lines(529:558,arima.f$mean,col=2)
legend("topleft",legend=c("state space","arima","var"),lty=1,col=c(1,2,3))
</code></pre>
<p><img src="http://i.stack.imgur.com/Qur4q.jpg" alt="enter image description here"></p>
|
g73207
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] |
<p>I have a data matrix as follows:</p>
<pre><code> samplename samplelot length height earlength micronire
DFG562 A 17 32 6 54
SGE512 A 12 23 5 29
TRE762 B 13 52 2 42
DFS509 C 17 24 5 62
HNB786 D 15 61 4 41
FWE523 A 14 42 1 92
WES715 B 52 67 9 81
RWQ635 D 24 92 3 72
HNG715 c 15 65 5 34
</code></pre>
<p>I would like to select the plant variety based on the characteristics(length,earlength,micronire and height) given but not sure how to go about it. I would like to obtain the best varieties in terms of each characteristic and also the varieties which are at its best for all characteristics together. </p>
<p>I know it is possible through regression but need a start as am new to statistical analysis.</p>
|
g73208
|
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<p>I am comparing Shannon entropy values (for zone occupation) obtained by soccer players during small-sided games in three pitch dimensions. I am also scrutinizing differences between expertise level (national- or regional-level players).
So, I used a General Linear Model RM ANOVA, with the within-subject factor being the 3 pitch dimensions and the between-subject factor being expertise (2 levels - national and regional).
I have checked for univariate and multivariate normality and it is okay, but I only have 16 participants (8 regional and 8 national players). Is it ok to perform this test, even if there aren't normality issues. </p>
<p>I also got a significant interaction effect between pitch_dim*expertise. To scrutinize for statistical differences, do you recommend performing an independent t-test with a bootstrap resampling of 1000 (since I only have 8 players per group)?</p>
|
g45150
|
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<p>I have a series of scores in a signal detection task. For each block of scores (i.e. a set of scores from one participant on one day) I have calculated a d' score which I am using as an indicator of performance.</p>
<p>These d' scores rise over time, which is an interesting result. Is there any way I can calculate whether the change is statistically significant?</p>
|
g45152
|
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<p>I am trying to estimate (fit) the distribution of a variable. The first step in doing so is to draw a normal probability plot. This is what I have obtained (using R):</p>
<pre><code>qqnorm(x)
qqline(x)
</code></pre>
<p><img src="http://i.stack.imgur.com/YoSHg.jpg" alt="enter image description here"></p>
<p>This is the histogram of the data:</p>
<p><img src="http://i.stack.imgur.com/MhqPm.jpg" alt="enter image description here"></p>
<p>As you can see, there is a quadratic pattern in the normal probability plot, but most point fall ABOVE the reference line.
The end purpose for this analysis is to detect outliers. Estimating the distribution of this variable would allow me to determine the threshold to set to determine outliers.</p>
<p>What can we deduce from both the normality plot and the histogram, in terms of the distribution of x, and the outliers?</p>
<p>Thank you!</p>
|
g73209
|
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] |
<p>What is a suppressor variable in multiple regression and what might be the ways to display suppression effect visually (its mechanics or its evidence in results)? I'd like to invite everybody who has a thought, to share.</p>
|
g49423
|
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<p>I was just curious. I was watching this movie phd comics where one of the professor says grade the papers so that it has a gaussian distribution with mean 81 and standard deviation 12.</p>
<p>I am a bit confused, to get the data to follow such distribution, I will have to change the data or the grades that I have already given. Is there a standard procedure to do this? I mean lets say I have already graded. So how can I change it to the given distribution</p>
|
g73210
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<p>I'm examining the effect of 3 different interventions on a DV with age and gender included in my model. Now, I'm curious as to whether I could apply the exact same analyses to test for non-inferiority? Specifically, as I examine the ANOVA table, I am provided with the adjusted mean difference between Intervention2 and intervention1 (and Intervention3 and Intervention1 for that matter). Am I correct in thinking that I could use these differences + the standard errors (also in the ANOVA table) to construct 95% CI of the difference in the means (again, between I1 and I2 and I1 and I3) to test for non-inferiority after deciding upon a suitable non-inferiority threshold?</p>
|
g35483
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<p>If I have some fixed non-recurrent (DAG) topology (fixed set of nodes and edges, but the learning algorithm can vary the weight on the edges) of sigmoid neurons with $n$ input neurons which can only take strings in $\{-1,1\}^n$ as input and lead to one output (that outputs a real value that we round up to 1 or down to -1 if it is a certain fixed threshold away from 0). Is there any fast way to compute (or approximate) the VC-dimension of this network?</p>
<hr>
<h3>Notes</h3>
<p>I asked a slightly more precise algorithmic reformulation on CS.SE:</p>
<p><a href="http://cs.stackexchange.com/q/1504/55">Efficiently computing or approximating the VC-dimension of a neural network</a></p>
|
g46854
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] |
<p>I have a list of (x,y) pairs that form a cluster of points. I was able to find the mean of the cluster, but I'd like to be able to find the standard deviation of the cluster. How can I define the standard deviation? I defined the mean as the point (mean of x values, mean of y values). </p>
<p>What type of standard deviation value is typical for clusters like this? I'd imagine I could get a standard deviation of the spread, or something like that?</p>
<p>This looks good. Gaussian on a cluster:</p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/EM-Gaussian-data.svg/500px-EM-Gaussian-data.svg.png" alt="Gaussian Data"></p>
<p><strong>How do I do this?</strong></p>
|
g73211
|
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] |
<p>$\rho$ here has been termed a linear correlation. </p>
<p>Does this correlation imply a structural or population correlation between two variables X and Y ?</p>
|
g35484
|
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<p>I am somehow unsure on the best option to analyze these data.
Here is my study case:</p>
<p>The response variable is a morphometric measure, one for each individual.</p>
<p>During 10 years, say 2000-2009, people went to the field to collect data (the response variable) during two specific months (always the same along the study period) on a variable number of occasions. For instance, in 2000 data came from three surveys made on days 4, 40, and 56, in 2001 data came from two surveys made on days 10 and 49, in 2002 data came from four surveys made on days 2, 34, 45, and 60, and so on. Day number is equal to 1 when made the first day of the specific two-months interval and it is equal to 60 when made the last day of that two-months interval. The number of observations (measures from individuals) is not the same for each survey but an individual is never sampled twice. Also, for each year I have a unique value of three environmental variables - I am interested in seeing if these interact with my response variable.</p>
<p>Thus, my predictors are on one hand, the day from which measures came, and on the other the environmental variables.</p>
<p>As you can see, the study is quite unbalanced.</p>
<p>I would attempt to analyze these data by using a mixed-effects model where the response variable depends on the day plus the three environmental variables and the random factor would be survey (numbered from 1 for the first survey in 2000 and, say, 49 for the last survey in 2009) nested under year. In <code>R</code> the <code>nlme</code> code is:</p>
<pre><code>mixmod <- lme(morph ~ poly(day) + env1 + env2 + env3, random=~1|year/survey, data=data)
</code></pre>
<p>Where <code>poly(day)</code> tests for the linear and quadratic effect of <code>day</code> and where <code>env1</code>, <code>env2</code>, and <code>env3</code> are the environmental variables, and the random structure refers to survey number nested to year. I have checked the normality and homoskedasticity of residuals.</p>
<p>I would really appreciate any commentary and suggestion on this.</p>
|
g73212
|
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] |
<p>What formula is used in the standard deviation function <code>sd</code> in R? </p>
|
g73213
|
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<p>I am trying to run survival analysis using the <code>Surv</code> and <code>survfit</code> functions from the <code>survival</code> package in R. Most of my data is left truncated, and I'm not sure if I'm entering it into the <code>Surv</code> function correctly. My response variable is time (measured in years) beginning from when a bridge is classified as deficient, and ending when it collapses. I can track each bridge's deficiency status from 2012 back to 1992, but no further. The censoring occurs because many bridges were classified as deficient from the time of their collapse back to 1992, and thus I don't know exactly when they became deficient, and therefore I don't know their true "lifetime" (number of years from deficient classification to collapse). Say for example a bridge collapsed in 1995, and was classified as being deficient in 1995, 1994, 1993, and 1992. It is possible that it was first classified as being deficient in 1992, it is also possible that it has been classified as deficient since 1984. Thus I believe my censoring is considered to be left truncated.</p>
<p>Some example data:</p>
<pre><code>Year0 = c(1992, 1992, 1999, 1992, 1993, 2007, 2005, 1992) # The years when each bridge was first observed as being deficient.
Year1 = c(1993, 1994, 2002, 1996, 2004, 2012, 2011, 2000) # The years in which each bridge collapsed
Defyears = Year1 - Year0 + 1 # The number of years for wich I can observe each bridge being deficient
time1 = Year0 - 1992 # Since I want the time scale to be from 0 to 21 instead of 1992 - 2012, I subtract 1992 from each time observation.
# This now becomes the beginning point for the lifetime of each bridge.
time2 = Defyears + time1 # This is the ending point of the lifetime of each bridge.
n = length(time2)
</code></pre>
<p>Notice that four out of the eight bridges are left truncated, bridge 1, 2, 4, and 8. I cannot observe exactly when they were first classified as being deficient. For bridges 3, 5, 6, and 7 I know their exact lifetimes since they became deficient after 1992, hence these observations are not censored.</p>
<p>I then fit the model:</p>
<pre><code>bridges = survfit(Surv(time = time1, time2 = time2, event = rep(1,n)) ~ 1) # I do "event = rep(1,n)" because each bridge collapsed.
</code></pre>
<p>I'm just not sure that this model is correct. For one thing, in the documentation it says that <code>time</code> is for right censored data or the starting time for interval censored data. For another, I don't see how this model accounts for the observations that aren't censored. Can anyone tell me if this is right, and if not, what I need to change and why. Any help is greatly appreciated. Thanks so much!</p>
|
g73214
|
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] |
<p>I am studying Statistics for business at introductory level, and having difficulty in handling the amount of information, partly because I am coming back to study after 5 years and I didn't do much stats at school.</p>
<p>I don't understand binomial distribution, inference and all the types of "errors" on my textbook. I did pretty well on the first 2 assignments, based on the excel templates provided by the course and some common-sense thinking.</p>
<p>My question is What are some key points that I should know about statistics? Would appreciate any help.</p>
|
g37946
|
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] |
<p>How does one calculate Cohen's d and confidence intervals after logit in Stata?</p>
|
g73215
|
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<p>hi all recently there was a ML-like question over on cstheory stackexchange & I posted an answer recommending powells method, gradient descent or genetic algorithms or other <a href="http://en.wikipedia.org/wiki/Approximation_algorithm">"approximation algorithms".</a> in a comment someone told me these methods were "heuristics" and <em>not</em> "approximation algorithms" and frequently did not come close to the theoretical optimum (because they "frequently get stuck in local minima").</p>
<p>my question, do others agree with that? also it seems to me there is a sense in which heuristic algorithms can be guaranteed to come close to theoretical optimums if they are set up to explore a large part of the search space (eg setting parameters/step sizes small), although I havent seen that in a paper. does anyone know if this has been shown or proven in a paper somewhere? (if not for a large class of algorithms maybe for a small class say NNs etc)</p>
|
g36742
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] |
<p>I have 6 similarity matrices reflecting the proximity of 100 pairs of sounds. Similarity indices are in the range [0,1], with higher values indicating sounds perceived as more alike. What is the most appropriate metric I can use to estimate the inter-rater reliability between them?
Thanks a lot.</p>
|
g37488
|
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<p>I've been asked a question - if I calculate some sd, can I change one value and still keep the same sd.</p>
<p>The answer is simply yes. For example: </p>
<pre><code>sd(c(2,3,4))
sd(c(3,4,5))
</code></pre>
<p>But what I wondered then is, assuming you change k values, under what rules do you change them so to always keep the same sd (is it true to ask what are the degrees of freedom here?!)</p>
<p>I am not sure how this applies to anything practical, but I imagine there was a good deal of theoretical work on such questions - but I don't know where to even look for them.</p>
<p>Thanks.</p>
|
g73216
|
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<p>I've been reading a lot recently about the concept of joint regularization in computer vision. Joint regularization builds on the observation that when learning multiple related concepts, for example "cat" and "dog" the most of the useful features to classify something as "cat" should be useful to classify something as "dog". </p>
<p>So a problem specific regularization term is designed. In the case I previously explained, the regularization term encourages "sharing" of useful useful features by mixing $L_1$ and $L_inf$ regularization terms. This is called joint regularization.</p>
<p>So, my questions are:</p>
<ol>
<li>Are there other types of problems (possibly outside of computer vision) where some type of "problem
specific" regularization is used and is successful? </li>
<li>Are there other
mixes of regularization terms that have been successfully
applied?</li>
</ol>
|
g35491
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<ul>
<li>I have 50 text documents</li>
<li>There are 500 possible words, after a stop list has been applied</li>
<li>My term/document sparse matrix is therefore 50x500</li>
</ul>
<p>I'd like to cluster these documents. One easy way to do this would be via k-means but that requires giving each document co-ordinates on a 2-d graph.</p>
<p>I've heard that I can reduce the 500-word long vectors per document using dimensionality reduction, specifically PCA. </p>
<p>Is it realistic that I could just reduce my 50x500 matrix to a 50x2 table and plot those values?</p>
|
g73217
|
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] |
<p>Trying to build a specific Neural Network arcitecture and testing it using 10 fold cross validation of a dataset.</p>
<p>Now building the model is a tedious job and Weka expects me to make it 10 times for each of the 10 folds.</p>
<p>Can't I just make the model for the first fold and ask weka to use that same model for the remaining 9?</p>
<p>Also, since building neural networks in weka is so easy, can I import a neural network structure to matlab for further use?</p>
|
g73218
|
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<p>"On the Behrens–Fisher Problem: A Review" by Seock-Ho Kim and Allen S. Cohen</p>
<p><em>Journal of Educational and Behavioral Statistics</em>, volume 23, number 4, Winter, 1998, pages 356–377</p>
<hr>
<p>I'm looking at this thing and it says:</p>
<blockquote>
<p>Fisher (1935, 1939) chose the statistic $$ \tau = \frac{\delta-(\bar x_2 - \bar x_1)}{\sqrt{s_1^2/n_1+s_2^2/n_2}} = t_2\cos\theta - t_1\sin\theta $$ [where $t_i$ is the usual one-sample $t$-statistic for $i=1,2$] where $\theta$ is taken in the first quadrant and $$ \tan\theta = \frac{s_1/\sqrt{n_1}}{s_2/\sqrt{n_2}}.\tag{13} $$ [ . . . ] The distribution of $\tau$ is the Behrens–Fisher distribution and is defined by the three parameters $\nu_1$, $\nu_2$, and $\theta$,</p>
</blockquote>
<p>The parameters $\nu_i$ had earlier been defined as $n_i-1$ for $i=1,2$.</p>
<p>Now the things that are unobservable here are $\delta$ and the two population means $\mu_1$, $\mu_2$, whose difference is $\delta$, and consequently $\tau$ and the two $t$-statistics. The sample SDs $s_1$ and $s_2$ are observable and are used to define $\theta$, so that $\theta$ is an observable statistic, not an unobservable population parameter. Yet we see it being used as one of the parameters of this family of distributions!</p>
<p>Could it be that they should have said the parameter is the arctangent of $\dfrac{\sigma_1/\sqrt{n_1}}{\sigma_2/\sqrt{n_2}}$ rather than of $\dfrac{s_1/\sqrt{n_1}}{s_2/\sqrt{n_2}}$?</p>
|
g73219
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<p>I'm somewhat new to using logistic regression, and a bit confused by a discrepancy between my interpretations of the following values which I thought would be the same: </p>
<ul>
<li>exponentiated beta values </li>
<li>predicted probability of the outcome using beta values. </li>
</ul>
<p>Here is a simplified version of the model I am using, where undernutrition and insurance are both binary, and wealth is continuous:</p>
<pre><code>Under.Nutrition ~ insurance + wealth
</code></pre>
<p>My (actual) model returns an exponentiated beta value of .8 for insurance, which I would interpret as:</p>
<blockquote>
<p>"The probability of being undernourished for an insured individual is .8 times the probability of being undernourished for an uninsured individual."</p>
</blockquote>
<p>However, when I calculate the difference in probabilities for individuals by putting in values of 0 and 1 into the insurance variable and the mean value for wealth, the difference in undernutrition is only .04. That is calculated as follows: </p>
<pre><code>Probability Undernourished = exp(β0 + β1*Insurance + β2*Wealth) /
(1+exp(β0 + β1*Insurance + β2*wealth))
</code></pre>
<p>I would really appreciate it if someone could explain why these values are different, and what a better interpretation (particularly for the second value) might be. </p>
<hr>
<p><strong>Further Clarification Edits</strong><br>
As I understand it, the probability of being under-nourished for an uninsured person (where B1 corresponds to insurance) is:</p>
<pre><code>Prob(Unins) = exp(β0 + β1*0 + β2*Wealth) /
(1+exp(β0 + β1*0+ β2*wealth))
</code></pre>
<p>While the Probability of being under-nourished for an insured person is:</p>
<pre><code>Prob(Ins)= exp(β0 + β1*1 + β2*Wealth) /
(1+exp(β0 + β1*1+ β2*wealth))
</code></pre>
<p>The odds of being undernourished for an uninsured person compared to an insured person is:</p>
<pre><code>exp(B1)
</code></pre>
<p>Is there a way to translate between these values (mathematically)? I'm still a bit confused by this equation (where I should probably be a different value on the RHS):</p>
<pre><code>Prob(Ins) - Prob(Unins) != exp(B)
</code></pre>
<p>In layman's terms, the question is why doesn't insuring an individual change their probability of being under-nourished as much as the odds ratio indicates it does? In my data, Prob(Ins) - Prob(Unins) = .04, where the exponentiated beta value is .8 (so why is the difference not .2?) </p>
|
g49286
|
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<p>I am confuse to either use a t-statistic or white-robust-t test as t-statistic is for homoskedastic and white-robust-t is for heteroskedastic error. Which test should i use after data with heteroskedastic has been corrected using e-views?</p>
<p>This is the data before correcting the errors for heteroskedasticity</p>
<pre><code>Dependent Variable: LOG_WAGE
Method: Least Squares
Sample: 1 514
Included observations: 514
Variable Coefficient Std. Error t-Statistic Prob.
C 1.758689 0.099402 17.69275 0.0000
EDUC 0.089089 0.007015 12.69990 0.0000
EXPER 0.041822 0.004884 8.562720 0.0000
EXPER^2 -0.000737 0.000109 -6.784465 0.0000
R-squared 0.330308 Mean dependent var 3.237487
Adjusted R-squared 0.326369 S.D. dependent var 0.505323
S.E. of regression 0.414744 Akaike info criterion 1.085441
Sum squared resid 87.72638 Schwarz criterion 1.118454
Log likelihood -274.9583 Hannan-Quinn criter. 1.098380
F-statistic 83.84807 Durbin-Watson stat 1.812307
Prob(F-statistic) 0.000000
</code></pre>
<p>This is the data after correcting</p>
<pre><code>Dependent Variable: LOG_WAGE
Method: Least Squares
Sample: 1 514
Included observations: 514
White heteroskedasticity-consistent standard errors & covariance
Variable Coefficient Std. Error t-Statistic Prob.
C 1.758689 0.102406 17.17369 0.0000
EDUC 0.089089 0.007513 11.85735 0.0000
EXPER 0.041822 0.004687 8.923171 0.0000
EXPER^2 -0.000737 0.000104 -7.101447 0.0000
R-squared 0.330308 Mean dependent var 3.237487
Adjusted R-squared 0.326369 S.D. dependent var 0.505323
S.E. of regression 0.414744 Akaike info criterion 1.085441
Sum squared resid 87.72638 Schwarz criterion 1.118454
Log likelihood -274.9583 Hannan-Quinn criter. 1.098380
F-statistic 83.84807 Durbin-Watson stat 1.812307
Prob(F-statistic) 0.000000
</code></pre>
<p>I need to do a a hypothesis testing is there any non-linear relationship between the variables. I am just confused which test i should use. </p>
|
g35493
|
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] |
<p>I am interested in knowing if the duration of treatment has an effect on treatment with two different drugs. We have used two different drugs to treat cerebral ischemia (brain damage) and continued the treatment for 30 days. We have observed the effects in terms of behavioral scores (quantitative data) at days 1, 3, 7 15 and 30 days post treatment and are interested in knowing the following three things: </p>
<ol>
<li>which is the time period where drug A and drug B (two separate groups) was maximally effective</li>
<li>in which time period is the difference between drug A and drug B maximal and minimal and if the difference is statistically significant (for example is the difference maximal in the period between days 3 and day 7) </li>
<li>from the data can we determine that a particular drug only needs to be given for a fixed length of time (say for 15 days), as there is no significant improvement after this. </li>
</ol>
<hr>
<p><strong>Edit: Sample data</strong><br>
This is not the actual data as the actual data looks a bit less fancier and may not be easy to understand the concept.</p>
<pre><code>+----------+----------+----------+----------+
|Time point|Score drug|Score drug| Control|
|(days post| A| B| |
| surgery)| | | |
+----------+----------+----------+----------+
| 1| 36| 32| 44|
+----------+----------+----------+----------+
| 3| 28| 30| 42|
+----------+----------+----------+----------+
| 7| 24| 29| 38|
+----------+----------+----------+----------+
| 14| 20| 24| 32|
+----------+----------+----------+----------+
| 30| 12| 18| 25|
+----------+----------+----------+----------+
| 60| 11| 15| 19|
+----------+----------+----------+----------+
| 120| 10| 14| 17|
+----------+----------+----------+----------+
| 150| 9| 13| 15|
+----------+----------+----------+----------+
</code></pre>
|
g73220
|
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] |
<p>I have cross-sectional regression model $\hat{Y}_i = a + bX_i + e_i$ estimated over 200 cross-sectional observations. The $\hat{Y}_i$'s were generated in 200 time series regressions, and so has measurement error. Suppose that the measurement error can be modeled by $\hat{Y}_i = Y_i - u_i$, with $u_i \sim N(0,\sigma^2)$. Then we have $Y_i - u_i = a + b X_i + e_i$ ..$\Rightarrow$.. $Y_i = a + b X_i + (e_i + u_i) = Y_i = a + b X_i + \epsilon_i$, where $(e_i + u_i) = \epsilon_i$. This means the diagonal of the residual variance covariance matrix is larger. The variance covariance matrix is given by $\Sigma = E[\epsilon \epsilon^T]$; under this expression, every element of the diagonal in $E[\epsilon \epsilon^T]$ is larger than every diagonal element of $E[e e^T]$. Given the formula for the coefficient variance covariance matrix, the coefficient SEs will be larger from $E[\epsilon \epsilon^T](X^T X)^{-1}$ than from $[e e^T](X^T X)^{-1}$, leading to more abundant type 2 errors.</p>
<p>Another way to express this problem is as follows. Assume that $u_i$ and $e_i$ are uncorrelated, we have $var(e_i + u_i) = var(\epsilon_i) = \sigma_e^2 + \sigma_u^2 > var(e_i) = \sigma_e^2$ ... Our coefficient standard errors will be incorrectly large..</p>
<p>Slide 4 of <a href="http://www.arts.uwaterloo.ca/~krybczyn/321/321w12p2.pdf" rel="nofollow">THIS</a> describes the issue (but gives no prescriptions). </p>
<p>So, what estimator do I use to reduce the instance of weak power/large type 2 errors in this econometric model? </p>
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<p>Students have completed a test containing 20 questions at both T1 and T2, with an intervention in the interval. Scores for each question are either 0 (incorrect) or 1 (correct). I am interested in knowing whether the improvement in students' scores was significantly greater for some questions than for others. I am thinking that this may involve an extension of the McNemar test, but open to all suggestions. Thanks!</p>
|
g73222
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<p><strong>Question:</strong> Assume we have the following equation:</p>
<p>$$\widehat{\Theta}(\rho) = \frac{1}{(1-\rho)\Delta t} \ln\left(\frac{1}{T} \sum_{t=1}^T \left(\frac{1+r_t}{1+rf_t}\right)^{1-\rho} \right) \ \ \ \ \cdots \ (1)$$</p>
<p>where:</p>
<p>$T =$ total number of observations</p>
<p>$\Delta t =$ length of time between observations</p>
<p>$r_t =$ a variable with random values at each $t$</p>
<p>$rf_t =$ a variable with random values at each $t$</p>
<p>$\rho =$ a constant 'coefficient'</p>
<p>(Note: for those familiar with finance terminology, $r_t$ is an asset's return at time $t$ and $rf_t$ is the risk-free rate at time $t$.)</p>
<p>Computing $\widehat{\Theta}$ does not require any specific distribution for $r_t$ or $rf_t$. I have a large sample of data (i.e, $T = 162,401$) for $r_t$ and $rf_t$. </p>
<p>Now define $\hat{\rho}$ where $\hat{\rho}$ satisfies $\widehat{\Theta}(\hat{\rho}) = 0$. Solving for $\hat{\rho}$ is relatively straightforward using Newton–Raphson method or other linear optimization methods. My aim is to derive the asymptotic distribution for $\hat{\rho}$, that is, as $T \rightarrow \infty$:</p>
<ol>
<li><p>What can we say about the asymptotic distribution of $\hat{\rho}$? </p></li>
<li><p>Can we derive a particular distribution to which it converges to? </p></li>
<li><p>Can we derive it's asymptotic variance/mean? </p></li>
<li><p>What other asymptotic properties can we derive?</p></li>
</ol>
<hr>
<p><strong>Attempt:</strong> My attempt so far has been related to a 2nd order linear approximation to Eqn.$(1)$ rather than working directly with Eqn.$(1)$. Using Taylor series expansion and properties of the <a href="http://en.wikipedia.org/wiki/Generalized_mean" rel="nofollow">Generalized Mean</a>, we can show that:</p>
<p>$$\widehat{\Theta}(\rho) \approx \frac{1}{\Delta t} \left[\overline{x} + \frac{1-\rho}{2} \left(s_x^*\right)^2\right] \ \ \ \ \ \cdots \ (2)$$</p>
<p>where:</p>
<p>$\overline{x} = \frac{1}{T} \sum_{t=1}^T x_t$ where $x_t = r_t - rf_t$</p>
<p>$\left(s_x^*\right)^2 = \left(\frac{T-1}{T}\right)s_x^2$ where $s_x^2 = \frac{1}{T-1}\sum_{t=1}^T (x_t - \overline{x})^2$</p>
<p>From Eqn.$(2)$, an approximation to $\hat{\rho}$ is given by:</p>
<p>$$\hat{\rho} \approx \frac{2\overline{x}}{\left(s_x^*\right)^2} +1 $$</p>
<p>Since there is no closed form solution to $\hat{\rho}$ from Eqn.$(1)$, how can we derive 'approximate' asymptotic properties of $\hat{\rho}$ using Eqn.$(2)$? </p>
|
g73223
|
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] |
<p>There is some confusion with respect to the measurement error. What is the definition in statistics and definition in psychometry ? The statistics does not seem to recognize the measurement error popularly called construct bias in psychometry.</p>
|
g73224
|
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] |
<p>I would like to know if it is valid to use a mixed effects model to analyze nested data where the lowest units of the hierarchy were <em>not</em> sampled randomly but are adjacent to each other spatially in a grid. Biologically, spatially adjacent sampling units can experience different conditions, but they might also be very similar. </p>
<p><strong>Details of the experiment:</strong><br>
I am analyzing data from a forestry experiment where we counted the number of tree seedlings in 12 m x 12 m plots. We have 10 plots, five that were fenced to exclude herbivores and five that were unfenced controls. For survey purposes each plot is divided into 36 subplots that are 2 m x 2m. The number of seedlings per subplot varies from 0 to >150, is poisson distributed and probably zero inflated. The plots in which the subplots are nested can therefore vary in two respects: the total number of seedlings summed across all subplots, and the number of subplots that have at least one seedling in them.</p>
<p>A single plot looks something like this, where each letter represents a 2 x 2 subplot:</p>
<pre><code>a b c d e f
g h i j k l
m n o p q r
s t u v w x
y z & @ # A
B C D E F G
</code></pre>
<p><strong>Questions:</strong><br>
*<em>1)</em>*Is it valid to analyze this data at the subplot level and use plot as a random effect, or does the spatial aggregation of the data require me to analyze it at the plot level?<br>
*<em>2)</em>*Could I represent the spatial aggregation of the subplots by adding another level to the hierarchy by grouping adjacent subplots together with another random effect (eg, grouping the above subplots a, b, c, g, h, i, and m, n, o together). </p>
|
g46866
|
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<p>I'm trying to analyse some data I've recently gotten my hands on, but I'm not entirely sure which model to use. One suggestion has been a Mixed Model, Repeated Measurements ANOVA, but I'm not sure if that such kind of model can answer the questions of interest.</p>
<p><strong>The data</strong>:
Two individual persons (A and B) have had a lot of different values (V1, V2, V3, ..., Vn) measured four times (At T0, T1, T2 and T3) - The spacing between times differs.</p>
<p>The different values have been grouped into categories (C1, C2, C3, ..., Cn). One value may belong to none, one or multiple categories. Each of the categories have a continuos value (Response_C1,Response_C1, ..., Response_Cn), which is the sum of the measured values belonging to that category. </p>
<p>In addition to this, person B was given a drug at T1.</p>
<p>What I would like to investigate now, is:</p>
<ol>
<li>Is there any observable effect after administering the drug</li>
<li>On which categories did the drug have an effect</li>
<li>If there is an effct on a category, what is the effect size</li>
<li>How does the effect vary over time</li>
<li>If there is an effect, is the effect observed from the drug at T1 still persistant at T3</li>
</ol>
<p>I realise one of the major pitfalls is the lack of both time points and samples, but it would be appreciated if you could suggest any articles/methods for this type of analysis.</p>
<p><strong>What I have tried so far</strong> is just Repeated Measurements ANOVA, using R:</p>
<pre><code>test.aov <- aov(Response_C ~ Category * Timepoint * Treatment + Error(Sample), data=df)
</code></pre>
<p>But I am not sure that the model is correct, neither am I sure that it actually answers my questions, even if I try to model it as a mixed model. </p>
<p>Any help is much appreciated. Please let me know if any additional information is needed</p>
<p><strong>Edit 1:</strong> After doing some more reading, it seems a Generalised Linear Model with a negative binomial distribution (since this kind of data is usually over-dispersed) might be better suited for this kind of data, but I'm still not sure if such a model would answer the questions. Potentially I could fit a model to each individual category, but that would inflate the Type-I error I guess, and so we would need to correct for multiple testing.</p>
<p><strong>Edit 2:</strong> Some more reading, and I thought the <code>lme4</code> R package would be a good way to fit a Linear mixed model to my data, and just do individual comparisons of each category. Here's the model I tried to fit:</p>
<pre><code>lm1 <- lmer(Response ~ Treatment * Timepoint + (1|Subject), data=my_data)
</code></pre>
<p>First off, I'm not sure whether Timepoint should be a factorial or a numerical value. As I mentioned, timepoints are not evenly distributed (To be precise, I have for time 0, 2days, 14 days, 90days), however, the design is balanced. If I enter the Timepoints as a numerical value, I don't get any estimate of what the value is at any given Timepoint, but just some numbers for Correlation of fixed effects, which I can't really use for anything. On the other hand, if I enter the Timepoints as factors, I do get an estimated value for the effect at each timepoint, but I'm not too sure how certain or reliable this value is.</p>
|
g73225
|
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] |
<p>I recently received the following email:</p>
<blockquote>
<p>I have a sample of 100 and approximately 6-7% missing data on each independent variable of interest, and non-normally distributed IVs. I have square root transformed the non-normal IVs so I could use EM imputation in SPSS to impute missing data. I then back transformed the variables by squaring them.</p>
</blockquote>
<h3>Questions</h3>
<ul>
<li>Is it necessary to make variables normally distributed in order to use EM imputation either in SPSS or in general?</li>
<li>Does it make sense then to back transform variables after imputation?</li>
</ul>
|
g73226
|
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<p>I'm trying to model a dose-response relationship between the incidence of cancer (dependent variable, counts) and the radiation dose (independent variable in gray). Can I change the unit of the independent variable from gray to milligray (gray × 1000) and have the same response? </p>
<p>I have built two models, 1 with independent variable as gray, and the second model with gray × 1000 as the independent variable. Should the model have similar parameter estimates, just different by a factor of 1000?
I have tried this, and my parameter for dose-response in two separate models goes from 1.000764 per milligray to 2.14 per gray.</p>
|
g73227
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<p>I have 2 independent variables with distributions: $X \sim \text{beta}(\alpha_1,\beta_1)$ and $Y \sim \text{beta}(\alpha_2,\beta_2)$</p>
<p>I would like to estimate $P(X * Y >= \text{val})$, and I am looking for a simple method, possibly approximation, so that I won't need to work with product of distributions. </p>
<p>What are the possible (simple) approaches to solve this problem?
I can probably simplify the question to accepting/rejecting the assumption of whether $X*Y=\text{val}$ with 95% confidence but I am not sure if it helps.</p>
<p>Sorry if the question is stupid, i just started learning statistics.</p>
|
g73228
|
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<p>I have been looking for examples of the TIC and couldn't find any. In particular I would like to know how exactly do you estimate the penalty term in TIC. That term consists of, as I found it somewhere, score function and Fisher information.
Are there any online resources where I can find that?</p>
|
g73229
|
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<p>I am reading a paper on "multi-SNP" GWAS data analysis method,
The author fitted a linear model $y = \beta_g g + \epsilon$, where $g$ is a genotype vector for a single gene, $\beta_g$ is the true regression coefficient, $\epsilon$ is the error, assuming the regression line goes through the origin. Let $\hat{y}$, $b_g$, $s^2(g)$ and $s^2(y)$ be the estimate of $y$, $\beta_g$, $\sigma^2(g)$ and $\sigma^2(y)$ respectively, since the intercept $b_{g0} = \overline{y} - b_g \overline{x} = 0$, we have $\overline{y} = b_g \overline{x}$, it follows that</p>
<p>\begin{align*}
SSR &= \sum (\hat{y} - \overline{y})^2 \\
&= \sum (b_g g_i - \overline{y})^2 \\
&= \sum(b_g g_i - b_g \overline{g})^2 \\
&= b_g^2 \sum (g_i - \overline{g})^2 \\
&= b_g^2 s^2(g)(n-1)
\end{align*}
\begin{align}
r^2 &= \frac{SSR}{SSR + SSE} \notag\\
&= \frac{b_g^2 s^2(g)(n-1)}{b_g^2 s^2(g)(n-1) + s^2(y)(n-1)} \notag\\
&= \frac{b_g^2 s^2(g)}{b_g^2 s^2(g) + s^2(y)}
\end{align}.</p>
<p>The equation above is quite similar to what the author offers in his first equation, but they essentially different unless the author has been confused about true and estimated quantities. The second equation about $\hat{r^2}_{locus}$ totally escapes my comprehension, any help will be appreciated.</p>
<h2><a href="http://www.ncbi.nlm.nih.gov/pubmed/23122585"><strong>The original article can be found here</strong></a></h2>
<p><img src="http://i.stack.imgur.com/6GaxO.png" alt="enter image description here"></p>
|
g49392
|
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] |
<p>Our code goes through multiple stages of review. I wish to use the number of defects at an earlier stage of review as a "defect density" estimate for later stages.</p>
<p>It sometimes happens that code has zero defects in the early stage of review. This is causing me trouble since if $\lambda = 0$ then $P(k)=\frac{e^{-\lambda t}(\lambda t)^k}{k!}=0$ for all $k$. </p>
<p>R does indeed just throw an error in this case:</p>
<pre><code>foo = 0:10
bar = 2 * foo
glm(bar ~ log(foo), family = poisson)
# fails because log(0) = -Inf
</code></pre>
<p>I could get around this in several ways:</p>
<ul>
<li>Ignore places with zeros (this would drop 1,486 of my 4,476 data points)</li>
<li>Replace all the zeros with some number</li>
<li>Add one to everything</li>
</ul>
<p>What's the best way to handle this?</p>
|
g73230
|
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<p>I was watching andrew ng's lecture on machine learning and I came across 'geometric margin' in the SVM lecture. I am confused about he obtained the equation for the point B ? </p>
<p><img src="http://i.stack.imgur.com/3FPNr.png" alt="enter image description here"></p>
<p>Notice that the hyperplane is the slanted line where $w^Tx + b = 0$</p>
<p>The main question: How did he obtain $$B = x^{(i)} - \gamma^{(i)} \frac{w}{||w||}$$</p>
<p>I have several questions to ask: </p>
<ol>
<li><p>is the line segment $AB$ perpendicular to the decision boundary (the hyperplane where $w^Tx + b = 0$) ? </p></li>
<li><p>The most confusing part for me is: why does he do $x^{(i)} minus$ ? What does it really mean in geometrically ? </p></li>
</ol>
<p>Thanks if someone can explain the ideas behind this . </p>
|
g73231
|
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] |
<p>I have a fairly long time-series of annual abundances ($N_t$) of a wildlife species (73 years of abundances). To forecast the population’s trajectory, I have used ARIMA modeling. Examination of the ACF and PACF of the first-order differenced time-series suggested a 10-year cycle exists. So I used a span 10 seasonal difference to account for this periodic pattern. Therefore, the response variable was:
$$
Y_t=(\sqrt{N_t}-\sqrt{N_{t-1}})-(\sqrt{N_{t-10}}-\sqrt{N_{t-11}})
$$
Typically, I would have used a logarithmic transformation but it resulted in heteroscedastic residuals. Examination of the ACF and PACF of $Y_t$ indicated a multiplicative seasonal structure so I fit the model:
$$
ARIMA(0,1,1)(0,1,1)_{10}
$$
using the Forecast Package in <code>R</code>....<code>library(forecast)</code>.</p>
<p>Example code for fitting the model:</p>
<pre><code>m1=Arima(y,order=c(0,1,1),seasonal=list(order=c(0,1,1),period=10),include.mean=FALSE)
</code></pre>
<p>The residuals of this model were normally distributed, not autocorrelated, and homoscedastic.</p>
<p>I have been using the fitted model from above for some additional simulation work using the <code>simulate.Arima</code> function. However, I would like to initialize the simulation with a different time-series. The <code>arima.sim</code> function allows this but the <code>arima.sim</code> function doesn't seem to handle seasonal ARIMA models. With the <code>simulate.Arima</code> function one can use the <code>future=TRUE</code> option to simulate values that are "future to and conditional on the data" in the model <code>m1</code>. Can the data in the model object <code>m1</code> simply be replaced to create a simulation that is conditional on different data?</p>
<p>For example:</p>
<pre><code># Create a new model object for simulation.
m.sim=m1
# Replace the data in the model object with the new data.
m.sim$x=new
# Simulation conditional on the new data.
sim.forecasts=replicate(1000,simulate.Arima(m.sim,future=TRUE,bootstrap=TRUE))
</code></pre>
|
g46874
|
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] |
<p>This is follow-up question by <a href="http://stats.stackexchange.com/q/100123/3277">"How to create item parcels in SPSS Amos?"</a>
My question is how to create item parcels for a factor that is not a unidimensional.
Several articles have mentioned that conducting item parceling only when the factor is unidimensional. I ran the EFA and found that the factor is three-dimensional.Total number of items are 10. Primary purpose of conducting item parceling is to make the parsimonious model. So, if unidimensional is necessary, I might need to find other way to make model more simple. </p>
|
g73232
|
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] |
<p>I have many thousands of event types. Some very frequent, but most fairly infrequent. I want to identify events types that could be related by virtue of the fact that they occur relatively closely in time. I'd like to be able to tune the correlation detection to be very liberal to very conservative.</p>
|
g73233
|
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] |
<p>What is a good metric for assessing the quality of a pca? I performed this algorithm on a dataset. My objective was to reduce the number of features (the information was very redundant). I know the percentage of variance kept is a good indicator of how much information we keep, be are there other information metrics I can use to make sure I removed redundant information and didn't 'lose' such information?</p>
|
g73234
|
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<p>I have two different models measuring the risk (categorical variable) of a particular variable. I want to statistically compare these two methods to find out how much different they are in their risk calculations. So, to give an example, I will have three only variables, 'A' (for which risk is calculated), variable 'B' & 'C' (categorical variable for risk from two models). B & C will have values "High", "Low" and "Medium". Can you suggest a good statistical models to do this if possible?</p>
|
g73235
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<p>Background: This is the costfunction of <a href="http://www.public.asu.edu/~jye02/Software/MALSAR/MTL-SDM12.pdf" rel="nofollow">Mean Regularized Multi Task Learning</a>.
This is a typical linear regression learning model, with the only difference being that there's multiple instances of trainings going on at the same time. So X has an additional 3rd dimension and W and Y a 2nd dimension.
X is training data, Y is targets, W is weights, m is number of tasks (3rd dimension), d is number of features, n is number of examples.</p>
<p>$X\in R^{n_i\times d \times m}$,
$Y\in R^{n_i\times m }$,
$W\in R^{d \times m}$</p>
<p><img src="http://i.stack.imgur.com/nzPg4.png" alt="enter image description here"></p>
<p>Question:
Given the cost function</p>
<p>$$
J =\min_W \frac{1}{2}||XW-Y||_F^2+\lambda\sum_{i=1}^m||W_i-\frac{1}{m}\sum_{s=1}^mW_s||^2_2
$$
What is
$\frac{\partial}{\partial W}J$?</p>
<p>I need to calculate the partial derivatives that can be used with steepest gradient descent optimization algorithm. I was thinking of calculating the derivative both with respect to a single weight, and the whole matrix. See my answer for my calculations so far.</p>
|
g35508
|
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] |
<p>Suppose I am testing the effectiveness of a new piece of machinery. The current machine has a success rate of 20%, that is, for every hundred widgets produced, 20 can be sold.</p>
<p>Now I've developed a new prototype and I want to know if it performs better. Additionally, it only makes sense to invest in the new machine if it is 10% better, i.e. a 22% success rate.</p>
<p>So I set up an experiment and collect this data:</p>
<pre><code>machine attempts successes
---------------------------------
Original n1 k1
Prototype n2 k2
</code></pre>
<p>Assume that<br>
* <code>alpha</code>= 5%<br>
* <code>beta</code>= 20%<br>
* I'd like to use the smallest sample size possible.</p>
<p>My understanding is that normally I'd want a 2-tailed difference of proportions test. But that test would only tell me if the two machines performed differently, not if one was 10% or more better. </p>
<p>How do I determine what sample size to use, what is the appropriate test(s) to use, and how do I report the magnitude of the difference? </p>
|
g73236
|
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<p>I'm trying to figure out which ICC type to use to calculate MY measurement error using a particular assessment tool:</p>
<p>background and data:</p>
<p>PhD feasibility phase only. </p>
<p>10 pairs of videos of people doing every day tasks. Videos were scored 3 times to assess measurement error. Videos were randomly scored purposely to reduce the learning effect.</p>
<p>There is one rater (me). </p>
<p>Each pair of tasks = one complete assessment per person. </p>
<p>Linear data from an assessment that yields two scales, (raw scores go into software that uses rasch analysis, transforming data into logits). Raw scores (36 skills scored either 1,2,3 or 4) could be used but not alone, to supplement is OK. </p>
<p>I have limited time to collect data, so 10 is all I can do. I'm looking for something simple, suitable and accurate. I am happy to do 2 or 3 different stats to get an accurate measurement of my scoring consistency. </p>
<p>I've read intra-rater reliability studies that are similar, but only retest once, (rather than twice, as I have), using ICC 1 and ICC 1,2, also studies with several raters and video scoring 5 times which used ICC fixed 3.1 version. </p>
<p>Answers and advice gratefully received.</p>
|
g73237
|
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<p>Let $X_1, \dots , X_n \sim \mathrm{N}(\mu,\sigma^2)$. $\sigma^2$ is known. We want to test $\mathrm{H}_0: \mu = 0$ versus $\mathrm{H}_1: \mu > 0$.</p>
<p>For the likelihood ratio I got: $\Lambda_1 = \exp(\frac{n(\mu_0^2 - \mu_1^2)}{2 \sigma^2}) \cdot \exp(\frac{\mu_1 - \mu_0}{\sigma^2} \cdot \sum x_i)$. Where the first term is a constant. Hope this is correct.</p>
<p>Now we know that for expected value of normal randowm sample $T(X_{1:n} = \sum X_i)$ is a sufficient statistic. I have to rewrite $\Lambda_1$ as a function of $T$, which gives me $\Lambda_2$. Can I now just exchange $\sum x_i$ in $\Lambda_1$ with $T$?</p>
<p>Another question is what I can say about the rejection region of $\Lambda_1$ and $\Lambda_2$, keeping in mind that $\mu$ is zero or bigger. I do not know what is meant here...</p>
|
g73238
|
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<p>I am trying to write a code (I am using MATLAB) for estimating the goodness of fit of the copula based on a Rosenblatt transformation ( Dobrić and Schmid 2007, <a href="http://dx.doi.org/10.1016/j.csda.2006.08.012" rel="nofollow">http://dx.doi.org/10.1016/j.csda.2006.08.012</a>) my question is this:</p>
<p>In the algorithm it says: "Generate i.i.d. observations from the copula with parameter theta (I can't use <code>copularnd</code> function because it only covers a few families). If my copula is bi-variate like C(u,v, theta) how can I generate these i.i.d. observations? what will be my input to copula function?</p>
<p>Thanks</p>
|
g73239
|
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<p>I have to apologise about my lack of experience but hopefully someone can clarify things for me.</p>
<p>I am interested in looking at change in psychosocial functioning over time and compare it between those with borderline personality disorder, another personality disorder and no personality disorder. My main focus is psychosocial functioning (PF) but I also want to show that full recovery (remission of symptoms plus improvement in functioning) is harder to attain than remission of symptoms alone. </p>
<p>So I was going to do a repeated measures ANOVA. My dataset is composed of the following variables:</p>
<ul>
<li>PF is measured at 4 time points (PF1, PF2, PF3 and P4);</li>
<li>Symptoms are measured at 4 time points (S1, S2, S3, S4); </li>
<li>I can then calculate another outcome variable at time 4 that is recovery (yes or no); </li>
<li>And another outcome variable for remission (yes or no).</li>
</ul>
<p>There are three groups: BPD, OPD and NPD.</p>
<p>To test my <strong>first hypothesis</strong> I was planning on doing repeated measures ANOVA to see if change in PF was less for the BPD group than the other groups. This seems simple enough.</p>
<p>However, it is my <strong>second aim</strong> as to where I get lost. I get stuck on how to test whether rates of recovery are less than rates of remission and compare the groups on this. I hypothesize that the BPD group will find it harder to achieve recovery than remission (i.e. the rates will be significantly different), while the NPD group will have similar recovery and remission rates, and the OPD will be somewhere in between. </p>
<p>I have no idea how to achieve this without using a mixed models approach. Unfortunately I cannot go down that route because of reasons that are out of my control (and in my supervisors control) but none the less I cannot. I have to keep the analysis as simple as I can.</p>
|
g73240
|
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0.029446393251419067
] |
<p>I've heard the term PMF and discrete distribution used interchangeably. Does each term mean something different? </p>
|
g35513
|
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<p>I've been told not to trim the dependent variable in a regression, but I don't know why. It makes sense that I shouldn't select my sample based on the outcome, but what assumption does this violate? Is their a theoretical reason why I shouldn't do this? Thanks!</p>
<p>Update: By "trim" I mean discard outliers. On the right hand side it is common (at lest in financial economics) to discard or trim observations at 0.5% to 1% in either tail. I've been told that doing the same on the left hand side is taboo. But I'm not sure exactly why.</p>
<p>I don't have a specific problem in mind, I just realized that I don't know the real <em>why</em>, other than you shouldn't pick you sample based on the outcome.</p>
|
g73241
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<p>I have some reasonable idea of what directional means are in the context of spatial statistics, but I am stumped by this use of the term in the methods section of <a href="http://www.pnas.org/content/suppl/2008/12/17/0810485105.DCSupplemental/0810485105SI.pdf" rel="nofollow">this computational biology paper</a> (emphasis mine):</p>
<blockquote>
<p>The raw ES values were normalized to account for variable numbers of shRNAs across different genes by dividing the raw ES by the <strong>directional mean</strong> of a size-matched null distribution generated by 100,000 random permutations of a hairpin set of the same size.</p>
</blockquote>
<p>To sum up the relevant part: one is supposed to compute the directional mean of a distribution obtained from a set of scores (no vectors involved). </p>
<p>How would one go about getting a directional mean from a set of values (or associated density function)?</p>
<p><strong>Edit:</strong> one piece of information that <em>could</em> be relevant: the score values whose distribution is being plotted and whose "directional mean" is supposed to be extracted, are obtained through a goodness-of-fit test applied to a subset of values ("the hairpin set") out of the whole ranked list (the microarray data, converted to a list of differential expression values). </p>
<p>I also doubt the spatial aspect of the microarray data could play any role here (it's long been eliminated through pre-treatment).</p>
|
g73242
|
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<p>I already asked this question <a href="http://math.stackexchange.com/questions/552091/can-posterior-distribution-for-a-continuous-variable-be-greater-than-one">here</a>, but I am not sure where would be better to ask it? This might sound a dumb question but I am really confused about it. According to Bayes' rule we do have the following:
$$p(\theta|X)=\frac{p(\theta)p(X|\theta)}{\int{p(\theta)p(X|\theta)d\theta}}$$I know that probability density function can be greater than one in general but it seems to me because there exist discrete summations of denominator integral which would is greater than the nominator, therefore posterior probability density function cannot be greater than one in any point. Is this correct?!</p>
<p>To explain reasoning a bit in more detail:</p>
<p>Suppose we are interested in $p(\theta=\theta_0|X)$ and we know that:
$$\int{p(\theta)p(X|\theta)}d\theta\approx\sum\limits_{n}{p(\theta_i)p(X|\theta_i)}$$ but now only consider the summations which include $p(\theta_0)p(\theta_0|X)$. Then the denominator will obviously be larger than the nominator.</p>
|
g35516
|
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<p>I'm interested in learning more about nonparametric Bayesian (and related) techniques. My background is in computer science and though I have never taken a course on measure theory or probability theory, I have had a limited amount of formal training in probability and statistics. Can any one recommend a readable introduction to these concepts to get me started?</p>
|
g73243
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<p>I am trying to model future sales data for products which have very low sales volume. I am a programmer with a smattering in statistics, so I apologise in advance if this qustion is naive!</p>
<p>My question is what distribution is most suitable for my sales profile and is it possible to verify the distribution. The exact framing of the problem is that we might have a product that has say 6 units of inventory and we may sell 8 units a year with a "standard deviation" of 5 units (i.e. the sales are lumpy so we calculate a standard deviation, but its not really a normal distribution)...we want to say with a certain probability how many days inventory we have left. For high volume products we can assume the normal distribution and its pretty easy to back out the days inventory left. However for low volume products we can't assume normal distribution (as obviously it is bounded by the fact that we can't have less than 0 sales). I have looked at Poisson, but I am not sure if that is the most suitable.</p>
<p>Could someone point me to some resources that would help me identify the right model/technique to use? </p>
<p>Thanks,</p>
<p>Mike.</p>
|
g35521
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] |
<p>What is the difference between the intuition behind Gamma and Weibull distributions? Is there any relationship between the two densities ?</p>
<p>Kindly help.</p>
|
g35522
|
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<p>I need to validate a model using `external model validation' and I have a question relating to deciding when a drop in $R^2$ when compared to $R_{prediction}^2$ is significant. </p>
<p><strong>DISCLOSURE</strong>: This is not a homework question. I am seeking clarification on something that is in the textbook that I am using for an applied regression class (textbook: A second course in statistics: regression analysis).</p>
<p>I have model whose goal is to predict $y$ from a set of covariates. The model has already been fit and I would like to validate the model using new data. My textbook states the following:</p>
<p><strong>FROM MY TEXTBOOK</strong> One simple technique is to calculate the percentage of variability in the new data explained by the the model, denoted $R_{prediction}^2$, and compare it to the coefficient of determination $R^2$ for the least squares fit of the final model. Let $y_1, y_2, ..., y_n$ represent the $n$ observations used to build and fit the final regression model and $y_{n+1}, y_{n+2}, ..., y_{n+m}$ represent the $m$ observations in the new data set. Then $$R_{prediction}^2= 1 - \left(\frac{\sum\limits_{i=n+1}^{n+m}\left(y_i - \hat{y_i}\right)^2}{\sum\limits_{i=n+1}^{n+m} \left(y_i - \bar{y} \right)^2}\right)$$ where $\hat{y_i}$ is the predicted value for the $i$th observation using the $\beta$ estimates from the fitted model and $\bar{y}$ is the sample mean of the original data. If $R_{prediction}^2$ compares favorably to $R^2$ from the least squares fit, we will have increased confidence in the usefulness of the model. However if a significant drop in $R^2$ is observed, we should be cautious about using the model for prediction in practice. (Page 316)</p>
<p><strong>MY QUESTION</strong> Unfortunately, this is all the textbook says about using this technique and I have no idea how I would go about determining if a significant drop occurred. For my model I have an $R^2$ of 0.8283 and using the technique described in the text, I have a calculated $R_{prediction}^2$ of 0.7444. Could anyone point me into the direction of other sources that would be able to describe the method of determining whether or not this is a significant drop---I performed several google searches but the results have not turned up anything useful.</p>
<p>Thank you for taking the time to read my question.</p>
|
g73244
|
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0.04152606055140495,
0.03589770570397377
] |
<p>I am working to approximate, to extrapolate rather, values of a function from a few known values. Here is what I have:</p>
<ol>
<li>Less than 100 known I/O pairs.</li>
<li>A monotonously positive correlation.en</li>
<li>Something that is not exactly Gaussian, Poisson, or inverse binomial.</li>
</ol>
<p>Right now I can choose between a genetic algorithm and an artificial neural network. If I use a genetic algorithm, then I will use it to approximate the relation with a polynomial or a rational function. If I use a neural network, I will simply find the first Google result for a C++ NN library (unless I am advised otherwise).</p>
<p>Here are my questions. Suppose I have access to a long time (1-2 week max) as well great computational might (university clusters).</p>
<ol>
<li>Would I achieve a closer approximation with a GA or an ANN?</li>
<li>Which would be faster?</li>
<li>For those ANN specialists out there: I am unacquainted with the world of ANN technology. If I am looking for portability, programmability, speed, and adaptability for such extrapolation, which C++ toolkit would you recommend?</li>
</ol>
<p>Thank you.</p>
|
g855
|
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<p>I need a hint for solving the following problem. The movement of a certain robot is modeled with a HMM. The robot moves on a circular path and at every time step, it either stays in the same location with $\epsilon$ probability or moves to the next location, with $1-\epsilon$ probability (CCW). Each location of the corridor is labeled from $1$ to $N$ and the robot has a sensor telling whether the current location has a prime label or not. The sensor works correctly with $\delta$ probability. It is known that the robot starts at a non-prime location.</p>
<p>I am asked to find the average number of steps for the filtering density $p(x_i|y_{1:i})$ to reach a maximum value (mode) equal or larger than %90, given the sensor correct reading probability $\delta=0.99$. </p>
<p>I am stuck with this problem but a possible analytical way of solving it which comes to my mind is to treat the average number of steps $i$ where $p(x_i|y_{1:i})$ attains a mode of $0.9$ or greater as a random variable. Then calculating the expected value of $i$, namely $E[i]$ should give me the answer.</p>
<p>The problem is I am not sure whether this can be solved by this way and I am suspicious that there is a much easier way to solve this which I fail to see. I am looking for any hints or comments about whether my way of thinking is correct or not.</p>
<p>This is a homework question and therefore I am only looking for hints.</p>
<p>Thanks in advance. </p>
|
g35525
|
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] |
<p>I have a number of objective functions like:</p>
<pre><code>y1 = a11* x11 + a12*x11*x11+ a13*x12+.......
y2 = a21* x21 + a22*x21*x21+ a23*x22+.......
:::::
:::::
:::::
</code></pre>
<p>These are multiple objective functions. However, the constraints of the objective functions have dependency on each other.
Something like, </p>
<pre><code>x11+ x21 + x22 < const1
x12 + x21 > const2
:::::
:::::
</code></pre>
<p>What is the way to optimize such a system of equations? I would ideally like to use R to do the same?</p>
<p>y1 = 0.32 x1 + 0.21 x1*x1 + 0.49 x2... y2... y3 . . . The equations that i have is a non-linear function. These are non-linear regression equations or non-linear Market Mix Models. The x's are TV spend, Digital Spend etc. I want to 'include' all these models, use some constraints on them and optimize the spends in all the models with respect to constraints like...x1 (TV spend) < 100, TV + Digital spend < 500. I want to be able to say that of an amount of 100, i should spend, 30 on model 1, 20 on model 2( equation 2) etc</p>
|
g73245
|
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] |
<p>How to do model selection for unbalanced data? how many data points from the whole data set should be selected for model selection? how many for training and testing?</p>
|
g73246
|
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0.007505722809582949,
-0.015473759733140469
] |
<p>I want to create a climate model ensemble, testing 5 parameters (real, uniformly distributed between two values), using a latin hypercube approach. The problem is that I'm not sure how many replications I want to do. Is it viable to do one latin hypercube of 20 samples, and then another of 10? How would I make sure the 30 samples are relatively evenly distributed? Or would it be possible to do 10-sized LHCs, and do multiples? ie. do 3 or 4 LHC samples of size 10, making sure that each LHC was independent of the others?</p>
|
g35526
|
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<p>At <a href="https://github.com/OpenMDAO/OpenMDAO-Framework/issues/599" rel="nofollow">https://github.com/OpenMDAO/OpenMDAO-Framework/issues/599</a> it is stated that non-square Latin Hypercube experimental design is not well defined (I assume that for higher dimensions that means hypercube must have the same length in every dimension). </p>
<p>I'm wondering why that is. Would it not be possible to, for example, have a LHC scheme where each row in each dimension had <em>one or more</em> samples, and the sample space was relatively evenly sampled, with no correlation between variables? I guess this is actually making a hypercube out of a hyperrectangle, but is there any reason that wouldn't work?</p>
<p>For example, I have a bunch of parameters that I want to change in a physical model. Some have 4 states, some only two. Could I make a hypercube where the Parameters with only two states just have those states duplicated (so that there are two model runs with each of those two states)? how about doing the same with 4-, 3- and 2-state parameters? Could I make an LHC scheme where each dimension has length equal to the smallest common multiple of the states count for each parameter (ie. 12)? </p>
|
g73247
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] |
<p>Is there a good way to measure smoothness of a time series in R? For example,</p>
<pre><code>-1, -0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1.0
</code></pre>
<p>is much smoother than</p>
<pre><code>-1, 0.8, -0.6, 0.4, -0.2, 0, 0.2, -0.4, 0.6, -0.8, 1.0
</code></pre>
<p>although they have same mean and standard deviation. It would be cool if there is a function to give me a smooth score over a time series.</p>
|
g73248
|
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] |
<p>If the Martingale Residuals indicate that a predictor $X$ violates the proportional hazards assumption but the Schoenfeld Residuals indicate that it does not....which one should you trust?</p>
|
g35527
|
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] |
<p>Is there a function in R to calculate the generalized determinant of a singular matrix? (similar to the <code>ginv()</code> used to compute the generalized inverse)</p>
|
g35528
|
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<p>I'm new to ML and decided to start learning by having a go at number recognition using the MNIST subset on kaggle <a href="http://www.kaggle.com/c/digit-recognizer" rel="nofollow">http://www.kaggle.com/c/digit-recognizer</a></p>
<p>The images are 28x28 pixel greyscale of the digits from 0 to 9, with ~34000 in the training set and 28000 in the test set. Random Forest using the raw image and 2000 trees gives a score of 0.96829.</p>
<p>I did some preprocessing of the images to extract more features and trained / tested on a equal sized subsets of the training data. Compared to normal random forest for subsets around 1000 - 3000 I was getting about a 3-4% improvement (e.g. 94% vs 90% for RF)</p>
<p>After training with the entire training set for 200 trees, I scored 0.97557 (a ~0.7% improvement on RF). However, increasing to 2000 trees I scored 0.97457 (0.1% less).</p>
<ul>
<li>Does this mean the features are 'saturated'? i.e. any minor performance gain / loss is just random fluctuations?</li>
<li>Is there anything I can try (apart from more features) to improve the result?</li>
<li>Is there any way to weight some features more than others so they are more likely to be evaluated?</li>
</ul>
|
g73249
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] |
<p>I have a set of around 300k text examples. As mentioned in the title, each example has at least one label, and there are only 100 possible unique labels. I've reduced this problem down to binary classification for Vowpal Wabbit by taking advantage of namespaces, e.g. </p>
<p>From:</p>
<pre><code>healthy fruit | bananas oranges jack fruit
evil monkey | bipedal organism family guy
...
</code></pre>
<p>To:</p>
<pre><code>1 |healthy bananas oranges jack fruit
1 |fruit bananas oranges jack fruit
0 |evil bananas oranges jack fruit
0 |monkey bananas oranges jack fruit
0 |healthy bipedal organism family guy
0 |fruit bipedal organism family guy 1 |evil bipedal organism family guy
1 |monkey bipedal organism family guy
...
</code></pre>
<p>I'm using the default options provided by VW (which I think is online SGD, with the squared loss function). I'm using the squared loss because it closely resembles the Hamming Loss. </p>
<p>After training, when testing on the same training set, I've noticed that all examples are predicted with the '0' label... which is one way of minimizing loss, I guess. At this point, I'm not sure what to do. I was thinking of using cost-sensitive one-against-all classification to try to balance the classes, but reducing multi-label to multi-class is unfeasible since there exists 2^100 label combinations. I'm wondering if anyone else have any suggestions. </p>
|
g73250
|
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] |
<p>Here's a hypothetical problem analogous to one that I am having trouble with:</p>
<p>Prostate cancer biopsies are scored according to Gleason pattern (0-10). The scale is ordinal. Over 7 warrants surgery.</p>
<p>Patients at risk for prostate cancer were followed with serial biopsies at irregular intervals. Our data consists of a series of biopsies (date and result) for many patients (i.e. 1000 results for 100 patients), along with patient characteristics that may influence risk like sex, birthdate (i.e. age), race etc.</p>
<p>What models could be estimated with this data to predict the probability of Gleason > 7 at next biopsy? Or if simpler, what model could predict Gleason score at next biopsy? Intuitively it should incorporate the last biopsy results, time since last biopsy, and the other patient characteristics.</p>
<p>I generally use R. Relevant papers, packages, etc. would be appreciated. Thanks in advance.</p>
|
g31029
|
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] |
<p>In order to calculate a sample size for a 1-proportion test in Minitab, one has to input the power and the comparison proportion. Could someone provide a definition for the comparison proportion please?</p>
|
g73251
|
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] |
<p>We can see on the figure (cf <em>Least Angle Regression</em> p30, Efron, Hastie, Johnstone, Tibshirani - link: <a href="http://www.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf" rel="nofollow">Least Angle Regression</a>) that there is a direct relationship between:</p>
<ul>
<li>LASSO T absolute norm of $\beta$: $T(\beta) = \sum_j\vert\beta_j\vert$</li>
<li>and the number of steps $k$ computed by LARS.</li>
</ul>
<p>I am trying to find a mathematical or at least a direct relationship between both LASSO T and LARS k, like $A = B$ or $A = x \Rightarrow B = f(x)$.</p>
|
g35534
|
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] |
<p>I have 60,000 data and around 45% of them is missing and the missing values are random. Can I simply use listwise or pairwise deletion or do I have to use imputation? If imputation is recommended which imputation is the best one?</p>
|
g35535
|
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<p><strong>Method:</strong> I presented 15 participants with audiovisual clips. There were six different clips I presented, and for each clip there was emotional incongruence between visual and auditory information. The combinations were: </p>
<ul>
<li>visual negative with auditory positive </li>
<li>visual negative with auditory neutral </li>
<li>visual positive with auditory negative</li>
<li>visual positive with auditory neutral</li>
<li>visual neutral with auditory negative</li>
<li>visual neutral with auditory positive</li>
</ul>
<p>I asked participants to make an emotional judgements, whether the clip was happy, angry or neutral. There were five repetitions. </p>
<p><strong>Research question</strong>: Are participants driven by visual or auditory information in their emotional choices, when they watch displays with incongruent emotional information?</p>
<p><strong>Basic analysis:</strong> Because there were no “correct” responses per se for the incongruent stimuli, I calculated the tendency to respond correctly when emotion was presented auditorily or visually. The tendency was estimated by subtracting the proportion of “auditory correct” responses from the proportion of “visual correct” responses for the six incongruent conditions. For example if the incongruent display combined visual negative with auditory positive information, and participants responded that it was a negative interaction, then it was counted as visual response. The estimated indices varied from 1 (participants always responded correctly to the visual information) to −1 (participants always responded correctly to the auditory information). Below is a figure produced in R that shows averaged tendency scores, with standard error bars. <a href="http://dl.dropbox.com/u/2505196/exp2tend.dat" rel="nofollow">The data is available here</a> - columns represent conditions, rows - tendency scores for each participant.</p>
<p><img src="http://i.stack.imgur.com/9cAsP.png" alt="enter image description here"></p>
<p>Now, getting to the point I have two questions:</p>
<blockquote>
<p><strong>Question 1:</strong> What would be the best way to check for significant differences between those different clips?</p>
</blockquote>
<p>I know I could simply run a series of 30 paired t test's but it doesn't seem as a pretty solution. I don't think I can use ANOVA here - I have no clue how I could define levels for all those incongruent conditions. Maybe I could organize this data in some different way, but I really not sure what it would be.</p>
<blockquote>
<p><strong>Question 2:</strong> Is there a better way you could use to visualize this?</p>
</blockquote>
<p>I don't love the above plot - in fact I really don't like it. The oversized legend is very heavy to read, and so are the patterns differentiating each condition. I could use color instead, but I am a bit color blind to be honest, so I would prefer to avoid it. </p>
<p><strong>EDIT</strong></p>
<p><em>Question 1</em> I decided to just compare the 6 pairs which had the same type of incongreunt information using paired t test. Works kind-of-ok to get the differences.</p>
<p><em>Question 2</em> has been answered well by @AndyW and @gung - I decided to use pure SE bars with vertical orientation of x axis. Done in R using <code>segplot()</code> - I need to tweak the details, but it's roughly the idea.</p>
<p><img src="http://i.stack.imgur.com/9wvAN.png" alt="enter image description here"></p>
|
g73252
|
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] |
<p>If <code>X</code> is a nonnegative random variable representing the life of a component having distribution function <code>F</code>, and S is the survival function and <code>T</code> be a nonnegative random variable representing the time until some specied event. What is the result of this integral?</p>
<p>$$
\int_0^x \int_0^t S(u) du dt + \int_x^\infty \int_t^\infty S(u) du dt
$$</p>
|
g35537
|
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<p>I am not a statistics expert but was interested in the validity of the reasoning below.</p>
<p>Somebody argued that many people had the letter 'J' in their initials. Can someone comment on the validity of the following approach and how it could be improved, notably what probability distribution would a list of firs tnames sorted by popularity follows?</p>
<hr>
<p>According to <a href="http://en.wikipedia.org/wiki/List_of_most_popular_given_names" rel="nofollow">wikipedia</a> the most common first names for males in the US according to the 1990 census are, in that order: </p>
<blockquote>
<p>'James','John','Robert','Michael','William','David','Richard','Charles','Joseph',
and 'Thomas'</p>
</blockquote>
<p>Let's use an approximate probability distribution (any better way?) that gives the probabilities to these names according to their order i (starting at 0) following:</p>
<blockquote>
<p>P(name_i) = 0.15 / (i + 2)</p>
</blockquote>
<p>This is a probability distribution for at least 1000 names (sums to 1), and starts like this:</p>
<blockquote>
<p>0.0749, 0.0499, 0.0374, 0.0299, 0.0249, ...</p>
</blockquote>
<p>meaning that someone has 7.49% chances of being called James. The sum of the probabilities of having a name starting with J from these list is 14% (P(James)+P(John)+P(Joseph)), lets call it <em>Pj</em>. Of course Pj is in fact higher because more names than these 8 in the list of 1000 may start with J.</p>
<p>Now let's assume a child is given three first names, the probability that at least of them starts with J given pj is <strong>36%</strong>!! (from (1-(1-pj)^3)). So every time you meet a new person, you have one third chances to see him having a J on his business card. Let's call this probability pIj, probability of at least one initial starting with a J.</p>
<p>However, when you say overwhelming majority, let's assume that you mean 8 out of 10. The probability that out of 10 people you meet in a row 8 have a name starting with a J is, using <a href="http://en.wikipedia.org/wiki/Binomial_distribution" rel="nofollow">binomial distribution</a>, only <strong>0.5%</strong> I'm afraid, by comb(10,8)<em>pIj^8</em>(1-pIj)^2 .</p>
<p>However, if you settle with 5 our of 10, your chances rise to <strong>16%</strong>.</p>
<hr>
<p>FYI the original question and post can be found <a href="http://english.stackexchange.com/a/57865/5437">here</a>.</p>
|
g73253
|
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] |
<p>I have a question.</p>
<blockquote>
<p>Is it better to use deviance or - 2 Log L for the likelihood ratio test? Or are they basically the same thing?</p>
</blockquote>
<p>SAS returns the "deviance" sometimes. But I just use the -2 Log L value for the likelihood ratio test (e.g. subtract the -2 Log L for two models to compare them). Is is that okay?</p>
|
g35539
|
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0.022146636620163918
] |
<p>Let’s say</p>
<p>$X_1$ ~ $uni(0,1)$</p>
<p>$X_2$ ~ $uni(0,1)$</p>
<p>$X_3$ ~ $uni(0,1)$</p>
<p>And</p>
<p>$Y=0.1X_1+0.3X_2+0.6X_3$</p>
<p>What’s the $F(Y)$ (i.e., CDF)?</p>
|
g46909
|
[
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<p>Does the non-normality matter in using regression for prediction?</p>
<p>Hi all,</p>
<p>In the Q-Q plot of the residuals after linear regression, the residuals turned out to be highly non-Gaussian. Most of the points (95%) are below a 45º straight line. And those below the straight line are all on the lower side. </p>
<p>The shape of the curve looks like $f(x)=x^{1/5}$ for $x$ on $[0, 1]$. (The 5% points in the middle of this curve are above the 45º straight line).</p>
<p>It turns out that the dependent variable $y$ has data that are highly non-Gaussian. They are all in $[0, 1]$, but mostly clustered around $1$.</p>
<p>So I tried various ways of transforming $y$. The latest one I've found was to do $y_{new} = y^7$.</p>
<p>Using this transformation, the $y_{new}$ data become much more symmetrical than before, but they still in no way look Gaussian in a histogram.</p>
<p>Being very disappointed, I don't have any more weapons in my bag...Instead, I began to wonder, if my end goal is just to get the $\hat{y}$, i.e. the prediction of the data on a wider data-set, does the non-normality even matter, in terms of accuracy for prediction?</p>
<p>Please shed some light for me. Thank you!</p>
<hr>
<p>The $y$ data looks very similar to the data generated using the following script:</p>
<pre><code>mydata=rt(10000, df=5)
mydata=mydata[mydata<0.8]
mydata=(mydata-min(mydata))/(max(mydata)-min(mydata))
hist(mydata, 100)
</code></pre>
|
g73254
|
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<p>I have a quick question: if I plot the diagnostic plots to an R regression, a couple of them have "Standardized Residuals" as their y-axis such as in this plot:</p>
<p><img src="http://i.stack.imgur.com/kZwaM.png" alt="enter image description here"> </p>
<p>My question is this: <strong>what are the residuals standardized over?</strong> That is, let us assume that in my model, there are 100 predicted values hence 100 residuals.</p>
<ol>
<li>Standardized residual $e_i$ is defined as $(e_i - \bar e)/s_e$(realized residual - mean of all 100 realized residuals)/(standard deviation of all 100 realized residuals)?</li>
<li>Since each residual $e_i$ is itself a realized value out of a distribution of possible realizations for this single residual $e_i$, is this residual $e_i$ normalized by its own mean $\bar e_i$ and variance $\text{Var}(e_i)$ (as opposed to the mean and variance from all other values 1 to 100 as described above)?</li>
</ol>
<p>I tried finding documentation clarifying this distinction but could not find any that was beyond doubt. Any help answering this question, and providing me tips on how to find such answers through documentation in the future would be immensely appreciated.</p>
|
g73255
|
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<p>I have been asked to develop control charts for my company - or some other means of quickly identifying when ticket sales are "out of control" and not just a random blip. The data we are looking at are seasonal with a positive trend (sales revenue). </p>
<p>It has been suggested that I use an exponentially-weighted moving average (EWMA) chart but my (limited) understanding is that these are only appropriate for use on data with a constant mean. </p>
<p>My gut instinct is to apply an ARIMA model and to assess whether observations fall within confidence limits derived from that... but I'm not confident enough to be sure this is the right approach.</p>
<p>My question therefore is:</p>
<ol>
<li>Is it appropriate to use control charts to monitor revenue sales</li>
<li>What would be the best model to use</li>
</ol>
<p>Please bear in mind that it needs to be administered by somebody with undergraduate maths, and explained to true lay people.</p>
|
g73256
|
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] |
<p>Can anyone suggest a good <strong>review</strong> reference (necessarily free online PDF) to brush up college-level statistics?</p>
<p>I'm looking at something which typically covers a first course in statistics ideally covering:</p>
<ul>
<li>Absolute basics (mean, variance etc.)</li>
<li>Large Samples</li>
<li>Confidence testing</li>
<li>Hypothesis testing (normal, t, chi, F)</li>
<li>Linear Regression/Correlation</li>
</ul>
<p>I don't need a book reference. I need something like a quick review which goes over the important aspects. Anything in free form will do : Presentations, Lecture Notes or otherwise. I just need it to be succinct; depth would be much appreciated.</p>
|
g73257
|
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] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://stats.stackexchange.com/questions/4040/r-compute-correlation-by-group">R: compute correlation by group</a> </p>
</blockquote>
<p>I have a data set with a 6 or so data points for groups of data.</p>
<p>e.g.:</p>
<pre><code>email_id date_sent number_sent number_of_views number_of_responses
1 5/4 600 25 6
1 5/5 500 22 8
1 5/6 450 23 4
1 5/7 700 34 12
2 5/5 900 30 10
2 5/6 750 28 11
...
</code></pre>
<p>(this is made up data that illustrates the point)</p>
<p>Assuming I have this in a data frame in R, I'd like to write something which will give me stats by group. I'm most interested in the correlation coefficient between some of the columns. </p>
<p>I know how to do this with a data frame that contains only one group:</p>
<p>cor(col1, col2)</p>
<p>but I'd like to learn a technique that will allow me to extract data that looks something like this:</p>
<pre><code>email_id cor(col3, col4)
1 .73
2 .85
3 .98
</code></pre>
<p>and so on.</p>
<p>Thanks, </p>
|
g49916
|
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<p>I am teaching a basic statistics course and today I will cover the chi-squared test of independence for two categories and the test for homogeneity. These two scenarios are conceptually different, but can use the same test statistic and distribution. In a test of homogeneity, marginal totals for one of the categories are assumed to be part of the design itself -- they represent the number of subjects selected for each experimental group. But since the chi-squared test revolves around conditioning on all marginal totals, there are no mathematical consequences to distinguishing between tests of homogeneity and tests of independence with categorical data -- at least none when this test is used.</p>
<p>My question is the following: is there any school of statistical thought or statistical approach that would yield different analyses, depending on whether we are testing for independence (where all marginals are random variables) or a test of homogeneity (where one set of marginals are set by the design)?</p>
<p>In the continuous case, say where we observe $(X,Y)$ on the same subject, and test for independence, or observe $(X_1, X_2)$ in different populations and test if they come from the same distribution, the method is different (correlation analysis vs t-test). What if the categorical data came from discretized continuous variables? Should the tests of independence and homogeneity be indistinguishable?</p>
|
g35544
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<p>I used a survey to collect information about injuries suffered while practicing and competing in gymnastics. I have count data on the injuries that looks something like this:</p>
<pre><code> Floor Vault Rings ...
Head 33 45 7
Neck 43 19 17
Shoulder 21 39 25
... ... ... ...
Toes 16 9 3
</code></pre>
<p>I wanted to see if there was a relationship between the body part injured and the equipment being used. I thought that using a chi square test of independence would work but I've hit a snag, I think. </p>
<p>When the participants filled out the survey, they were able to check multiple responses. For example, if someone was injured while performing the vault, they could have injured both their head and neck and both would show up in the injury count. Thus one injury contributed to two cells.</p>
<p>I've considered running separate analyses for each body part but I don't think that exactly answers my question. Is there another way to tackle this problem or a different statistical test that might work?</p>
|
g73258
|
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<p>I am really new to Granger Causality and am just rabidly experimenting with this MATLAB function: </p>
<pre><code>granger_cause(x,y,alpha,max_lag)
</code></pre>
<p><a href="http://www.mathworks.com/matlabcentral/fileexchange/25467-granger-causality-test" rel="nofollow">http://www.mathworks.com/matlabcentral/fileexchange/25467-granger-causality-test</a></p>
<p>I have two series x and y which I need to check for causality. I need to check if y at a lag of 180 samples has a causal relationship with x or not.</p>
<p>Based on my experimentation, I noticed that if I vary the values of alpha and the lag, then I am able to find that almost anything seems to correlate with x (such as a random set of data). Can someone tell me just how should I should vary the alpha and lag values?</p>
<p>I found that if I put alpha as 0.8 then I get a good answer for x and y but not for the random data; however considering that other resources tell me to have alpha at 0.01 or so, I'm pretty suspicious about this. Can someone please help me out here?</p>
|
g35546
|
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] |
<p>My question is essentially simple: suppose we have a sequence of heads and tails with an apparent chance of getting heads $\hat{p} = 0.5$. </p>
<blockquote>
<p>h h t h t t t h t t h ...</p>
</blockquote>
<p>How do we tell if this sample was drawn from a binomial distribution with this $\hat{p}$ or if it comes from a combination of different distributions which produces the same average? (e.g. $p = 0.25$ or $p = 0.75$)</p>
<p>Here's what I was thinking of doing:</p>
<ul>
<li>We chop the sequence into subsections of length $n$, for example $n=5$, and calculate $\hat{p}$ in every such window:<blockquote> {h h t h t}, {t t h t t}, {h ...}</blockquote><blockquote>0.6, 0.2, ...</blockquote></li>
<li>We then calculate the standard deviation in these $\hat{p}$ values:
$\sigma_{ex}=\sqrt{\frac{\sum_{i=1}^M{(\hat{p}_i - \hat{\mu})^2}}{M}}$, where $\hat{\mu}$ is the average $\hat{p}$ and $M$ is the total number of windows of size $n$ we can make. </li>
<li>We calculate the standard deviation in $\hat{p}$ based on a binomial distribution, $\sigma_{th}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$.</li>
</ul>
<p>Now comes the problem: how to determine if these two values are the same? After a lot of research, I decided to try using an F-ratio test and plugging the result into an f-distribution.</p>
<p>F-ratio: $F = \frac{\sigma_{ex}^2}{\sigma_{th}^2}$ (only valid for normal-distributions :S)</p>
<p>And then an f-distribution to get to a p-value we can check against. However, for the f-distribution I need to know the degrees of freedom in the nominator and denominator. And therein lies my problem: what are the degrees of freedom for the variance calculated from theory? (In the experimental case I think it is M)</p>
<p>If you have this answer or any suggestions on how to solve this problem differently, I would love to hear about it!</p>
|
g49917
|
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<p>I am reading up on orthogonal regression for possible implementation in one of my datasets. My question relates to computation of prediction errors as "mean prediction errors -MPE" or "mean absolute prediction errors-MAPE" in orthogonal regression where my dependent and independent variables (both measured in the same units) may not have the same errors as they may come from different sources. </p>
<p>In normal least squares where the dependent variable is regressed on the independent variable, the MPE or MAPE can be taken from mean of the predicted - observed. How does one compute the MPE or MAPE in the scenario when both the variables have error in them.
This may be simple but was not obvious to me. Hope the question is clear enough.</p>
<p>VJ</p>
|
g37696
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] |
<p>Can someone recommend a textbook(s) that covers the same topics as <a href="http://www.whfreeman.com/Catalog/product/probabilityandstatistics-secondedition-evans/tableofcontents" rel="nofollow">Probability and Statistics</a> by by Michael J. Evans and Jeffrey S. Rosenthal?</p>
<p>I find this particular textbook to be very poorly written and terse.</p>
|
g1003
|
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] |
<p>I have a confusion regarding notation of the expectation. Consider the following:</p>
<p>$$E_x(x^2) = \sum_x x^2p(x)$$
$$E_x(x|y) = \sum_x xp(x|y)$$</p>
<p>So the same notation here is giving different meaning right isn't it?</p>
<p>Up to now I was assuming $E_x$ taking $p(x)$ and calculating the expectation. However after looking at $E_x(x|y) = \sum_x xp(x|y)$, I am a bit confused</p>
|
g73259
|
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<p>Let's say I have a time series that indicates the number of visitors to a website, so each value is non-negative. </p>
<p>For example: [100, 120, 40, 200, 1000, 1400, 1300, 1500]</p>
<p>In this case it's clear that the website is busier over the last days. </p>
<p>Similarly, [2000, 1000, 100, 100, 50, 70, 20, 30, 20, 30] would indicate that the traffic on the website is decreasing.</p>
<p>What would be a good way to calculate a value in the range [0, 1] to indicate this? Moreover, assuming these two series belong to two different sites, how would I be able to compare one with another? (I assume some kind of normalization should be made over the results, is that correct?)</p>
<p>Thanks in advance.</p>
|
g73260
|
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<p>In my field, psychophysics/experimental psychology, sometimes a lot of measures are collected for each subject. Then, a model is fitted for each subject and with the estimated parameters sometimes a global test like a t-test or ANOVA is performed to reach conclusions. It seems that this approach sometimes produces wrong conclusions and I wanted to know references that already made this point. Below a toy example:</p>
<p>Let's suppose that I want to know whether the color of an object (red or green) influences its visibility. To measure visibility I presented a tiny object in a computer screen and ask the subject to report whether can or cannot see the object. After she responds, I display another tiny object and so on. I use four different sizes and two colors and presented them randomly. Each size and color is presented 50 times. This is a possible outcome of the experiment:</p>
<p><img src="http://i.stack.imgur.com/3ou12.jpg" alt="Results toy example"></p>
<p>Each panel shows the data for one subject. The y-axis is the frequency of reports 'yes, I saw it'. The curves are cumulative normal distributions fitted using generalized linear models and the vertival lines are the estimated means of the underlying distributions. </p>
<p>The confidence intervals of the fits indicate that the color influences the visibility for each subject. For subjects 1,2 and 3 green is easier to perceive. For subjects 4,5 and 6 red is easier. Given that the color does not affect equally each subject, it is possible that if I use the mean of the fitted distributions to perform a t-test it turns out not significant. </p>
<p>So sometimes in my field, based on the results of the t-test, it is concluded that color does not affect visibility. The individual analysis for each subject is not performed and discussed. So I am searching for references (articles/books) that point this problem out. </p>
<p>Below the code of the toy example in R:</p>
<pre><code> library('plyr')
library('ggplot2')
set.seed(100)
n<-50
size<-1:4
prob<-c(0.1,.3,.5,.7)
variables1<-expand.grid(subject=1:3,color=c('red','green'))
df1<-ddply(variables1,.(subject,color),function(d){
if (d$color=='red') nyes<-rbinom(4,n,prob)
if (d$color=='green') nyes<-rbinom(4,n,prob+.2)
data.frame(size,nyes,nno=n-nyes,p=nyes/n)
})
variables2<-expand.grid(subject=4:6,color=c('red','green'))
df2<-ddply(variables2,.(subject,color),function(d){
if (d$color=='green') nyes<-rbinom(4,n,prob)
if (d$color=='red') nyes<-rbinom(4,n,prob+.2)
data.frame(size,nyes,nno=n-nyes,p=nyes/n)
})
dat<-rbind(df1,df2)
curves<-ddply(dat,.(subject,color),function(d){
model<-glm(cbind(nyes,nno)~size,binomial(probit),d)
x<-seq(0,5,.1)
y<-predict(model,data.frame(size=x),type='response',se.fit=T)
data.frame(x,y=y$fit,ymin=y$fit-y$se.fit,ymax=y$fit+y$se.fit)
})
means<-ddply(dat,.(subject,color),function(d){
model<-glm(cbind(nyes,nno)~size,binomial(probit),d)
coe<-coef(model)
m<- -coe[[1]]/coe[[2]]
data.frame(m)
})
q<-ggplot()+
facet_wrap(~subject)+
geom_point(data=dat,aes(x=size,y=p,color=color))+
geom_line(data=curves,aes(x=x,y=y,color=color))+
geom_ribbon(data=curves,aes(x=x,ymin=ymin,ymax=ymax,fill=color),alpha=.3)+
geom_linerange(data=means,aes(x=m,color=color),ymin=0,ymax=.5)
q
t.test(m~color,data=means,paired=T)
</code></pre>
|
g73261
|
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] |
<p>The <a href="http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test" rel="nofollow">Kolmogorov–Smirnov test</a> rejects the null hypothesis at level $\alpha$ if $$\sqrt{n}D_n>K_\alpha$$</p>
<p>where $$D_n=\sup_x |{F}_n(x)-F(x)| $$, and </p>
<p>$$\operatorname{Pr}(K\leq K_\alpha)=1-\alpha$$
, where $K$ follows Kolmogorov distribution.</p>
<p>There are tables for $K_\alpha$, but <a href="http://www.real-statistics.com/statistics-tables/kolmogorov-smirnov-table/" rel="nofollow">this website</a> gives formula for $K_\alpha$ for big $n$.</p>
<p>For example, it says, if $n$ is over 50, $$K_{\alpha=0.01} = 1.63 $$ $$K_{\alpha=0.05} = 1.63$$ $$K_{\alpha=0.01} = 1.36$$ $$K_{\alpha=0.1} = 1.22 $$ $$K_{\alpha=0.15} = 1.14 $$ $$K_{\alpha=0.2} = 1.07 $$</p>
<p>How could such number be reached?</p>
|
g35556
|
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] |
<p>I have been trying to discern what exactly the "coef" and "(exp)coef" output of coxph signify. It seems that the "(exp)coef" are comparisons of the first variable in the model according to the group assigned in the command. </p>
<p>How does the coxph function arrive at the values for "coef" and "(exp)coef"?</p>
<p>Additionally, how does coxph determine these values when there is censoring involved?</p>
|
g73262
|
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0.012232638895511627,
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0.0034842444583773613
] |
<p>I am exploring the use of the <code>survreg</code> function in R to analyze my current experiment. </p>
<p>Does anyone know what the "Value" column in the output of the function stands for? </p>
|
g73263
|
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<p>I have a number of time series which are derived of same underlying data. However, the data in each comes from a different source, so they may be slightly lagged or differently enriched but essentially representing the same underlying data.</p>
<p>Is it possible to find out if there is one of these series that is odd and severely delayed or out of line?</p>
<p>As an example, imagine you subscribing to market data for the same stock from 5 different providers and trying to find out which is running slow in a dynamic way. However, stock prices are very deterministic so that makes the problem slightly simplified. In my case I am working on data that doesn't have a single source to check.</p>
|
g73264
|
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<p>With Univariate regression it's very easy to see if the correlation is linear or otherwise, but in a multiple regression things can look very complicated, polynomial or other correlations can be hidden by the interaction of of the variables. I understand that you can use power terms in the variables but the relationship to the dependent variable should still be linear. How do I know if multiple regression is appropriate?</p>
|
g73265
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] |
<p>The following code:</p>
<pre><code>require(zoo)
data <- read.csv(file="summary.csv",sep=",",head=TRUE)
cum = zoo(data$dcomp, as.Date(data$date))
data = zoo(data$compressed, as.Date(data$date))
data <- aggregate(data, identity, tail, 1)
cum <- aggregate(cum, identity, sum, 1)
days = seq(start(data), end(data), "day")
data2 = na.locf(merge(data, zoo(,days)))
pdf(file='timeseries.pdf',width=9,height=5)
par(bty = 'n')
plot(data2,xlab='',ylab='entropy (bytes)',axes=FALSE)
axis(side = 2, at=c(991, 20000, 40000, 53048))
axis(side = 2, at=c(10000, 30000),labels=FALSE)
lines(cum,type="h",lwd=0.3,col=rgb(0.64,0.08,0.00))
axis.Date(side = 1, days, at=c("2007-07-25", "2008-01-01", "2009-01-01", "2010-01-01", "2010-06-21"))
</code></pre>
<p>Yields the following Graph:</p>
<p><img src="http://i.stack.imgur.com/k3Yei.png" alt="alt text"></p>
<p>The questions (all related to the bottom axis) are:</p>
<ol>
<li>How can I make it display '2007/07' and '2010/06' in the beginning and end labels?</li>
<li>How can I make it to automatically add minor ticks to the months (without labels)? </li>
</ol>
|
g73266
|
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0.0446271188557148,
0.009527536109089851,
-0.024070149287581444,
-0.042453985661268234,
-0.03280934318900108,
0.014545674435794353,
-0.02606581337749958,
0.024196777492761612,
0.048618558794260025,
0.050473280251026154,
-0.005302118137478828,
0.05257481336593628,
-0.048135969787836075,
-0.021119385957717896,
-0.03582879528403282,
-0.005969999358057976,
0.08776579797267914,
0.0425703227519989,
-0.011179137043654919,
0.006870537530630827,
-0.05613788217306137
] |
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