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Tags
list
9367
2
null
9331
1
null
I learnt about the use of splines in regression from the book "Regression Modeling Strategies" by Frank Harrell. Harrell's R package rms allows you to easily fit regression models in which some predictor variables are represented as splines.
null
CC BY-SA 3.0
null
2011-04-08T20:21:18.013
2011-04-08T20:21:18.013
null
null
3835
null
9368
2
null
9312
1
null
You should use the point estimate of the reliability, not the lower bound or whatsoever. I guess by lb/up you mean the 95% CI for the ICC (I don't have SPSS, so I cannot check myself)? It's unfortunate that we also talk of Cronbach's alpha as a "lower bound for reliability" since this might have confused you. It should...
null
CC BY-SA 3.0
null
2011-04-08T20:40:25.080
2011-04-08T20:40:25.080
null
null
930
null
9369
2
null
9365
12
null
It's a bit difficult for me to see what paper might be of interest to you, so let me try and suggest the following ones, from the psychometric literature: > Borsboom, D. (2006). The attack of the psychometricians. Psychometrika, 71, 425-440. for dressing the scene (Why do we need to use statistical models that b...
null
CC BY-SA 3.0
null
2011-04-08T21:02:38.377
2011-04-08T21:02:38.377
null
null
930
null
9370
2
null
9365
12
null
Here are five highly-cited papers from the last 40 years of the [Journal of the Royal Statistical Society, Series C: Applied Statistics](http://www.blackwellpublishing.com/journal.asp?ref=0035-9254) with a clear application in the title that caught my eye while scanning through the Web of Knowledge search results: - S...
null
CC BY-SA 3.0
null
2011-04-08T21:33:23.330
2011-04-13T06:57:43.827
2011-04-13T06:57:43.827
183
449
null
9371
2
null
9329
3
null
First idea is just to mimic the knock-out strategy from variable importance and just test how mixing each attribute will degenerate the forest confidence in object classification (on OOB and with some repetitions obviously). This requires some coding, but is certainly achievable. However, I feel it is just a bad idea ...
null
CC BY-SA 3.0
null
2011-04-08T23:21:36.193
2011-04-08T23:21:36.193
null
null
null
null
9372
1
null
null
2
374
How would I go about finding out the confidence intervals around a set of distinct bianary occurrences where each occurence has a different associated probability and each occurence is weighted? To be more specific, we typically determine a milestone budget by assigning reasonable probabilities to each milestone. Each...
How do I determine confidence intervals around weighted, probilized events?
CC BY-SA 3.0
null
2011-04-08T23:28:23.310
2011-04-09T00:41:18.617
2011-04-09T00:27:18.753
null
null
[ "probability" ]
9373
2
null
9276
4
null
There is one general and "in-universe" criterion for goodness of Monte Carlo -- convergence. Stick to one M and check how the PG behaves with the number of juries -- it should converge, so will show you a number of repetitions for which you will have a reasonable (for your application) number of significant digits. Re...
null
CC BY-SA 3.0
null
2011-04-09T00:04:02.477
2011-04-09T00:04:02.477
null
null
null
null
9374
2
null
9372
2
null
Basically you would need to make a [probability tree](http://www.google.com/search?q=probability+tree) with resulting penalty sums in leafs and sum the whole thing up for a criterion of your choice, possibly using some software for more milestones than few (there will be $2^N$ leafs for $N$ milestones). You will be abl...
null
CC BY-SA 3.0
null
2011-04-09T00:26:56.037
2011-04-09T00:26:56.037
null
null
null
null
9375
2
null
9372
1
null
It rather depends on how many milestones you have. But if this (call it $n$) is small enough and each one either happens or does not, then you can work out the $2^n$ possibilities, working out the probabilities by multiplying the inidividual probabilies. So for example the probability of paying out $20,000,000$ is $...
null
CC BY-SA 3.0
null
2011-04-09T00:41:18.617
2011-04-09T00:41:18.617
null
null
2958
null
9376
2
null
8669
0
null
Canonical Correlation Analysis was one way to go and it works! Credits to @schenectady for this. Thanks a lot for your help. I want to write this for future reference and for others who might have a similar query, if you want to perform a regression analysis in such a situation, you should attempt to minimize the squar...
null
CC BY-SA 3.0
null
2011-04-09T07:49:30.520
2011-04-09T18:43:50.403
2011-04-09T18:43:50.403
930
3859
null
9377
1
9380
null
7
841
In the paper > M. Avellaneda and J. H. Lee, Statistical arbitrage in the U.S. equities market, July 2008, in the Appendix on page 46, how does he get equilibrium standard deviation as following: $$\sigma_{eq} = \sqrt{\frac{\text{Variance}(\zeta)}{1 − b^2}}$$ If anyone knows the paper, please explain. Much appreciat...
Origin of strange formula for equilibrium standard deviation
CC BY-SA 3.0
null
2011-04-09T11:29:27.753
2011-04-19T13:04:46.690
2011-04-19T13:04:46.690
2970
862
[ "regression", "probability", "variance", "stochastic-processes" ]
9378
1
9401
null
4
4826
I'm working with a CSV which contains approximately 220,000 entries. My aim is to predict one of the attributes (ATT1) using the other 3 (ATT2, ATT3, ATT4). I've been able to do this using NaiveBayes, but now I feel unsatisfied with the result. The reason is that ATT1 can be one of 6 values (VAL1-6), but these are not ...
How to choose a data subset in RapidMiner?
CC BY-SA 3.0
null
2011-04-09T12:49:36.187
2017-05-19T12:31:50.697
2017-05-19T12:31:50.697
101426
1522
[ "dataset", "rapidminer" ]
9380
2
null
9377
15
null
The authors are providing a simple means for estimating the parameters of a mean-reverting Orstein-Uhlenbeck process via a regression on returns at discretized points in time. The model they are considering has a representation as a stochastic differential equation of the form [pg. 16, Eq. (12)] $$ \newcommand{\rd}{\m...
null
CC BY-SA 3.0
null
2011-04-09T13:32:30.010
2011-04-11T02:17:49.223
2011-04-11T02:17:49.223
2970
2970
null
9381
1
null
null
4
149
I was wondering from the view of dividing the topics of statistical theory into inference part and non-inference part, what inference topics and non-inference topics statistical theory is covering? By inference, I mean the task in logic to reach some conclusion from some premises. Probabilistic inference is a way of lo...
Inference and noninference parts of statistical theory
CC BY-SA 3.0
null
2011-04-09T14:00:11.930
2017-03-15T19:34:48.247
2017-04-13T12:44:33.550
-1
1005
[ "inference" ]
9383
1
null
null
2
666
I'm doing 10-fold cross validation on a dataset. But in some folds there are edge cases that the denominator in precision-recall calculation is zero (tp + fp =0). What are the correct values for precision and recall in this case? And what is the correct way of doing cross-validation (should I include these results when...
What are the correct edge case values of precision and recall and how to integrate them into cross validation?
CC BY-SA 3.0
null
2011-04-09T15:24:45.393
2011-04-09T20:05:43.907
2017-04-13T12:44:39.283
-1
4091
[ "cross-validation", "precision-recall" ]
9384
2
null
9342
11
null
The Ward clustering algorithm is a hierarchical clustering method that minimizes an 'inertia' criteria at each step. This inertia quantifies the sum of squared residuals between the reduced signal and the initial signal: it is a measure of the variance of the error in an l2 (Euclidean) sens. Actually, you even mention ...
null
CC BY-SA 3.0
null
2011-04-09T15:57:28.113
2011-04-09T15:57:28.113
null
null
1265
null
9385
1
null
null
7
11210
I am using the Holt-Winters' exponential smoothing technique to forecast expenditure data 2 years into the furture. The monthly data has an increasing trend and annual seasonality. I'm using MS Excel with the Solver add-in to calculate the optimal values of $\alpha$, $\beta$ and $\gamma$ to give the smallest MSE for th...
Forecasting beyond one season using Holt-Winters' exponential smoothing
CC BY-SA 3.0
null
2011-04-09T15:59:58.363
2013-01-16T11:28:44.610
2013-01-16T11:28:44.610
1352
4092
[ "time-series", "forecasting", "excel", "exponential-smoothing" ]
9387
2
null
9365
9
null
On a wider level I would recommend the ["Statistical Modeling: The Two Cultures"][1] paper by Leo Breiman in 2001 (cited 515) I know it was covered by the journal club recently and I found it to be really interesting. I've c&p'd the abstract. > Abstract. There are two cultures in the use of statistical modeling to ...
null
CC BY-SA 4.0
null
2011-04-09T16:49:38.487
2019-03-02T12:41:01.320
2019-03-02T12:41:01.320
166514
3597
null
9388
2
null
3898
1
null
If the problem at issue consists of testing for the optimal number of factors, Jushan Bai and Serena Ng in several articles provide a test based on AIC/BIC that minimizes, for different options, the variance of the error. They supply to my knowledge the most updated approach to resolve this issue. See also Alexei Onats...
null
CC BY-SA 3.0
null
2011-04-09T18:09:15.317
2011-04-09T18:09:15.317
null
null
4093
null
9390
1
null
null
9
2126
An English soccer team plays a series of matches against different opponents of varying ability. A bookmaker offers odds for each match as to whether it will be a home win, away win, or draw. Part-way through the season, the team has played $n$ matches and has drawn $k$ of them, which is more than might be expected fro...
What's the probability that a bookmaker is mispricing odds on soccer games?
CC BY-SA 4.0
null
2011-04-09T18:24:23.090
2018-06-04T01:09:24.283
2018-06-04T01:09:24.283
116107
null
[ "probability", "games", "gambling" ]
9391
2
null
9390
0
null
Bookmakers use an overround so they don't actually care what the result is because they win whatever. That is why you never meet a poor bookie. If a bookmaker is mispricing draws your ability to make profit would depend on the odds the bookmaker was offering and whether the profits generated would cover the times you l...
null
CC BY-SA 3.0
null
2011-04-09T18:49:59.820
2011-04-09T18:49:59.820
null
null
3597
null
9392
1
null
null
0
237
My data looks like this (F=Features) ``` F1 F2 F3 F4 F5 F6 F7 F8.... ID1 0.67 0.76 0.3 0.54 0.21 0.88 0.97 0.45.... ID2 0.76 0.68 0.10 0.45 0.12 0.44 0.79 0.54.... ID3 0.67 0.76 0.3 0.54 0.21 0.88 0.68 0.76.... ID4 0.67 0....
How to get scored combination of features
CC BY-SA 3.0
null
2011-04-09T18:54:22.423
2011-04-13T02:59:16.640
2011-04-11T20:52:30.830
3111
3111
[ "feature-selection", "text-mining" ]
9393
2
null
9383
1
null
Instead of using CV to estimate precision and recall, use it to obtain the expected TP, TN, FP, and FN rate. Then use those values to compute the expected precision and recall and the standard errors. (Taylor expansions come in handy for the latter.)
null
CC BY-SA 3.0
null
2011-04-09T20:05:43.907
2011-04-09T20:05:43.907
null
null
3567
null
9394
2
null
9365
8
null
From a genetic epidemiology perspective, I would now recommend the following series of papers about [genome-wide association studies](http://en.wikipedia.org/wiki/Genome-wide_association_study): - Cordell, H.J. and Clayton, D.G. (2005). Genetic association studies. Lancet 366, 1121-1131. - Cantor, R.M., Lange, K., an...
null
CC BY-SA 3.0
null
2011-04-09T20:39:39.403
2011-04-09T20:39:39.403
null
null
930
null
9395
1
null
null
8
429
I don't know what is the appropriate term for my question. The scenario is described as following. In the analysis there one dependent variable Y and two independent variable X1 and X2. All three variables are continuous. I converted X1 into a categorical variable which has three levels A, B, and C. It was found that Y...
How can I demonstrate non-linearity without categorising a predictor?
CC BY-SA 4.0
null
2011-04-09T23:20:10.947
2020-02-17T00:16:09.207
2020-02-17T00:16:09.207
11887
400
[ "regression", "categorical-data", "data-visualization", "nonlinear-regression", "continuous-data" ]
9396
1
null
null
6
2895
In the paper > M. Avellaneda and J. H. Lee, Statistical arbitrage in the U.S. equities market, July 2008, in the Appendix on page 44, I have some questions. First he runs the regression of stock-return ($R_n^S$) with index/ETF-return ($R_n^I$). $R_n^S = \beta_0 + \beta R_n^I + \epsilon_n, ~~~~~n=1,2,...,60$ Then h...
Why are cumulative residuals from regression on stock and index returns mean reverting
CC BY-SA 3.0
null
2011-04-09T23:24:44.063
2011-07-09T18:29:14.500
null
null
862
[ "regression", "mean", "stochastic-processes" ]
9397
2
null
9395
5
null
Converting a continuous variable into categorical may be a bad idea, but may be a good idea as well, this depends on the problem. When the relationships of the variable can be best described using thresholds, categorisation may be one of the best options. You wrote that in different categories of X1 the correlation bet...
null
CC BY-SA 3.0
null
2011-04-09T23:49:17.103
2011-04-09T23:49:17.103
null
null
3911
null
9398
1
9406
null
15
3042
Suppose you get to observe "matches" between buyers and sellers in a market. You also get to observe characteristics of both buyers and sellers which you would like to use to predict future matches & make recommendations to both sides of the market. For simplicity, assume there are N buyers and N sellers and that e...
Supervised learning with "rare" events, when rarity is due to the large number of counter-factual events
CC BY-SA 3.0
null
2011-04-09T23:31:25.733
2011-04-10T17:54:19.620
2011-04-10T17:54:19.620
919
4095
[ "machine-learning" ]
9399
2
null
9398
1
null
Concerning (1). You need to keep positive and negative observations if you want meaningful results. (2) There is no wiser method of subsampling than uniform distribution if you don't have any a priori on your data.
null
CC BY-SA 3.0
null
2011-04-09T23:47:33.450
2011-04-10T00:28:15.327
null
null
3896
null
9400
1
9403
null
6
387
My actual project is a bit complicated, but I'll explain by analogy (which I hope facilitates response): I have 3 substances, say water, motor oil, and ethanol. For each substance, I have 5 samples in a beaker (total 15 beakers). I heat all the beakers on a hot-plate up to 70 degrees Celsius, and over the next hour, I ...
How can I compute regression for several longitudinal data sets (thus, with auto-correlated error)?
CC BY-SA 3.0
null
2011-04-10T00:58:48.477
2011-04-10T17:25:16.590
2011-04-10T03:07:18.390
3911
4096
[ "regression", "autocorrelation", "nonlinear-regression", "panel-data", "exponential-distribution" ]
9401
2
null
9378
4
null
Use the Sample operator with the Balance checkbox. You can set the sample size per class that way (to a balanced one) @steffen, the mandate for this site covers stats AND stats software. There are tons of R questions on here, so it's fair to ask questions about other software too.
null
CC BY-SA 3.0
null
2011-04-10T01:21:50.127
2011-04-10T01:21:50.127
null
null
74
null
9402
2
null
9342
2
null
Another way of thinking about this, which might lend itself to an adaptation for $\ell_1$ is that choice of the mean comes from the fact that the mean is the point that minimizes the sum of squared Euclidean distances. If you're using $\ell_1$ to measure the distance between time series, then you should be using a cent...
null
CC BY-SA 3.0
null
2011-04-10T02:10:19.477
2011-04-10T02:10:19.477
null
null
139
null
9403
2
null
9400
3
null
As we have strong reasons to believe that the cooling will follow the $y(t) = a + e^{-kt}$ function for each beaker I would first check if this model fits the data well indeed. If it does I wouldn't bother with analysing the autocorrelation at all, but focus on the estimation of $k_1$, $k_2$ and $k_3$, and testing the ...
null
CC BY-SA 3.0
null
2011-04-10T02:37:10.260
2011-04-10T13:02:01.177
2011-04-10T13:02:01.177
3911
3911
null
9404
2
null
9390
9
null
The answer to your question depends intricately on what information and assumptions you are going to use. This is because the result of a game is an extraordinarily complicated process. It can become arbitrarily complicated depending on what information you have about: - Players in the particular team - perhaps even...
null
CC BY-SA 3.0
null
2011-04-10T03:24:53.640
2011-04-14T03:21:44.263
2011-04-14T03:21:44.263
2392
2392
null
9405
1
null
null
0
2305
I have two random poisson variables $x_1$ and $x_2$ with value 10 and 25 respectively. I am interested to use likelihood ratio test to test the null hypothesis: $\lambda_1=\lambda_2$, versus alernate hypthesis $\lambda_1$ not equal to $\lambda_2$. I want to use simulation to calculate power and alpha values. I would wa...
Simulation of maximum likelihood ratio test to test two poisson random variables
CC BY-SA 3.0
null
2011-04-10T05:15:44.633
2011-04-11T17:48:03.737
2011-04-10T12:18:59.777
3911
4098
[ "r", "maximum-likelihood", "poisson-distribution", "statistical-power", "likelihood-ratio" ]
9406
2
null
9398
13
null
If I understand correctly, you have a two class classification problem, where the positive class (matches) is rare. Many classifiers struggle with such a class imbalance, and it is common practice to sub-sample the majority class in order to obtain better performance, so the answer to the first question is "yes". How...
null
CC BY-SA 3.0
null
2011-04-10T08:29:11.100
2011-04-10T08:29:11.100
null
null
887
null
9407
1
9408
null
4
13484
I'm trying to compute the minimum sample size for a psychometric test based on 7 point Likert scales. I'd like to run ANOVA on each scale to look for differences between groups. Most online survey sample size calculators seem to be designed for polls, e.g. Yes/No, Agree/Disagree. They take as input population size, a c...
Statistical power and minimum sample size for ANOVA with likert scale as dependent variable
CC BY-SA 3.0
null
2011-04-10T09:58:24.353
2011-04-12T06:59:48.757
2011-04-11T05:55:35.603
183
4099
[ "anova", "likert", "statistical-power", "finite-population" ]
9408
2
null
9407
5
null
The commonly used statistical methods assume that you take a sample of an infinite or very large population. ANOVA, too, has this assumption. When the subjects of your survey can be viewed as a representative sample of an existing or hypothetical much larger population, you do not need the finite population methods. Th...
null
CC BY-SA 3.0
null
2011-04-10T11:29:49.783
2011-04-10T11:29:49.783
null
null
3911
null
9409
2
null
9405
2
null
This is a particularly ill-formed question. If by "alpha" you mean Type I error, you need to go back to Square One and get definitions straight. Type I error is not something inherent in the data, or even in the hypothesis; it's a subjectively and externally applied measure of risk. And without the Type I error, you ...
null
CC BY-SA 3.0
null
2011-04-10T12:07:16.413
2011-04-10T12:07:16.413
null
null
5792
null
9410
2
null
9405
2
null
For the simulation let's first choose sample sizes N1 and N2 for the two Poisson samples: ``` require(lmtest) N1 = 20; N2 = 15 ``` Generate a random sample and run a likelihood ratio test: ``` # CODE BLOCK "A" x = c(rpois(N1, 10), rpois(N2, 25)) group = factor(c(rep('a', N1), rep('b', N2))) m1 = glm(x ~ 1, family=pois...
null
CC BY-SA 3.0
null
2011-04-10T12:09:13.697
2011-04-11T17:48:03.737
2011-04-11T17:48:03.737
3911
3911
null
9411
2
null
9400
4
null
If I understand your question correctly, you should be able to achieve what you want to do using a non-linear mixed-effects model. If you use R, you can use the `nlme` package. Basically as fixed factors you have a covariate (a) and a factor (substance or $i$ in $k_{i}$). You also have a random effect (individual measu...
null
CC BY-SA 3.0
null
2011-04-10T13:09:08.573
2011-04-10T17:25:16.590
2011-04-10T17:25:16.590
2020
2020
null
9412
2
null
9330
1
null
I believe that this is an experiment where it is safe to assume a monotone relationship: for a longer exposition time the infection probability can not be smaller. So you can run monotone/isotonic regression. You can even incorporate into your model that the infection probability at time=0 is 0.
null
CC BY-SA 3.0
null
2011-04-10T13:13:06.367
2011-04-13T02:40:18.117
2011-04-13T02:40:18.117
3911
3911
null
9413
2
null
2715
11
null
Think hard about the underlying data generating process (DGP). If the model you want to use doesn't reflect the DGP, you need to find a new model.
null
CC BY-SA 4.0
null
2011-04-10T14:26:46.080
2018-06-29T02:38:26.897
2018-06-29T02:38:26.897
164061
3265
null
9414
2
null
2
3
null
Other answers have covered what is normality and suggested normality test methods. Christian highlighted that in practice perfect normality barely exists. I highlight that observed deviation from normality does not necessarily mean that methods assuming normality may not be used, and normality test may not be very usef...
null
CC BY-SA 4.0
null
2011-04-10T14:30:50.133
2022-11-23T13:01:37.863
2022-11-23T13:01:37.863
362671
3911
null
9415
1
9418
null
14
7267
Covariance between two random variables defines a measure of how closely are they linearly related to each other. But what if the joint distribution is circlular? Surely there is structure in the distribution. How is this structure extracted?
Measuring non-linear dependence
CC BY-SA 3.0
null
2011-04-10T14:46:33.510
2012-12-05T10:30:41.000
null
null
4101
[ "covariance-matrix" ]
9416
1
null
null
1
253
I have done an experiment to find the effective n/w bandwidth. The data I got in kbps is 223, 221, 510, 220, 471, 229, 222, 221, 220, 221 How can I find the effective bandwidth? Averaging gives 275.8. But if I have done only first 4 rounds then the average is 293.5. How can I find out a more reasonable value as the e...
How to find the effective bandwidth correctly using statistics?
CC BY-SA 3.0
null
2011-04-10T14:55:57.757
2011-04-11T07:51:46.153
2011-04-11T07:38:25.130
183
4102
[ "estimation" ]
9417
2
null
9415
5
null
[Mutual information](http://en.wikipedia.org/wiki/Mutual_information) has properties somewhat analogous to covariance. Covariance is a number which is 0 for independent variables and nonzero for variables which are linearly dependent. In particular, if two variables are the same, then the covariance is equal to varianc...
null
CC BY-SA 3.0
null
2011-04-10T16:30:36.543
2011-04-11T18:37:15.167
2011-04-11T18:37:15.167
3369
3369
null
9418
2
null
9415
10
null
By "circular" I understand that the distribution is concentrated on a circular region, as in this contour plot of a pdf. ![Contour plot of a circular distribution](https://i.stack.imgur.com/qGDE6.png) If such a structure exists, even partially, a natural way to identify and measure it is to average the distribution cir...
null
CC BY-SA 3.0
null
2011-04-10T16:51:07.647
2011-04-11T14:20:58.970
2011-04-11T14:20:58.970
919
919
null
9420
1
null
null
2
637
Contingency tables are typically formatted as tables similar to matrices in mathematics, see [this example](http://en.wikipedia.org/wiki/Contingency_table#Example). Is the equation below an accepted notation of expressing the probabilities of the outcomes as a matrix? If not, what would be the accepted way? Are there a...
Notation of probability matrix corresponding to a contingency table
CC BY-SA 4.0
null
2011-04-10T17:20:13.737
2022-07-11T16:46:21.610
2022-07-11T16:46:21.610
282433
3911
[ "contingency-tables", "matrix", "notation" ]
9421
2
null
9420
1
null
It looks reasonable to me. Though realize that with an N larger than say 1,000, your table of probabilities won't represent exact counts because you'll end up truncating to three or so decimal places.
null
CC BY-SA 3.0
null
2011-04-10T19:42:39.777
2011-04-10T19:42:39.777
null
null
1499
null
9422
1
9443
null
6
203
Suppose I have survey responses that look like this: ``` N=60000, Population n=1000, Total sample n=800, Users of Company X n=200, Randomly chosen from 800 and asked about their Future Use of Company X n=100, Planning to use Company X less in the future ``` The reason that only 200 of 800 users were asked about futu...
Resampling within a survey to account for missing data
CC BY-SA 3.0
null
2011-04-11T01:00:28.697
2011-04-13T04:57:11.190
2011-04-13T04:57:11.190
776
776
[ "sampling", "inference", "resampling" ]
9423
2
null
7019
3
null
If you really only have one data point greater than 1000, it would be easiest just to delete that point from the graph. You can make a note in the caption or as a text box that there is an outlier.
null
CC BY-SA 3.0
null
2011-04-11T01:13:15.487
2011-04-11T01:13:15.487
null
null
1569
null
9424
2
null
9416
2
null
From what I can understand, I think you have the following options: - Sample more! n = 10 is hardly enough for drawing conclusions - If you don't/can't do "enough" sampling, you can always try to do some Monte Carlo type study with bootstrapping
null
CC BY-SA 3.0
null
2011-04-11T07:51:46.153
2011-04-11T07:51:46.153
null
null
3014
null
9425
1
null
null
25
112345
Reading Field's Discovering Statistics Using SPSS (3rd Edition) I was struck by a bit about post-hoc tests in ANOVA. For those wanting to control the Type I error rate he suggests Bonferroni or Tukey and says (p. 374): > Bonferroni has more power when the number of comparisons is small, whereas Tukey is more power...
Bonferroni or Tukey? When does the number of comparisons become large?
CC BY-SA 3.0
null
2011-04-11T12:08:13.933
2015-12-04T16:04:40.800
2015-12-04T16:04:40.800
28666
3597
[ "anova", "multiple-comparisons", "post-hoc", "bonferroni", "tukey-hsd-test" ]
9426
2
null
9420
2
null
I'm not sure I can justify what I'm about to say, but I would be uneasy about expressing probabilities in a form like this. The structure is too reminiscent of other things that don't properly apply and suggests you should be able to do stuff like matrix multiplication that wouldn't mean anything here. If the goal is t...
null
CC BY-SA 3.0
null
2011-04-11T12:23:03.697
2011-04-11T12:23:03.697
null
null
174
null
9427
1
9428
null
5
6929
> Possible Duplicate: Probability distribution value exceeding 1 is OK? I'm a bit confused how I am getting probabilities greater than 1 when calculating p(x | mu, sigma) when x = mu. For example, if I run: ``` >> gaussProb(0, 0, 0.1) ans = 1.2616 ``` where gaussProb is a matlab function from the PMTK toolbox...
Interpreting Gaussian probabilities greater than 1
CC BY-SA 3.0
null
2011-04-11T12:58:01.893
2011-04-11T13:01:11.077
2017-04-13T12:44:36.927
-1
4108
[ "normal-distribution", "matlab" ]
9428
2
null
9427
11
null
The code in the question returns the values of [probability density function](http://en.wikipedia.org/wiki/Probability_density_function). The values of probability density function can be greater than one. The actual probability $P(X<x)$ for random variable $X$ with probability density function $p(x)$ is integral $\int...
null
CC BY-SA 3.0
null
2011-04-11T13:01:11.077
2011-04-11T13:01:11.077
null
null
2116
null
9429
1
10415
null
6
3431
I am trying to fit a multilevel longitudinal model and i have a question regarding how to specify it. The data consist of about 8k observations collected from about 3k individuals at four time points. Individuals are nested in groups and there are about 200 groups. I have two different types of fixed effects: (a) repea...
Correct specification of longitudinal model in lme4
CC BY-SA 3.0
null
2011-04-11T13:42:47.047
2011-05-06T15:27:14.023
2020-06-11T14:32:37.003
-1
1871
[ "r", "multilevel-analysis", "panel-data" ]
9430
2
null
9385
6
null
I am not very familiar with Holt-Winters, however I have this [excellent book](http://www.amazon.co.uk/Forecasting-Exponential-Smoothing-Approach-Statistics/dp/3540719164/ref=sr_1_1?ie=UTF8&s=books&qid=1302529451&sr=8-1) by @Rob Hyndman. The package forecast (which is based on the book) of statistical package R gives t...
null
CC BY-SA 3.0
null
2011-04-11T13:45:02.443
2011-04-11T13:51:21.390
2011-04-11T13:51:21.390
2116
2116
null
9431
1
9528
null
9
1662
I'm running a binary logit regression where I know the dependent variable is miscoded in a small percentage of cases. So I'm trying to estimate $\beta$ in this model: $prob(y_i) = 1/(1 + e^{-z_i})$ $z_i = \alpha + X_i\beta$ But instead of the vector $Y$, I have $\tilde{Y}$, which includes some random errors (i.e. $y_i...
How can I correct for measurement error in the dependent variable in a logit regression?
CC BY-SA 3.0
null
2011-04-11T14:03:13.367
2011-04-13T18:13:24.987
2011-04-11T14:38:25.397
3911
4110
[ "logistic", "measurement-error" ]
9432
2
null
1610
0
null
This is how I remember the difference between Type I and Type II errors Type I is a false POSITIVE Type II is a false NEGATIVE Type I is so POSITIVE it jumps out of bed first, runs downstairs and finds a significant breakfast while Type II is so NEGATIVE it stays in bed all day so when it eventually crawls out all the ...
null
CC BY-SA 3.0
null
2011-04-11T14:31:06.300
2011-04-11T14:31:06.300
null
null
3597
null
9434
2
null
9431
2
null
This situation is often referred to as misclassification error. [This paper](http://www.ncbi.nlm.nih.gov/pubmed/20552681) my help you correctly estimating $\beta$. EDIT: I found relevant-looking papers using [http://www.google.com/search?q=misclassification+of+dependent+variable+logistic](http://www.google.com/search?q...
null
CC BY-SA 3.0
null
2011-04-11T14:41:17.657
2011-04-11T15:34:28.983
2011-04-11T15:34:28.983
3911
3911
null
9435
1
null
null
4
695
I'm trying to create something similar to this. ![enter image description here](https://i.stack.imgur.com/QQVtd.png) So, 3 different Node classes, and a whole bunch of relationships between them. In my case, there should be roughly half of the number of nodes present at most. What I'm looking for is recommendations as ...
Displaying relationships between nodes
CC BY-SA 4.0
null
2011-04-11T14:46:09.620
2019-03-02T00:40:43.843
2019-03-02T00:40:43.843
11887
4112
[ "data-visualization" ]
9436
2
null
9429
3
null
You have a large number of groups, so I speculate that (depending on the setting) you may think about group as a random effect, so your `(…|grp)` terms are probably justified. It may also be reasonable to associate random effects with individuals (`(…|id)` terms). However you have `time` as a covariate in all your mode...
null
CC BY-SA 3.0
null
2011-04-11T15:09:01.237
2011-04-11T17:57:45.803
2011-04-11T17:57:45.803
3911
3911
null
9437
1
null
null
2
224
I am quite a newbie in this area: - What are the boosting methods for regression systems? I know about Gradient boosting; are there any other approaches? - Are there textbooks or tutorials devoted to this area?
Boosting for regression systems
CC BY-SA 3.0
null
2011-04-11T15:10:56.120
2011-04-12T06:49:35.103
2011-04-12T04:46:37.933
183
976
[ "regression", "boosting" ]
9438
2
null
9276
0
null
It seems to me that the problem here is whether the model is too complex to look out without using Monte Carlo simulation. If the model is all relatively simple then it should be possible to look at it through conventioanl statistics and derive a solution to the question being asked, without re-running the model multip...
null
CC BY-SA 3.0
null
2011-04-11T16:37:21.353
2011-04-11T16:37:21.353
null
null
210
null
9441
2
null
8898
2
null
The ROC curve (Receiver Operating Characteristics) is one of the techniques available. You can check the questions with the tag roc on this site for further details. The wikipedia article [http://en.wikipedia.org/wiki/Receiver_operating_characteristic](http://en.wikipedia.org/wiki/Receiver_operating_characteristic) an...
null
CC BY-SA 3.0
null
2011-04-11T17:33:41.190
2011-04-11T18:21:18.727
2011-04-11T18:21:18.727
4116
4116
null
9442
2
null
9190
2
null
[Visual explanations](http://www.edwardtufte.com/tufte/books_visex) or anything else by Tufte is inspirational.
null
CC BY-SA 3.0
null
2011-04-11T18:45:10.307
2011-04-11T18:45:10.307
null
null
2817
null
9443
2
null
9422
2
null
Your question is above my pay grade, as it were, but I can suggest a first look at [the R survey package](http://faculty.washington.edu/tlumley/survey/), which might implement some of the routines that you'd use to answer your questions.
null
CC BY-SA 3.0
null
2011-04-11T18:52:07.253
2011-04-11T18:52:07.253
null
null
1764
null
9444
2
null
9220
2
null
Why not test it out? ``` set.seed(347) x <- rnorm(10000) y <- rnorm(10000) x2 <- rnorm(10000) y2 <- rnorm(10000) qdf <- data.frame(x,y,x2,y2) qdf <- data.frame(qdf,(x-x2)^2+(y-y2)^2) colnames(qdf)[5] <- "euclid" plot(c(x,y),c(x2,y2)) plot(qdf$euclid) hist(qdf$euclid) plot(dentist(qdf$euclid)) ``` ![Plot 1](https:...
null
CC BY-SA 3.0
null
2011-04-11T19:19:33.157
2011-04-11T19:19:33.157
null
null
776
null
9446
1
null
null
3
2765
### Context: My research aims to assess whether parents who have been involved in a relationship with a social worker are at higher risk of child abuse/neglect. I am trying to establish whether there exists a relationship between social workers' attitude toward the parents that reflect an overall outcome of the case...
How to carry out a Likert scale analysis?
CC BY-SA 3.0
null
2011-04-11T19:37:39.740
2011-04-12T04:28:22.427
2011-04-12T04:28:22.427
183
4119
[ "self-study", "psychometrics", "scales", "likert" ]
9447
1
null
null
6
383
I would like to predict the average number of days in a year for which two conditions are true: - daily average temperature is below zero celsius - the day was preceded by at least four days with daily average temperature below zero celsius I've historical daily average temperature data for the location available f...
Estimating event probability from historical time series with clear seasonality
CC BY-SA 3.0
null
2011-04-11T20:01:06.680
2011-04-12T04:32:44.390
2011-04-12T04:32:44.390
183
4120
[ "time-series", "predictive-models", "seasonality" ]
9448
2
null
9447
2
null
I think the joint distribution of temperature data on successive days could be reasonably modelled using a multi-variate Gaussian (Gaussian distributions are often used in statistical downscaling of temperature). What I would try would be to regress the mean and covariance matrix of the temperature time series on sine...
null
CC BY-SA 3.0
null
2011-04-11T20:28:41.743
2011-04-11T20:35:07.073
2011-04-11T20:35:07.073
887
887
null
9449
1
9451
null
9
11446
How do you compute confidence intervals for positive predictive value? The standard error is: $$SE = \sqrt{ \frac{PPV(1-PPV)}{TP+FP}} $$ Is that right? (here my concern is the denominator) Does that formula work for any similar ratio in a 2x2 table. E.g. for sensitivity, it would be $$SE = \sqrt{ \frac{SENS(1-SENS)}{F...
How do you compute confidence intervals for positive predictive value?
CC BY-SA 3.0
null
2011-04-11T20:33:14.453
2011-04-12T02:45:56.907
2011-04-12T02:45:56.907
3911
3186
[ "confidence-interval", "binomial-distribution", "contingency-tables" ]
9450
2
null
9392
2
null
As I understand (see comments to the original question) you want to select a subset of the features by two criteria: - the subset covers most of the information content of the dataset, - the subset includes as few features as possible. The paper [Variable selection in large environmental data sets using principal c...
null
CC BY-SA 3.0
null
2011-04-11T22:43:54.183
2011-04-13T02:59:16.640
2011-04-13T02:59:16.640
3911
3911
null
9451
2
null
9449
12
null
Your first SE formula is correct. The second SE formula which concerns sensitivity should have the total number of positive cases in the denominator: $$SE_\text{sensitivity} = \sqrt{ \frac{SENS(1-SENS)}{TP+FN}} $$ The logic is that sensitivity = $\frac{TP}{TP+FN}$, and the denominator in the SE formula is the same. A...
null
CC BY-SA 3.0
null
2011-04-11T23:22:22.870
2011-04-11T23:22:22.870
null
null
3911
null
9452
2
null
9447
0
null
I know little about meteorology, so my following assumptions may be wrong: today's temperature is similar to yesterday's and the day before yesterday's (maybe more days going back), and also similar to temperature a year age, two years ago, three years ago, etc. If these assumptions got reinforcement I would use an ARM...
null
CC BY-SA 3.0
null
2011-04-11T23:46:32.527
2011-04-11T23:46:32.527
null
null
3911
null
9454
1
9458
null
10
8090
### Context: I have two data sets from the same questionnaire run over two years. Each question is measured using a 5-Likert scale. ### Q1: Coding scheme At the moment, I have coded my responses on a [0, 1] interval, with 0 meaning "most negative response", 1 meaning "most positive response", and other responses ...
Statistical significance of changes over time on a 5-point Likert item
CC BY-SA 3.0
null
2011-04-12T02:44:24.163
2011-04-13T03:23:53.867
2011-04-12T04:01:04.667
183
4123
[ "statistical-significance", "likert" ]
9456
1
32961
null
7
844
Over the years, I picked up many Statistics Concepts in by a variety of situations and means. I studied some Statistics maybe for a couple semesters almost 10 years back. But I also picked up concepts while doing Machine Learning work. I only understood things in a narrow scope - I always tried to get away knowing only...
Hard exemplary problem sets to work through to solidify my understanding of statistical concepts?
CC BY-SA 3.0
null
2011-04-12T03:14:53.957
2015-11-11T11:28:53.737
2015-11-11T11:28:53.737
22468
24040
[ "regression", "anova", "t-test", "references", "structural-equation-modeling" ]
9457
1
9460
null
9
17075
This is a question of definition, does the stats community differentiate these terms?
Is there a difference between seasonality / cyclicality / periodicity
CC BY-SA 3.0
null
2011-04-12T03:25:49.320
2023-03-10T14:20:04.163
null
null
1709
[ "seasonality" ]
9458
2
null
9454
7
null
### 1. Coding scheme In terms of assessing statistical significance using a t-test, it is the relative distances between the scale points that matters. Thus, (0, 0.25, 0.5, 0.75, 1) is equivalent to (1, 2, 3, 4, 5). From my experience an equal distance coding scheme, such as those mentioned previously are the most c...
null
CC BY-SA 3.0
null
2011-04-12T04:16:34.013
2011-04-13T03:23:53.867
2017-04-13T12:44:54.643
-1
183
null
9459
2
null
9457
5
null
Yes, there is a difference. A classic time series decomposition model is $$ Y = T + S + C + I, $$ where \begin{align} Y & = \text{data,} \\ T & = \text{trend,} \\ S & = \text{seasonal,} \\ C & = \text{cyclical,} \\ I & = \text{irregular (i.e. error left over).} \end{align} 'seasonal' refers to REGULAR patterns that occ...
null
CC BY-SA 4.0
null
2011-04-12T04:41:37.783
2023-03-10T14:20:04.163
2023-03-10T14:20:04.163
285236
3919
null
9460
2
null
9457
3
null
Perhaps. Though my take could easily be construed as a bit too anal retentive: I tend to use the term seasonality as a metaphor for the 'seasons' of the year: i.e. Spring, Summer, Fall, Winter (or 'Almost Winter', Winter, 'Still Winter', and 'Construction' if you live in Pennsylvania...). In other words, I would expe...
null
CC BY-SA 3.0
null
2011-04-12T05:41:23.373
2011-04-12T05:41:23.373
null
null
1499
null
9461
1
null
null
5
201
I'm wondering how to test the significance of factor(s) and/or covariate(s) along with modeling the causal relationship among responses. Let me explain this with a concrete example. ### Example: Suppose a researcher observed four responses Y1, Y2, Y3, and Y4 along with three covariates X1, X2, and X3 from an experim...
Testing significance of factors and covariates along with modeling causality among responses
CC BY-SA 3.0
null
2011-04-12T05:42:54.500
2011-09-30T01:33:27.793
2011-04-12T06:48:16.857
3903
3903
[ "multivariate-analysis", "experiment-design", "structural-equation-modeling" ]
9462
2
null
9422
2
null
- Standard formulas for standard errors of a proportion would be suitable. With regards to your question about which companies the "n=100 sample" plan to use in the future, these standard errors would be based on n = 100. If this yields standard errors that are too large for your liking, then you need to increase your...
null
CC BY-SA 3.0
null
2011-04-12T05:54:54.803
2011-04-13T03:30:18.077
2011-04-13T03:30:18.077
183
183
null
9463
2
null
9437
4
null
While I haven't seen anything specifically, I doubt that it would achieve much, at least for linear regression. Each regression equation is just a linear combination of the predictors: $$\hat{y}^{(j)} = \sum_i \hat{\beta}_i^{(j)} x_i$$ Most boosting algorithms in turn combine multiple predictors by taking a weighted av...
null
CC BY-SA 3.0
null
2011-04-12T06:49:35.103
2011-04-12T06:49:35.103
null
null
1569
null
9464
1
9466
null
4
495
I'm trying to fully understand the confidence interval formal given on [this site](http://www.iro.umontreal.ca/~lisa/twiki/bin/view.cgi/Public/DeepVsShallowComparisonICML2007#Results): $$\hat{\mu}\pm z_{1-\alpha/2}\sqrt{\frac{\hat{\mu}(1-\hat{\mu})}{n}}$$ so I can reproduce the same type of intervals for my own data. ...
Can someone give me details about a particular confidence interval formula?
CC BY-SA 3.0
null
2011-04-12T06:54:42.497
2012-01-10T15:00:45.907
2012-01-10T15:00:45.907
919
4127
[ "confidence-interval", "binomial-distribution" ]
9465
2
null
9407
4
null
### 1. Power analysis for one-way ANOVA: Download [G-Power 3](http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3/download-and-register). It allows you to do for a range of statistical tests including ANOVA - a priori power analysis (sample required given effect size, desired power, and alpha), and - pos...
null
CC BY-SA 3.0
null
2011-04-12T06:59:48.757
2011-04-12T06:59:48.757
null
null
183
null
9466
2
null
9464
2
null
If $\hat{\mu}$ is the mean error rate computed averaging $N$ error rates from different $N$ tests, an explanation could be: Let $X$ be the number of errors on $N$ tests, so $X$ is a binomial distributed random variable with mean $N\hat{\mu}$ and variance $N\hat{\mu}(1-\hat{\mu})$ (it is sum of $N$ Bernoulli random var...
null
CC BY-SA 3.0
null
2011-04-12T07:45:02.760
2011-07-21T13:21:28.917
2011-07-21T13:21:28.917
2719
2719
null
9467
1
9473
null
9
568
Following on from my [earlier question](https://stats.stackexchange.com/questions/9341/regularized-fit-from-summarized-data), the solution to the normal equations for ridge regression is given by: $$\hat{\beta}_\lambda = (X^TX+\lambda I)^{-1}X^Ty$$ Could you offer any guidance for choosing the regularization parameter ...
Regularized fit from summarized data: choosing the parameter
CC BY-SA 3.0
null
2011-04-12T08:21:07.817
2011-04-12T13:05:16.340
2017-04-13T12:44:52.660
-1
439
[ "regression", "regularization", "ridge-regression" ]
9468
1
9471
null
4
422
Suppose I have a model of stock prices developed using Brownian motion. I have a second time series derived from the first. At each price point in the first time series, I take the arithmetic mean up to that point and that is the data point for my second time series. The volatility of the second time series is lower...
How do I model the volatility of an arithmetic mean?
CC BY-SA 3.0
null
2011-04-12T10:33:33.660
2011-07-11T14:10:11.577
null
null
4128
[ "standard-deviation" ]
9469
2
null
9454
3
null
Wilcoxon Ranksum Test aka Mann-Whitney is the way to go in the case of ordinal data. The bootstrapping solution is also elegant albeit not the "classic" way to go. The Bootstrapping method might also be valuable in case you aim for other things like factor analysis. In case of regression analysis you might chose ordere...
null
CC BY-SA 3.0
null
2011-04-12T10:39:25.950
2011-04-12T10:39:25.950
null
null
null
null
9470
1
null
null
1
813
I'm trying to replicate the paper of Blundell et al. (2008) to separate permanent and transitory shocks on income on a panel dataset. He solves the non-linear system of equations using Chamberlain's minimum distance estimator (it is shown in the appendix of the paper), but I haven't found a library, nor in R, nor in ST...
Minimum distance estimator
CC BY-SA 3.0
null
2011-04-12T12:12:56.453
2012-12-07T23:03:30.100
2011-04-12T12:23:58.203
2116
null
[ "nonlinear-regression" ]
9471
2
null
9468
2
null
Let's say your stock price series is $S_t$ so that your arithmetic average series is $X_t = \frac{1}{t}\sum_{j=1}^t S_j$. The series of returns that you use to calculate the volatility can be defined in several ways, the most popular being the log-returns series $R_t = \frac{1}{\delta t} \log \frac{S_t}{S_{t-1}}$ and t...
null
CC BY-SA 3.0
null
2011-04-12T12:57:20.417
2011-04-12T13:32:31.587
2011-04-12T13:32:31.587
2425
2425
null
9472
2
null
9464
3
null
Answering the following part of your question: > I don't quite understand what the parameters such as alpha and Z mean $\alpha$ is the parameter that defines the confidence level of the interval. Specifically, the confidence level will be $100(1-\alpha)$%, so to get a 95% confidence interval, set $\alpha=0.05$. $Z...
null
CC BY-SA 3.0
null
2011-04-12T13:01:17.443
2011-04-12T13:01:17.443
null
null
279
null
9473
2
null
9467
7
null
My answer will be based on a nice review of the problem by Anders Bjorkstorm [Ridge regression and inverse problems](http://www2.math.su.se/matstat/reports/seriea/2000/rep5/report.pdf) (I would recommend to read the whole article). Part 4 in this review is dedicated to the selection of a parameter $\lambda$ in ridge re...
null
CC BY-SA 3.0
null
2011-04-12T13:05:16.340
2011-04-12T13:05:16.340
null
null
2645
null
9474
1
9527
null
1
450
I'm looking for an implementation of a fast maximum rank correlation (MRC) estimator. This will be applied to large-ish sparse matrices (~100,000 by 10,000) in a text-mining application. I'm working in python and R, so it would be nice to find something in those languages. Failing that, I could probably convert code fr...
Is there a library that implements a fast maximum rank correlation estimator?
CC BY-SA 3.0
null
2011-04-12T13:42:54.853
2011-04-13T18:07:07.070
2017-05-23T12:39:26.523
-1
4110
[ "r", "estimation", "algorithms", "python" ]
9475
1
null
null
11
5239
I have many time series in this format 1 column in which I have date (d/m/yr) format and many columns that represent different time series like here: ``` DATE TS1 TS2 TS3 ... 24/03/2003 0.00 0.00 ... 17/04/2003 -0.05 1.46 11/05/2003 0.46 -3.86 04/06/2003 -2.21 -1.08 28/06/2003 -1.1...
Time series clustering
CC BY-SA 3.0
null
2011-04-12T14:33:45.357
2020-05-05T04:21:24.840
2011-11-28T09:32:21.230
2116
4133
[ "r", "time-series", "clustering" ]
9476
2
null
9385
5
null
The formulae for Holt-Winters' method include forecasting the seasonal component. You don't need $\gamma=0$. See a forecasting textbook for the details.
null
CC BY-SA 3.0
null
2011-04-12T14:48:00.777
2011-04-12T14:48:00.777
null
null
159
null
9477
1
9480
null
13
40144
My attempts: - I couldn't get confidence intervals in interaction.plot() - and on the other hand plotmeans() from package 'gplot' wouldn't display two graphs. Furthermore, I couldn't impose two plotmeans() graphs one on top of the other because by default the axis are different. - I had some success using plotCI() ...
How to draw an interaction plot with confidence intervals?
CC BY-SA 3.0
null
2011-04-12T16:07:15.017
2011-12-09T15:59:19.010
2011-12-09T15:59:19.010
930
1084
[ "r", "data-visualization", "confidence-interval", "interaction" ]