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Tags
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10249
1
null
null
0
281
I was reading OkTrends and [came across this](http://blog.okcupid.com/index.php/page/3/): > In fact, 32% of successful couples agreed on all of them—which is 3.7× the rate of simple coincidence. So, my question is: what is simple coincidence? How is it calculated? I can't find a Wikipedia article about simple c...
What is simple coincidence?
CC BY-SA 3.0
null
2011-05-02T18:04:51.363
2013-09-04T21:17:02.627
null
null
4441
[ "probability" ]
10250
1
null
null
10
4083
I have data on the percent of organic matter in lake sediments from 0 cm (i.e., the sediment - water interface) down to 9 cm for approximately 25 lakes. In each lake 2 cores were taken from each location so I have 2 replicate measures of organic matter percentage at each sediment depth for each lake. I am intereste...
How to summarize and compare non-linear relationships?
CC BY-SA 3.0
null
2011-05-02T22:05:57.513
2012-06-25T06:33:28.883
null
null
4048
[ "regression", "nonlinear-regression" ]
10251
1
10256
null
62
29861
Principal component analysis can use matrix decomposition, but that is just a tool to get there. How would you find the principal components without the use of matrix algebra? What is the objective function (goal), and what are the constraints?
What is the objective function of PCA?
CC BY-SA 3.0
null
2011-05-02T23:10:16.580
2015-02-07T01:06:13.063
2015-02-07T01:06:13.063
28666
74
[ "pca" ]
10253
2
null
10250
2
null
Check out [Generalized Additive Models](http://en.wikipedia.org/wiki/Generalized_additive_model), which permit fitting non-linear functions without a priori specification of the non-linear form. I'm not sure how one would go about comparing the subsequent fits however. Another similar (in that I believe they both emplo...
null
CC BY-SA 3.0
null
2011-05-02T23:20:45.080
2011-05-03T02:21:12.163
2011-05-03T02:21:12.163
364
364
null
10254
2
null
10220
1
null
If you know the domain of the random variable and maybe have knowledge of some other properties like the mean, variance, etc. but want to be ignorant in a fair way about all other aspects of the distribution, you can find a distribution by applying the [principle of maximum entropy](http://en.wikipedia.org/wiki/Princip...
null
CC BY-SA 3.0
null
2011-05-03T00:58:11.377
2011-05-03T01:11:31.460
2011-05-03T01:11:31.460
4360
4360
null
10255
2
null
10251
5
null
See NIPALS ([wiki](http://en.wikipedia.org/wiki/Non-linear_iterative_partial_least_squares)) for one algorithm which doesn't explicitly use a matrix decomposition. I suppose that's what you mean when you say that you want to avoid matrix algebra since you really can't avoid matrix algebra here :)
null
CC BY-SA 3.0
null
2011-05-03T01:50:30.833
2011-05-03T01:50:30.833
null
null
26
null
10256
2
null
10251
58
null
Without trying to give a full primer on PCA, from an optimization standpoint, the primary objective function is the [Rayleigh quotient](http://en.wikipedia.org/wiki/Rayleigh_quotient). The matrix that figures in the quotient is (some multiple of) the sample covariance matrix $$\newcommand{\m}[1]{\mathbf{#1}}\newcommand...
null
CC BY-SA 3.0
null
2011-05-03T02:27:02.357
2011-05-04T07:49:25.030
2011-05-04T07:49:25.030
4376
2970
null
10257
2
null
421
5
null
So many wonderful recommendations! It's not quite what you asked for, but [How to Lie with Statistics](http://en.wikipedia.org/wiki/How_to_Lie_with_Statistics) is short and quite wonderful. It doesn't directly teach the things you want, but it does help point out violation of assumptions and other flaws.
null
CC BY-SA 3.0
null
2011-05-03T02:40:27.687
2011-05-03T02:40:27.687
null
null
3874
null
10258
2
null
10049
0
null
Based on the output you shared, Maximum # of branches from a node is set at 2. It's possible that raising that limit would give you more options for branches, especially if SAS can take continuous variables and break them up into categories. It's data dredgy, but that's the game we're in, and as long as you crossvali...
null
CC BY-SA 3.0
null
2011-05-03T03:14:21.113
2011-05-03T03:14:21.113
null
null
2669
null
10259
2
null
10049
0
null
If you are using tree-based methods, you can play around with the splitting criterion. For example, at each step, choose the split that gives the highest weighted accuracy (the average of the two classes' accuracies). This can be used as the basis for a random forest too, which should give you a good classifier. I once...
null
CC BY-SA 3.0
null
2011-05-03T03:56:31.520
2011-05-03T03:56:31.520
null
null
2067
null
10260
2
null
10251
30
null
The solution presented by cardinal focuses on the sample covariance matrix. Another starting point is the reconstruction error of the data by a q-dimensional hyperplane. If the p-dimensional data points are $x_1, \ldots, x_n$ the objective is to solve $$\min_{\mu, \lambda_1,\ldots, \lambda_n, \mathbf{V}_q} \sum_{i=1}^n...
null
CC BY-SA 3.0
null
2011-05-03T04:20:44.130
2011-05-04T06:25:29.590
2011-05-04T06:25:29.590
4376
4376
null
10261
1
10263
null
3
1347
While im going through the derivation of E step in EM algorithm for pLSA, i came across the following derivation [at this page](http://www.hongliangjie.com/2010/01/04/notes-on-probabilistic-latent-semantic-analysis-plsa/). Could anyone explain me how the following step is derived. $\sum_z q(z) log \frac{P(X|z,\theta)P...
Derivation of E step in EM algorithm
CC BY-SA 3.0
null
2011-05-03T06:23:35.117
2014-04-02T04:29:02.523
2011-05-03T12:57:33.020
930
4290
[ "expectation-maximization", "latent-semantic-analysis" ]
10262
2
null
6705
4
null
Moran's I statistic is used to explore a specific type of spatial clustering: whether high values are located in proximity to other high values and whether low values are located in proximity to other low values. The trick then is 1st to get a sense of what you mean by proximity and 2nd formulating this mathematically....
null
CC BY-SA 3.0
null
2011-05-03T06:40:58.367
2011-05-03T08:46:51.997
2011-05-03T08:46:51.997
4329
4329
null
10263
2
null
10261
4
null
It looks like [Bayes' formula](http://en.wikipedia.org/wiki/Bayes%27_theorem) : $\Pr[A \mid B] = \frac{\Pr[B \mid A] \Pr[A]}{\Pr[B]}$ Here, it gives: $\Pr[X \mid z, \theta] = \frac{\Pr[z \mid X, \theta] \Pr[X \mid \theta]}{\Pr[z \mid \theta]}$
null
CC BY-SA 3.0
null
2011-05-03T06:47:38.257
2011-05-03T06:47:38.257
2020-06-11T14:32:37.003
-1
3019
null
10264
2
null
3268
2
null
An alternative to multidimentional scaling is making a map of the each group's position to one another as a SOM (Self Organising Maps). Just like you see with a geographic map of the United States with Kansas in the middle, the groups that are positioned near the middle of your SOM map would be the groups that are most...
null
CC BY-SA 3.0
null
2011-05-03T06:52:24.267
2011-05-03T08:26:00.337
2011-05-03T08:26:00.337
4329
4329
null
10265
1
10278
null
5
974
In the paper of [Probabilistic Latent Semantic Analysis](http://www.cs.brown.edu/~th/papers/Hofmann-UAI99.pdf) by Hofmann, the author fits the model for document $\times$ word matrix through EM Algorithm in section 3. I was able to follow the derivation and meaning of the model derived in it. However in the later sect...
What is a "tempered EM algorithm"?
CC BY-SA 3.0
null
2011-05-03T09:12:35.067
2019-10-04T09:30:43.383
2011-05-03T11:06:56.247
null
4290
[ "expectation-maximization", "latent-semantic-analysis" ]
10267
1
null
null
6
5216
I am building a Box-Jenkins model in Excel using solver. The model is AR(2). The data that I have contains trend and seasonality both. I know how to remove seasonality using seasonal indexes and add it back to the forecast. But, how do I handle trend? If I remove trend from the data, how should I add it back to the f...
Predicting forecasts for next 12 months using Box-Jenkins
CC BY-SA 3.0
null
2011-05-03T12:08:37.473
2016-05-23T10:12:22.290
2016-05-23T10:12:22.290
1352
4445
[ "time-series", "forecasting", "arima", "box-jenkins" ]
10268
1
null
null
3
449
I've got a question concerning the estimation of a tobit model with the [AER](http://cran.r-project.org/web/packages/AER/index.html) package in R. I observed t-distributed residuals, so that the assumption of normal distributed std errors is violated. Fortunately it's possible to choose "t" as the distribution when fit...
Tobit model with t-distribution
CC BY-SA 3.0
null
2011-05-03T10:58:28.040
2023-03-31T00:06:30.737
2011-05-03T18:42:17.707
71
null
[ "r", "regression", "tobit-regression" ]
10269
2
null
10267
1
null
Your approach suggests initially adjusting in a deterministic manner the impact of seasonality. This approach may or may not be applicable as the impact of seasonality may be auto-projective in form. The best way to answer this question is to evaluate alternative final models for adequacy in terms of separating the obs...
null
CC BY-SA 3.0
null
2011-05-03T12:28:47.897
2011-05-03T12:53:10.690
2011-05-03T12:53:10.690
3382
3382
null
10270
2
null
10049
4
null
The problem is more with the choice of the accuracy scoring rule. Make sure that the ultimate goal is classification as opposed to prediction. The proportion classified correctly is a discontinuous improper scoring rule. An improper scoring rule is one that is optimized by a bogus model. With an improper scoring ru...
null
CC BY-SA 3.0
null
2011-05-03T13:25:29.633
2011-05-03T13:25:29.633
null
null
4253
null
10271
1
null
null
14
12439
I am working with a time series of anomaly scores (the background is anomaly detection in computer networks). Every minute, I get an anomaly score $x_t \in [0, 5]$ which tells me how "unexpected" or abnormal the current state of the network is. The higher the score, the more abnormal the current state. Scores close to ...
Automatic threshold determination for anomaly detection
CC BY-SA 3.0
null
2011-05-03T13:35:45.367
2011-05-19T18:56:20.710
2011-05-05T08:59:25.660
4446
4446
[ "time-series", "outliers", "threshold" ]
10272
5
null
null
0
null
For two or more dependent variables, use [multivariate-regression](/questions/tagged/multivariate-regression). Linear regression models a variable (the "dependent variable") as varying randomly with respect to a linear combination of other variables (the "independent variables"). Multiple regression includes two or mo...
null
CC BY-SA 4.0
null
2011-05-03T13:39:20.200
2022-07-25T13:54:29.357
2022-07-25T13:54:29.357
121522
919
null
10273
4
null
null
0
null
Regression that includes two or more non-constant independent variables.
null
CC BY-SA 4.0
null
2011-05-03T13:39:20.200
2022-07-25T13:55:51.503
2022-07-25T13:55:51.503
919
919
null
10276
1
10281
null
3
1775
I have a response variable measured at three time points per individual (week 0, 18, and 36). I am interested in differences in the change of the response over the 36 weeks within some categorical variable X. I see two ways of modeling this. - One way ANOVA with response = week_36_score - week_0_score (this seems li...
Best model for change in scores over three time points
CC BY-SA 3.0
null
2011-05-03T14:06:30.987
2011-05-04T01:56:24.750
2011-05-03T15:38:06.650
183
2310
[ "anova", "modeling", "repeated-measures", "panel-data" ]
10277
1
10282
null
9
507
This is a rather general question (i.e. not necessarily specific to statistics), but I have noticed a trend in the machine learning and statistical literature where authors prefer to follow the following approach: Approach 1: Obtain a solution to a practical problem by formulating a cost function for which it is possi...
Advantages of approaching a problem by formulating a cost function that is globally optimizable
CC BY-SA 3.0
null
2011-05-03T14:46:00.920
2016-08-19T23:05:55.560
2016-08-19T22:47:54.237
22468
2798
[ "optimization", "function" ]
10278
2
null
10265
3
null
I found an answer via Google in a [UTexas Paper](http://www.ma.utexas.edu/users/zmccoy/report.pdf). As I suspected from the name, it combines a temperature that decreases ala Simulated Annealing, changing the E step of the algorithm slightly.
null
CC BY-SA 3.0
null
2011-05-03T15:03:25.993
2011-05-03T15:03:25.993
null
null
1764
null
10279
1
null
null
0
96
I am analyzing a large of dataset (n>100) of incident rates, with the aim of forming a normal distribution. Then I will know if a future incident rate (x%) is either close to a historical mean or not, and can score/rate it accordingly with an already created formula. The data is positively-skewed, as most data points ...
Analyzing historical incident rates and rating future performance
CC BY-SA 3.0
null
2011-05-03T15:23:07.630
2011-05-03T17:17:19.583
2011-05-03T17:17:19.583
null
4450
[ "normal-distribution", "data-transformation", "skewness" ]
10280
2
null
10279
4
null
You don't need to transform to a normal distribution to see if a particular value is the top tenth or top fifth of observations. All you need to do is sort your observations (and count them).
null
CC BY-SA 3.0
null
2011-05-03T16:12:25.170
2011-05-03T16:12:25.170
null
null
2958
null
10281
2
null
10276
2
null
In general, I would go with a repeated measures design. There is nothing technically wrong with the first option. However, you are essentially throwing away 1/3 of your data (and 1/2 of your non-baseline data!), which may result in a lost of power. Additionally, since you have a measurement in between baseline and 36 ...
null
CC BY-SA 3.0
null
2011-05-03T16:12:50.613
2011-05-03T16:12:50.613
null
null
2144
null
10282
2
null
10277
3
null
My believe is that the goal should be to optimize the function you are interested in. If that happens to be the number of misclassifications - and not a binomial likelihood, say - then you should try minimizing the number of misclassifications. However, for the number of practical reasons mentioned (speed, implementati...
null
CC BY-SA 3.0
null
2011-05-03T17:45:30.897
2011-05-04T16:12:42.777
2011-05-04T16:12:42.777
4376
4376
null
10283
2
null
10271
1
null
Do you have any 'labeled' examples of what constitutes an anomaly? i.e. values associated with a network failure, or something like that? One idea you might consider applying is a ROC curve, which is useful for picking threshholds that meet a specific criteria, like maximizing true positives or minimizing false negativ...
null
CC BY-SA 3.0
null
2011-05-03T18:18:53.510
2011-05-03T18:18:53.510
null
null
2817
null
10284
2
null
10267
5
null
If you are at all familiar with [R](http://www.r-project.org/) (if you're building time series models, you should be), check out the [forecast](http://cran.r-project.org/web/packages/forecast/index.html) package. It's designed to choose parameters for Arima as well as exponential smoothing models, and uses a solid meth...
null
CC BY-SA 3.0
null
2011-05-03T18:23:46.203
2011-05-04T15:17:58.293
2011-05-04T15:17:58.293
2817
2817
null
10285
1
null
null
5
25168
### Context I ran an experiment with `3 x 2` design with three levels of within subjects factor (repeated measures) and two levels to the between subjects factors. I am interested in examining the changes from baseline and the interaction effect. ### Question - How do I compute the required sample size for a ...
Sample size required for mixed design ANOVA to achieve adequate statistical power
CC BY-SA 3.0
null
2011-05-03T18:31:11.137
2011-05-04T16:12:13.730
2011-05-04T04:03:35.047
183
4453
[ "anova", "repeated-measures", "statistical-power" ]
10289
1
null
null
171
289532
At work we were discussing this as my boss has never heard of normalization. In Linear Algebra, Normalization seems to refer to the dividing of a vector by its length. And in statistics, Standardization seems to refer to the subtraction of a mean then dividing by its SD. But they seem interchangeable with other possibi...
What's the difference between Normalization and Standardization?
CC BY-SA 3.0
null
2011-05-03T20:26:45.730
2021-10-09T18:06:13.350
2017-11-15T08:39:52.533
101426
4455
[ "descriptive-statistics", "normalization", "standardization" ]
10290
2
null
10121
1
null
If you are trying to generate random correlation matrices, consider sampling from the Wishart distribution. This following question provides information the Wishart distribution as well as advice on how to sample: [How to efficiently generate random positive-semidefinite correlation matrices?](https://stats.stackexchan...
null
CC BY-SA 3.0
null
2011-05-03T20:40:19.043
2011-05-03T20:40:19.043
2017-04-13T12:44:26.710
-1
2773
null
10291
2
null
10289
50
null
In the business world, "normalization" typically means that the range of values are "normalized to be from 0.0 to 1.0". "Standardization" typically means that the range of values are "standardized" to measure how many standard deviations the value is from its mean. However, not everyone would agree with that. It...
null
CC BY-SA 3.0
null
2011-05-03T21:02:01.230
2011-05-04T03:51:50.550
2011-05-04T03:51:50.550
2775
2775
null
10292
2
null
10289
7
null
The answer is simple, but you're not going to like it: it depends. If you value 1 standard deviation from both scores equally, then standardization is the way to go (note: in fact, you're [studentizing](http://en.wikipedia.org/wiki/Studentized_range), because you're dividing by an estimate of the SD of the population)....
null
CC BY-SA 3.0
null
2011-05-03T21:08:58.627
2011-05-03T21:08:58.627
null
null
4257
null
10293
1
null
null
3
961
I have some data that a downstream system needs an optimized function of boolean logic for. Essentially I have data similar to: ``` User cat1 cat2 cat3 cat4 1 0 0 0 1 2 1 0 0 1 3 0 1 1 0 ``` I must optimize cat4 as a function like this: `(cat1 or cat2 or cat3)`. "Or" is th...
Optimize a boolean function
CC BY-SA 3.0
null
2011-05-03T21:47:17.023
2017-04-08T18:21:13.197
2017-04-08T18:21:13.197
11887
739
[ "machine-learning", "optimization", "many-categories" ]
10294
2
null
10276
4
null
There are difficulties in computing change. This doesn't work on ordinal repsonses, and for continuous responses makes a strong assumption of proper choice of transformations for the variables. I recommend adjusting for baseline and modeling the 2nd and 3rd measurements as longitudinal measurements. Repeated measur...
null
CC BY-SA 3.0
null
2011-05-03T22:08:01.730
2011-05-04T01:56:24.750
2011-05-04T01:56:24.750
4253
4253
null
10295
1
null
null
22
391
I am trying to put together a data-mining package for StackExchange sites and in particular, I am stuck in trying to determine the "most interesting" questions. I would like to use the question score, but remove the bias due to the number of views, but I don't know how to approach this rigorously. In the ideal world, I...
"Interestingness" function for StackExchange questions
CC BY-SA 3.0
null
2011-05-03T21:53:26.910
2011-05-05T01:16:53.857
2011-05-05T00:13:04.400
4456
4456
[ "data-mining", "predictive-models" ]
10297
2
null
498
1
null
I have had the exact same problem . . . in fact I'm having right now! It seems to matter whether or not I include the blue-colored labels from the output window. Try copying only the text in black (the table fillin's) and see if that does the trick. It worked for me just now, and then when I go back and try again to...
null
CC BY-SA 3.0
null
2011-05-03T22:59:01.330
2011-05-03T22:59:01.330
null
null
4459
null
10298
2
null
10289
122
null
Normalization rescales the values into a range of [0,1]. This might be useful in some cases where all parameters need to have the same positive scale. However, the outliers from the data set are lost. $$ X_{changed} = \frac{X - X_{min}}{X_{max}-X_{min}} $$ Standardization rescales data to have a mean ($\mu$) of 0 and...
null
CC BY-SA 3.0
null
2011-05-04T00:05:54.767
2016-12-31T18:27:47.567
2016-12-31T18:27:47.567
73527
2202
null
10299
2
null
498
1
null
I have the problem sometimes. It seems as long as I do not highlight the whole output window but instead highlight all of it except the last line and leave a little extra space at the end of the line it always works. If you are facing the problem try copying just the middle section and see if it works, if so then this...
null
CC BY-SA 3.0
null
2011-05-04T02:39:22.600
2011-05-04T02:39:22.600
null
null
2310
null
10300
2
null
7200
13
null
I suppose I'm too late the hero, but I wanted to comment on cardinal's post, and this comment became too big for its intended box. For this answer, I'm assuming $x >0$; appropriate reflection formulae can be used for negative $x$. I'm more used to dealing with the error function $\mathrm{erf}(x)$ myself, but I'll try t...
null
CC BY-SA 3.0
null
2011-05-04T03:37:21.730
2011-05-04T13:33:45.540
2011-05-04T13:33:45.540
830
830
null
10301
2
null
10293
1
null
Think you mean something like which categories you should take into account to union them with the OR operator to get a good probability to predict the last variable? On your training set, try to develop a model based on minimum binary integer programming (mBIP; as proposed here: [http://www.sce.carleton.ca/faculty/ch...
null
CC BY-SA 3.0
null
2011-05-04T04:30:36.277
2011-05-04T04:30:36.277
null
null
1158
null
10302
1
10340
null
57
44387
I came across term perplexity which refers to the log-averaged inverse probability on unseen data. Wikipedia [article](http://en.wikipedia.org/wiki/Perplexity) on perplexity does not give an intuitive meaning for the same. This perplexity measure was used in [pLSA](http://www.cs.brown.edu/~th/papers/Hofmann-UAI99.pdf)...
What is perplexity?
CC BY-SA 3.0
null
2011-05-04T06:04:26.560
2021-12-10T23:40:29.340
2021-12-10T23:40:29.340
11887
4290
[ "intuition", "information-theory", "measurement", "perplexity" ]
10303
1
10304
null
4
108
Using OLS, I've estimated the following equation: $y_i = \alpha_0 + \alpha_1 X_i + \epsilon_i$ I know that theoretically, the following should be true: $y_i = a + (1-e^{-\lambda 60}) X_i$ Is there any way, having an estimate of $\alpha_1$ I can translate it to an estimate of $\lambda$? As a follow up, if this is not ...
Using an OLS coefficient to estimate a non-linear coefficient
CC BY-SA 3.0
null
2011-05-04T06:45:56.653
2011-05-04T07:20:52.663
null
null
726
[ "distributions", "estimation", "normal-distribution", "log-linear" ]
10304
2
null
10303
5
null
Judging from your equations there is no reason for the OLS estimate of $\alpha_1$ not to be consistent and asymptotically normal. So you can use plug-in estimate for $\lambda$: $$\hat{\lambda}=-\frac{1}{60}\log(1-\hat{\alpha}_1)$$ Using [delta method](http://en.wikipedia.org/wiki/Delta_method) it would be possible to s...
null
CC BY-SA 3.0
null
2011-05-04T07:20:52.663
2011-05-04T07:20:52.663
null
null
2116
null
10305
1
null
null
4
1329
When does/can one use the likelihood ratio significance test instead of Fisher's exact test or its Pearson $\chi^2$ approximation for comparing two binomial datasets? Given two binomial datasets (distributions), I'm seeing the LR test being used to compare one distribution against the global (combined) distribution. Us...
Likelihood ratio test vs. $\chi^2$/Z-test for comparing binomial datasets
CC BY-SA 3.0
null
2011-05-04T07:38:37.180
2017-11-06T12:21:09.443
2017-11-06T12:21:09.443
101426
1720
[ "hypothesis-testing", "likelihood-ratio", "fishers-exact-test" ]
10306
2
null
10267
3
null
The time series are usually [decomposed](http://en.wikipedia.org/wiki/Decomposition_of_time_series) into 3 parts, trend, seasonality and irregular. (The link gives 4 parts, but cyclical and seasonality are usually lumped together). Strictly speaking ARIMA type of models are only used for irregular part and by their des...
null
CC BY-SA 3.0
null
2011-05-04T08:02:11.270
2011-05-04T08:02:11.270
null
null
2116
null
10307
2
null
10285
8
null
- You need to decide what is acceptable statistical power for a given significance test. The rule of thumb of 80% power being reasonable is often bandied about. However, I think it is more sensible to see sample size selection as an optimisation problem, where statistical power is but one consideration, and the cost o...
null
CC BY-SA 3.0
null
2011-05-04T08:25:15.447
2011-05-04T16:12:13.730
2011-05-04T16:12:13.730
183
183
null
10308
1
null
null
9
2492
I would like to explore the different ways one can detrend a time series without look ahead bias. I wanted to use the Hodrick Prescott filter, which seems like a quite good frequency filter, but it is based on an optimization method, and I understand that it may give strange and volatile results at the border. Wavelet ...
How to remove trend with no look ahead bias?
CC BY-SA 3.0
null
2011-05-04T08:30:37.473
2013-10-09T06:01:19.347
2011-05-04T11:02:09.977
1709
1709
[ "time-series", "econometrics", "trend" ]
10309
1
null
null
6
9142
I am carrying out a statistical analysis for my research. I am using a Friedman's test with post hoc analysis. At present I am using the function `friedman.test.with.post.hoc` available for R software. This function reports "maxT" value instead of the chi-square value. Someone can explain me what is maxT and its relati...
Friedman's test and post-hoc analysis
CC BY-SA 3.0
null
2011-05-04T09:07:08.330
2011-05-13T09:55:18.950
2011-05-04T09:46:04.787
930
4461
[ "hypothesis-testing", "anova", "nonparametric", "repeated-measures", "permutation-test" ]
10310
2
null
10308
0
null
De-trending requires a pre-specification of of how many values do you require before declaring that a new trend has started. Given this specification , say n values then one has to be concerned with distinguishing between Level Shifts ( i.e. intercept changes ) and time trend changes. If you assume that there are no Le...
null
CC BY-SA 3.0
null
2011-05-04T09:12:27.980
2011-05-04T09:12:27.980
null
null
3382
null
10311
1
10312
null
7
730
I analyze a set of multivariate measurements. It is known that several pairs of independent variables show high linear correlation. The graph below shows a scatterplot of one such pair (X and Y, upper pane), as well the residuals as a function of Y (lower left pane) and the histogram of these residuals (lower right pan...
Weird residuals in linear regression
CC BY-SA 3.0
null
2011-05-04T11:03:30.273
2012-07-25T15:10:14.870
2012-07-25T15:10:14.870
3748
1496
[ "regression", "dataset", "outliers", "residuals" ]
10312
2
null
10311
9
null
What is the value of the residual that shows such a high count? It does not appear to be zero (slightly to the right of 0), so maybe 1? In any case, there may be something about that value that may provide you with some insight about the underlying mechanism. For example, if X and Y are measurements taken by observers,...
null
CC BY-SA 3.0
null
2011-05-04T12:03:26.133
2011-05-04T12:03:26.133
null
null
1934
null
10313
2
null
10305
3
null
Generally speaking, the likelihood ratio and the ordinary Pearson $\chi^2$ tests are more accurate than Fisher's "exact" test. But for your situation you need an extremely heavy multiplicity adjustment thrown in, not matter which statistical test is used. Decision trees such as the one you are building require amazin...
null
CC BY-SA 3.0
null
2011-05-04T12:42:45.710
2011-05-04T12:42:45.710
null
null
4253
null
10314
2
null
9040
4
null
checkout Gephi, this software has some very good layout algorithms to handle the spaghetti problem: [http://gephi.org/features/](http://gephi.org/features/) Especially, try the ForceAtlas layout: [http://forum.gephi.org/viewtopic.php?f=26&t=926](http://forum.gephi.org/viewtopic.php?f=26&t=926) The software let you cont...
null
CC BY-SA 3.0
null
2011-05-04T13:50:39.353
2011-05-04T13:50:39.353
null
null
4443
null
10315
2
null
9435
1
null
Gephi, an open source network visualization software, can do that: [http://gephi.org](http://gephi.org) See [this recent discussion](http://forum.gephi.org/viewtopic.php?f=29&t=1016) on what a user was able to do with a bipartite graph, which is what you have. It is also called a bipartite network, or a two-mode netwo...
null
CC BY-SA 3.0
null
2011-05-04T13:57:44.040
2011-05-04T13:57:44.040
null
null
4443
null
10316
1
null
null
13
43904
I'm working on a multiple logistic regression in R using `glm`. The predictor variables are continuous and categorical. An extract of the summary of the model shows the following: ``` Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 2.451e+00 2.439e+00 1.005 0.3150 Age 5.74...
Interpreting logistic regression output in R
CC BY-SA 3.0
null
2011-05-04T14:49:20.663
2018-02-07T22:11:40.747
2013-10-24T13:32:53.260
28740
2824
[ "r", "logistic", "interpretation", "p-value" ]
10317
2
null
10316
8
null
There are a host of questions here on the site that will help with the interpretation of the models output (here are three different examples, [1](https://stats.stackexchange.com/q/3628/1036) [2](https://stats.stackexchange.com/q/8106/1036) [3](https://stats.stackexchange.com/q/6740/1036) , and I am sure there are more...
null
CC BY-SA 3.0
null
2011-05-04T15:15:26.640
2018-02-07T22:11:40.747
2018-02-07T22:11:40.747
194258
1036
null
10318
2
null
10308
3
null
There is no way to get rid of the end effects. Like any interpolation technique, the HP method depends on data before and after the current location to provide a filtered point/line for that location. As you approach either end of the data series and drop below the required number of future (or past) points, you eith...
null
CC BY-SA 3.0
null
2011-05-04T15:42:02.307
2011-05-04T15:42:02.307
null
null
2775
null
10320
1
null
null
5
154
Context I have a set of data that was collected from several inertial measurement units (orientation and acceleration data). I want to determine to what extent an inference method degrades when the data becomes noisy (or, should I say "noisier"). Questions How do I determine what type of noise to use? Is there a way in...
Determing noise type and level of noise
CC BY-SA 3.0
null
2011-05-04T15:56:25.277
2011-05-04T15:56:25.277
null
null
3052
[ "regression", "white-noise" ]
10321
2
null
10058
3
null
Following Nick Sabbe's answer, here is the simplest GLMM solution I can come up with: ``` dej$location <- factor(rep(1:25,2)) library(lme4) glmer(count ~ type1 + type2*species + perc.for.100m + perc.dry.100m + perc.wet.100m + (1|location), family = poisson, data = dej) ``` It would be a good idea to check for ...
null
CC BY-SA 3.0
null
2011-05-04T16:50:48.563
2011-05-04T16:50:48.563
null
null
2126
null
10322
1
10327
null
4
338
My girlfriend is an Actuarial Analyst at a large insurance company in the Netherlands and because we'll soon have our two year anniversary, I thought of gifts for her. On [Proof: Math is beautiful](http://proofmathisbeautiful.tumblr.com/post/5104877044/baseln-statistical-distribution-plushies-am) I discovered these [Di...
What distribution pluffy to buy for an aspiring econometrician?
CC BY-SA 3.0
null
2011-05-04T18:25:56.640
2013-05-06T21:09:32.367
2013-05-06T21:09:32.367
25315
4468
[ "distributions" ]
10323
2
null
10322
0
null
From the list I would pick standard normal. After all regression is the main tool of econometrician and usually econometrician can rely only on asymptotic results, hence standard normal rules them all :) Having said that I would not like to get a standard normal distribution pluffy (I am not a girl, but can be conside...
null
CC BY-SA 3.0
null
2011-05-04T18:39:13.447
2011-05-04T18:39:13.447
null
null
2116
null
10324
2
null
10322
6
null
You're in big trouble if you're asking us for gift advice.
null
CC BY-SA 3.0
null
2011-05-04T19:10:31.520
2011-05-04T19:10:31.520
null
null
2775
null
10325
1
null
null
7
1700
In the book “Programming Collective Intelligence” Segaran explains the Fisher method for categorizing text as an alternative to Naive Bayes classifier. The Fisher method uses inverse-chi-square-distribution, which I do not really understand. I watched this video found on stats.stackexchange about chi-square-distributio...
What does inverse-chi-square in Fisher method (classifying) exactly do?
CC BY-SA 3.0
0
2011-05-04T19:24:03.320
2021-02-06T17:05:42.443
2021-02-06T17:05:42.443
11887
4350
[ "text-mining", "chi-squared-distribution", "combining-p-values", "inverse-gamma-distribution" ]
10326
2
null
10322
2
null
Insurance is all about skewed distributions with long tails: think amount of loss. These also typically have only positive values. The log-normal distribution looks most like one of those. Another good option is the Gumbel distribution, which comes up in extreme value theory.
null
CC BY-SA 3.0
null
2011-05-04T19:31:35.703
2011-05-04T19:31:35.703
null
null
279
null
10327
2
null
10322
13
null
You gotta get her one with some Kurtosis. Maybe the t-distribution. And be sure and write a loving note along the lines of, "Baby, when I think of fat tails, I think of you. Your kurtosis makes you non-normal." My wife digs it when I get sappy like that. I have the scars to prove it.
null
CC BY-SA 3.0
null
2011-05-04T20:10:51.810
2011-05-04T20:10:51.810
null
null
29
null
10328
1
10336
null
7
8117
I know that I, and others, sometimes get confused by the hypergeometric distribution (HD) as it pertains to overlapping lists. This is because the HD is usually described with the "balls in an urn" metaphor and not using "overlapping lists." What is the proper way to calculate the p-value, according to the hypergeometr...
Using R's phyper to get the probability of list overlap
CC BY-SA 3.0
null
2011-05-04T15:13:26.520
2011-05-05T07:29:10.630
2011-05-05T07:29:10.630
null
3561
[ "r" ]
10329
1
10333
null
8
495
What functionality should exist in a [CAS](http://en.wikipedia.org/wiki/Computer_algebra_system) that was specifically geared toward Statistics? Symbolic algebra systems like Mathematica and Maple are often used for calculus, logic, and physics problems but are rarely used for statistics. Why is this? What statistical ...
Symbolic computer algebra for statistics
CC BY-SA 3.0
null
2011-05-04T20:32:27.960
2019-01-19T23:04:45.170
2019-01-19T23:04:45.170
99274
3830
[ "python", "computational-statistics", "mathematica", "maple" ]
10330
2
null
10322
2
null
Aren't [econometricians](http://en.wikipedia.org/wiki/What%27s_that_got_to_do_with_the...?) concerned with the [price of t (distributions) in China](http://supertart.com/priceofteainchina/index.php)? It has the large (on occasion, infinite) kurtosis recommended by @JD Long, too.
null
CC BY-SA 3.0
null
2011-05-04T20:52:28.667
2011-05-04T20:52:28.667
null
null
919
null
10331
1
10332
null
5
1210
I'm working on some practice test problems, and one of them says to design a rejection sampling algorithm to produce draws from a unit exponential using draws from a Gamma(2,1). I don't understand how this is possible, because I am under the impression that the "envelope function" g(x) needs to be scalable in such a ...
How to use rejection sampling to generate draws from Unit Exponential
CC BY-SA 3.0
null
2011-05-04T21:17:49.260
2011-05-05T21:09:49.177
2011-05-05T21:09:49.177
8
2984
[ "self-study", "monte-carlo", "simulation" ]
10332
2
null
10331
5
null
Try a location shift on the Gamma(2,1) EDIT: [Illustration](http://www.wolframalpha.com/input/?i=3%2a%28x%2b1%29%20%2a%20exp%28-%28x%2b1%29%29%20vs%20exp%28-x%29%20from%200%20to%206)
null
CC BY-SA 3.0
null
2011-05-04T23:17:36.520
2011-05-05T17:07:45.637
2011-05-05T17:07:45.637
3567
3567
null
10333
2
null
10329
9
null
Support for matrix algebra. The vast majority of practiced statistics is multivariate and involves matrices, and often simplifying matrix forms requires special rules that aren't easily translated from a univariate case, so good matrix support would be really helpful.
null
CC BY-SA 3.0
null
2011-05-04T23:29:40.427
2011-05-04T23:29:40.427
null
null
2839
null
10334
2
null
10295
1
null
This is my theory. I think there are two kinds of questions: those that remain mostly within SE (which usually have fewer views), and those that are viewed by outsiders because it was linked from somewhere else (usually have more views). For the questions that remain mostly within SE, votes are a good measure of inter...
null
CC BY-SA 3.0
null
2011-05-05T01:09:16.273
2011-05-05T01:09:16.273
null
null
2965
null
10335
2
null
10295
3
null
One might define an interesting question as one that has received comparatively many votes given the number of views. To this end, you can create a baseline curve that reflects the expected number of votes given the views. Curves that attracted a lot more votes than the baseline were considered particularly interesting...
null
CC BY-SA 3.0
null
2011-05-05T01:16:53.857
2011-05-05T01:16:53.857
null
null
198
null
10336
2
null
10328
10
null
Trying to translate this into a statistical question, it seems you have a population with $a$ members and you take two random samples without replacement sized $b$ and $c$, and you want the distribution of $X$, the number appearing in both samples. As an illustration, suppose $a=5$, $b=2$ and $c=3$. There are 100 ways ...
null
CC BY-SA 3.0
null
2011-05-05T01:29:25.800
2011-05-05T01:29:25.800
null
null
2958
null
10337
1
22173
null
8
34425
What would be $\operatorname{Var}(X^2)$, if $\operatorname{Var}(X)=\sigma^2$?
$\operatorname{Var}(X^2)$, if $\operatorname{Var}(X)=\sigma^2$
CC BY-SA 4.0
null
2011-05-05T03:42:06.087
2018-12-18T23:35:56.927
2018-12-18T23:35:56.927
5176
3903
[ "mathematical-statistics", "variance" ]
10338
1
null
null
3
1980
I want to perform bootstrapping for calculation of efficiency score from data envelopment analysis (DEA) using R. - Are there any examples of data and results for this type of analysis in R to enable me to check my results? - Are there any online or other resources that might assist my task?
Bootstrapping data envelopment analysis efficiency score using R
CC BY-SA 3.0
null
2011-05-05T05:47:30.180
2012-10-09T09:41:04.573
2011-05-05T08:03:28.140
183
4472
[ "r", "bootstrap", "efficiency" ]
10339
2
null
10337
13
null
As a simple example of the responses of @user2168 and @mpiktas: The variance of the set of values 1,2,3 is 0.67, while the variance of its square is 10.89. On the other hand, the variance of 2,3,4 is also 0.67, but the variance of the squares is 24.22. These are just variances for finite sets of data, but the idea exte...
null
CC BY-SA 3.0
null
2011-05-05T06:35:12.517
2011-05-05T06:35:12.517
null
null
4257
null
10340
2
null
10302
25
null
You have looked at the [Wikipedia article on perplexity](http://en.wikipedia.org/wiki/Perplexity). It gives the perplexity of a discrete distribution as $$2^{-\sum_x p(x)\log_2 p(x)}$$ which could also be written as $$\exp\left({\sum_x p(x)\log_e \frac{1}{p(x)}}\right)$$ i.e. as a weighted geometric average of the...
null
CC BY-SA 3.0
null
2011-05-05T07:07:56.453
2011-05-05T07:07:56.453
null
null
2958
null
10342
1
null
null
4
3131
Given a panel of countries over time, a fixed effects estimator makes sense to control for country-specific effects. My intuition tells me that if the dependent variable is correlated with lags of the independent variables, then bias will be introduced into the estimator. However, I'm having difficulty rigorously under...
Panel Data: In a fixed effects model, does auto-correlation introduce bias?
CC BY-SA 3.0
null
2011-05-05T08:06:46.827
2011-05-05T08:06:46.827
null
null
726
[ "autocorrelation", "panel-data", "fixed-effects-model" ]
10343
1
10351
null
8
2393
I am totally confused: On the one hand you can read all kinds of explanations why you have to divide by n-1 to get an unbiased estimator for the (unknown) population variance (degrees of freedom, not defined for sample size 1 etc.) - see e.g. [here](http://en.wikipedia.org/wiki/Bessel%27s_correction) or [here](https://...
When estimating variance, why do unbiased estimators divide by n-1 yet maximum likelihood estimates divide by n?
CC BY-SA 4.0
null
2011-05-05T08:11:02.280
2019-03-02T22:56:03.470
2018-09-12T08:27:00.863
11887
230
[ "normal-distribution", "variance", "unbiased-estimator" ]
10344
2
null
10343
7
null
The MLE is indeed found through division by n. However, MLE's are not guaranteed to be unbiased. So there is no contradiction in the fact that the unbiased estimator (divided by n-1) is used. In practice, for reasonable sample sizes, it should not make a big difference anyway.
null
CC BY-SA 3.0
null
2011-05-05T08:18:56.053
2011-05-05T08:18:56.053
null
null
4257
null
10345
2
null
423
54
null
![enter image description here](https://i.stack.imgur.com/z55DL.jpg) Found this one in the [comments on Andrew Gelman's blog](http://www.stat.columbia.edu/~cook/movabletype/archives/2011/04/worst_statistic.html#comment-2512168).
null
CC BY-SA 3.0
null
2011-05-05T09:27:32.327
2011-05-05T09:27:32.327
null
null
442
null
10346
1
10348
null
4
102
I am running a logistic regression with customer event data with multiple predictors. However, one variable is extremely important, alone predicting 60% of the customers for the event. When this main predictor is included in the model, other predictors add very little to prediction over and above this main predictor. ...
Is it problematic if one predictor in a set accounts for almost all the prediction?
CC BY-SA 3.0
null
2011-05-05T09:34:46.440
2011-05-05T10:32:03.557
2011-05-05T10:31:15.537
183
1763
[ "logistic", "modeling" ]
10347
1
null
null
6
8846
I have made a heatmap based upon a regular data matrix in R, the package I use is `pheatmap`. Regular clustering of my samples is performed by the `distfun` function within the package. Now I want to attach a precomputed distance matrix (generated by Unifrac) to my previously generated matrix/heatmap. Is this possible...
Making a heatmap with a precomputed distance matrix and data matrix in R
CC BY-SA 3.0
null
2011-05-05T09:39:26.173
2019-01-15T23:26:36.430
2011-05-05T11:18:43.750
930
4473
[ "r", "data-visualization" ]
10348
2
null
10346
2
null
I understand your gut feeling. But depending on the type of response and predictor, this has not to be unsual (example: response = "weight", predictors "height" and others with presumably less meaning like "state", "favorite movie" etc.). However, you should check that for the creation of the predictor only information...
null
CC BY-SA 3.0
null
2011-05-05T10:32:03.557
2011-05-05T10:32:03.557
null
null
264
null
10349
2
null
10347
4
null
Ok, so you can just look at the code by typing the name of the function at the R prompt, or use `edit(pheatmap)` to see it in your default editor. Around line 14 and 23, you'll see that another function is called for computing the distance matrices (for rows and columns), given a distance function (R `dist`) and a meth...
null
CC BY-SA 3.0
null
2011-05-05T11:02:11.647
2011-05-05T11:02:11.647
null
null
930
null
10350
1
10352
null
6
673
I am working on insurance data in which a customer has a field named `customer_no_dependent` (customer's number of dependent). Its coming out to be a significant variable( just that it has $p<0.0001$). This variable has almost 20% missing values. For imputation, I thought to determine proxy indicators for number of de...
Advice on missing value imputation
CC BY-SA 3.0
null
2011-05-05T11:20:13.343
2012-12-19T20:10:02.963
2011-05-05T12:10:32.370
2116
1763
[ "data-imputation" ]
10351
2
null
10343
6
null
The answer to your question is contained within your question. When choosing an estimator for a parameter, you should ask yourself, what property would you like your estimator to have: - Robustness - Unbiasedness - Have the distributional properties of a MLE - Consistency - Asymptotically normal - You know the p...
null
CC BY-SA 3.0
null
2011-05-05T12:15:11.133
2011-05-05T12:15:11.133
null
null
3805
null
10352
2
null
10350
5
null
First of all: it is not clear from your explanation whether or not you have done multiple imputation. If not: please do so: single imputation could be worse than simple complete case analysis, and can both lead to severely biased results. Next, if I understand correctly, your problem is that you don't know which variab...
null
CC BY-SA 3.0
null
2011-05-05T12:24:24.350
2011-05-05T12:24:24.350
null
null
4257
null
10353
1
null
null
8
2124
### Context: My question concerns a typical design in my area – a researcher takes a group of subjects (say 10) and then applies three different conditions to them to measure the change in a response variable, e.g. vertical jump height performed after drinking a glucose drink, coloured plain water, and fruit juice (...
How to analyse repeated measure ANOVA with three or more conditions presented in randomised order?
CC BY-SA 3.0
null
2011-05-05T12:26:43.317
2014-12-06T05:40:54.650
2013-05-03T13:18:51.167
6029
4474
[ "hypothesis-testing", "anova", "repeated-measures" ]
10354
2
null
9653
-1
null
Another consequence of a small sample is the increase of type 2 error. Nunnally demonstrated in the paper "The place of statistics in psychology", 1960, that small samples generally fail to reject a point null hypothesis. These hypothesis are hypothesis having some parameters equals zero, and are known to be false in t...
null
CC BY-SA 3.0
null
2011-05-05T12:28:58.153
2011-05-05T12:28:58.153
null
null
4443
null
10356
1
null
null
10
7830
I am building a propensity model using logistic regression for a utility client. My concern is that out of the total sample my 'bad' accounts are just 5%, and the rest are all good. I am predicting 'bad'. - Will the result be biassed? - What is optimal 'bad to good proportion' to build a good model?
Is a logistic regression biased when the outcome variable is split 5% - 95%?
CC BY-SA 3.0
null
2011-05-05T14:03:29.927
2017-08-30T17:11:38.003
2011-05-06T14:07:42.000
495
4478
[ "logistic", "modeling" ]
10357
2
null
10356
1
null
In theory, you will be able to discriminate better if the proportions of "good" and "bad" are roughly similar in size. You might be able to move towards this by stratified sampling, oversampling bad cases and then reweighting to return to the true proportions later. This carries some risks. In particular your model...
null
CC BY-SA 3.0
null
2011-05-05T14:42:39.460
2011-05-05T14:42:39.460
null
null
2958
null
10358
2
null
10271
2
null
You might find [this paper](http://www.stat.duke.edu/~mw/Smith+West1983.pdf) of interest. See also more detailed presentation of similar models in [West & Harrison](http://rads.stackoverflow.com/amzn/click/0387947256). There are other examples of this sort of monitoring as well, many which are more recent, but this isn...
null
CC BY-SA 3.0
null
2011-05-05T14:44:07.957
2011-05-05T14:49:44.440
2011-05-05T14:49:44.440
26
26
null
10359
1
10555
null
6
1190
How can I generate dependent time series from a given marginal distribution? I want to be able to adjust the level of dependence, to influence the predictability of the series, which will be given as input to a Monte Carlo simulation. The dependence parameter can be the correlation, the mutual information, or something...
Generating dependent time series from a given distribution?
CC BY-SA 3.0
null
2011-05-05T14:48:53.297
2011-05-09T15:45:40.490
2011-05-06T14:42:03.297
4479
4479
[ "time-series", "monte-carlo", "simulation", "non-independent", "prediction-interval" ]