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38.7k
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Tags
list
9590
1
9591
null
13
7756
I am currently using principal components analysis to select variables to use in modelling. At the moment, I make measurements A, B and C in my experiments -- What I really want to know is: Can I make fewer measurements and stop recording C and or B to save time and effort? I find that all 3 variables load heavily ...
How to use principal components analysis to select variables for regression?
CC BY-SA 3.0
null
2011-04-15T17:57:38.110
2015-05-31T07:34:30.303
2011-04-16T08:04:39.547
930
4054
[ "regression", "pca", "model-selection" ]
9591
2
null
9590
16
null
You haven't specified what "modeling" you plan on, but it sounds like you're asking about how to select independent variables among $A$, $B$, and $C$ for the purpose of (say) regressing a fourth dependent variable $W$ on them. To see that this approach can go wrong, consider three independent Normally distributed varia...
null
CC BY-SA 3.0
null
2011-04-15T19:38:16.313
2011-04-15T20:45:56.973
2011-04-15T20:45:56.973
919
919
null
9592
1
null
null
5
5454
I want to predict a continuous variable like porosity from remote sensing data. Let's say I have a measure of the reflectivity of the surface of the earth, densely sampled over an area. And I have rock porosity at some locations. So I'd like to calibrate the former to the latter, and transform reflectivity to porosity....
Which parameter on x axis for linear regression?
CC BY-SA 4.0
null
2011-04-15T19:58:13.213
2018-10-25T09:30:04.200
2018-10-25T09:30:04.200
128677
4187
[ "regression", "linear" ]
9593
2
null
9592
1
null
As far as I can tell, you have a lot of reflectivity measurements and a few porosity measurements, and you want to estimate porosity in areas where you only have reflectivity information. In that case, you want to regress porosity ($y$) on reflectivity ($x$) to minimise the sum of squares error in the porosity estimate...
null
CC BY-SA 3.0
null
2011-04-15T20:23:14.450
2011-04-15T20:23:14.450
null
null
2958
null
9595
1
null
null
9
635
I am using a distributed lag model to analyze a time series data. The duration of study period is 18 years, and the observation is yearly data. When including a 1-year lag effect, the first year of the lag variable becomes missing. Then, a 2-year lag effect makes the first two data of lag variable missing, and so on. ...
How to decrease the information loss from lag variables?
CC BY-SA 3.0
null
2011-04-15T22:57:39.797
2012-08-26T05:00:29.040
2011-04-16T08:02:51.610
930
4083
[ "time-series", "missing-data" ]
9596
1
null
null
3
791
The health screening for immigration to the US includes a mandatory chest x-ray screening for all adults, with the aim of detecting signs of tuberculosis. If the x-ray indicates the possibility of TB, the applicant then submits sputum samples for culturing. That's a lot of x-rays - and many of them don't result in po...
Using non-random sample to make population estimates
CC BY-SA 3.0
null
2011-04-15T23:05:00.143
2017-04-29T21:14:14.553
2017-04-29T21:14:14.553
28666
71
[ "logistic", "proportion", "resampling" ]
9597
2
null
9592
1
null
It's not a good idea to rearrange an OLS fit equation. If you do, you're changing the assumptions of what variables were assumed to be "independent" versus "dependent". If you have to rearrange things, one way around this is to use Principal Component Analysis rather than Ordinary Least Squares. Here's an article t...
null
CC BY-SA 3.0
null
2011-04-15T23:23:06.797
2011-04-17T17:47:38.030
2011-04-17T17:47:38.030
2775
2775
null
9598
2
null
9588
1
null
I did a Google search and bumped into the following title: "A study of cross-validation and bootstrap for accuracy estimation and model selection" I would post the link but it's one of those citeseerx.ist.psu.edu links that comes across with an IP number for the URL. If you do the search, you should be able to find i...
null
CC BY-SA 3.0
null
2011-04-16T00:01:36.560
2011-04-16T00:10:23.233
2011-04-16T00:10:23.233
2775
2775
null
9599
1
null
null
9
5684
For example, say we have three coins. Due to several tests, we have 95% confidence intervals for X (the heads percentage) of each coin. Coin A is 0-5%, coin B is 1-9%, and coin C is 40-70%. [For the curious, these CI's were created using inverse binomial CDF, based a small sample of ~30 flips of the coin. Not su...
Can confidence intervals be added?
CC BY-SA 3.0
null
2011-04-16T00:10:36.150
2011-04-16T09:58:53.657
2011-04-16T05:37:24.497
4191
4191
[ "confidence-interval", "binomial-distribution", "frequentist" ]
9600
2
null
9596
1
null
The $24,000$ applicant population was divided into two strata - The $N_1$ applicants who had chest x-rays indicative of TB - The $N_2=24,000-N_1$ who had chest x-rays not indicative of TB A stratified random sample was taken. This included $n_1$ participants with x-rays indicative of TB and $n_2=1,500-n_1$ particip...
null
CC BY-SA 3.0
null
2011-04-16T00:26:16.457
2011-04-16T00:34:17.477
2011-04-16T00:34:17.477
3874
3874
null
9601
2
null
9596
1
null
You have measured 3 variables, X-ray (pos or neg), sputum (pos, neg or not tested), new diagnostic (pos, neg or not tested), and you may have 9 outcome groups: ``` group X-ray sputum new a 1 + + + a 2 + + - a 3 + + nt b 4 + - + b 5 + - - ...
null
CC BY-SA 3.0
null
2011-04-16T00:43:15.787
2011-04-16T01:03:15.690
2011-04-16T01:03:15.690
3911
3911
null
9602
2
null
9599
3
null
There are multiple methods to calculate the [binomial confidence intervals](http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval), and in case of your small (~30) sample size this may mean notable differences. Can we say anything about the number of heads we would expect to see if we flipped all three? ...
null
CC BY-SA 3.0
null
2011-04-16T01:35:00.803
2011-04-16T01:54:07.583
2011-04-16T01:54:07.583
3911
3911
null
9603
2
null
9573
4
null
The central limit theorem establishes (under the required conditions) that the numerator of the t-statistic is asymptotically normal. The t-statistic also has a denominator. To have a t-distribution you'd need the denominator to be independent and square-root-of-a-chi-square-on-its-df. And we know it won't be independe...
null
CC BY-SA 4.0
null
2011-04-16T01:44:37.743
2022-07-18T22:26:17.110
2022-07-18T22:26:17.110
805
805
null
9604
1
null
null
6
2932
Is it possible have an SES where the component equations are probabilistic, say, logit or probit? I am evaluating a number of quality metrics of services provided by a number of providers. The metrics are binary (pass/fail quality certification). The obvious approach would appear to be to estimate the logit/probit equa...
Simultaneous Equation System for logit/probit?
CC BY-SA 3.0
null
2011-04-16T05:18:41.593
2014-06-12T17:46:09.247
2012-06-20T19:01:37.370
null
3671
[ "r", "regression", "logit", "probit" ]
9605
1
null
null
2
589
I am interested in using the MacKinnon product of coefficients test to assess mediation. Is there a quick way to carry out these calculations and determine significance based on the obtained statistic?
Calculating the MacKinnon empirical distribution test to test mediation
CC BY-SA 3.0
null
2011-04-16T06:50:43.337
2011-04-16T08:00:23.233
2011-04-16T08:00:23.233
930
null
[ "mediation" ]
9606
2
null
9605
4
null
Tests for full and partial mediation are well explained on the [Mediation FAQ](http://www.public.asu.edu/~davidpm/ripl/q&a.htm) webpage by David P. MacKinnon, and they can be implemented in any statistical package offering tools for regression modeling. Bootstraping can be used to derive standard errors and confidence ...
null
CC BY-SA 3.0
null
2011-04-16T07:59:30.117
2011-04-16T07:59:30.117
null
null
930
null
9607
1
9683
null
2
1391
Background: I've modeled a project effort prediction as a Google Spreadsheet template. Details of the Model: [http://sites.google.com/site/effortprediction/methodology](http://sites.google.com/site/effortprediction/methodology) .Google Spreadsheet does not implement beta distribution functions. In PERT a beta distribut...
Summing normal instead of beta distributions, consequences for the density function of the sum?
CC BY-SA 3.0
null
2011-04-16T09:03:50.340
2011-06-17T12:59:36.540
2011-04-16T11:24:25.440
1390
778
[ "normal-distribution", "central-limit-theorem", "beta-distribution" ]
9608
2
null
9599
1
null
This is a problem which can be relatively easily solved using a Bayesian approach. This is one of the "re-using" the original data answers, rather than one which uses the CIs. Each coin has some long run frequency of heads $\theta_i$ $(i=1,\dots,50)$. Now you have some partial information about these frequencies, tha...
null
CC BY-SA 3.0
null
2011-04-16T09:58:53.657
2011-04-16T09:58:53.657
null
null
2392
null
9609
2
null
1040
2
null
model misspecification is irrelevant when you are interpreting co-efficients in a model, but any such interpretation is always conditional on the model. This is because a model is about an association, not about a causal relationship - the OLS coefficients just tells you about the linear association between $X$ and $Y...
null
CC BY-SA 3.0
null
2011-04-16T10:55:20.060
2011-04-16T10:55:20.060
null
null
2392
null
9610
1
9613
null
15
7248
Is there such a formula? Given a set of data for which the mean, variance, skewness and kurtosis is known, or can be measured, is there a single formula which can be used to calculate the probability density of a value assumed to come from the aforementioned data?
Closed form formula for distribution function including skewness and kurtosis?
CC BY-SA 3.0
null
2011-04-16T14:28:54.517
2011-09-26T17:22:30.127
2011-09-26T17:22:30.127
919
226
[ "distributions", "density-function", "kurtosis", "skewness" ]
9611
2
null
9610
2
null
[D’Agostino’s K2 test](http://en.wikipedia.org/wiki/D%27Agostino%27s_K-squared_test) will tell you whether a sample distribution came from a normal distribution based on the sample's skewness and kurtosis. If you want to do a test assuming a non-normal distribution (perhaps with high skewness or kurtosis), you'll need ...
null
CC BY-SA 3.0
null
2011-04-16T14:46:25.153
2011-04-16T14:46:25.153
null
null
3874
null
9612
2
null
9278
0
null
You might be looking for a goodness-of-fit test to check one of the following - whether the sample distribution are likely to have come from the population distribution or - whether multiple sample distributions are likely to have come the same unknown population distribution Look at chi-square and Kolmogorov-Smirn...
null
CC BY-SA 3.0
null
2011-04-16T15:12:30.973
2011-04-16T15:12:30.973
null
null
3874
null
9613
2
null
9610
14
null
There are many such formulas. The first successful attempt at solving precisely this problem was made by Karl Pearson in 1895, eventually leading to the system of [Pearson distributions](http://en.wikipedia.org/wiki/Pearson_distribution). This family can be parameterized by the mean, variance, skewness, and kurtosis....
null
CC BY-SA 3.0
null
2011-04-16T17:10:33.647
2011-04-16T17:10:33.647
null
null
919
null
9614
1
9624
null
9
4062
I am modeling Diabetes Prediction using Logistic Regression. The dataset used is the [Behavioral Risk Factor Surveillance System (BRFSS)](http://www.cdc.gov/BRFSS/) of the Center for Disease Control (CDC). One of the independent variables is High Blood Pressure. It is categorical with the following levels 'Yes', 'No',...
Treating 'Don't know/Refused' levels of categorical variables
CC BY-SA 3.0
null
2011-04-16T17:27:46.990
2011-04-16T20:11:08.790
2011-04-16T20:01:35.560
919
3897
[ "logistic", "missing-data" ]
9615
1
null
null
3
537
I wonder if two identical time series are cointegrated. Can anyone shed some light on this? Thanks
Are two identical time series cointegrated?
CC BY-SA 3.0
null
2011-04-16T17:29:20.930
2011-04-16T17:38:37.700
null
null
4192
[ "time-series", "cointegration" ]
9616
2
null
9615
3
null
If I understand your question correctly, you are asking if you take two identical time series (i.e. a time series and a direct copy of it), are these two cointegrated? If that is your question, then it really reduces to a simpler form: is a time series stationary? As I understand it, cointegration is the phenomenon wh...
null
CC BY-SA 3.0
null
2011-04-16T17:38:37.700
2011-04-16T17:38:37.700
null
null
781
null
9617
1
9635
null
44
16316
I'm hoping that someone can explain, in layman's terms, what a characteristic function is and how it is used in practice. I've read that it is the Fourier transform of the pdf, so I guess I know what it is, but I still don't understand its purpose. If someone could provide an intuitive description of its purpose and pe...
What is the purpose of characteristic functions?
CC BY-SA 3.0
null
2011-04-16T18:00:25.273
2017-11-27T22:34:54.713
2017-11-27T22:34:54.713
128677
1913
[ "probability", "mathematical-statistics", "characteristic-function" ]
9618
2
null
9614
0
null
Do you have any reason to think that study subjects with diabetes were more likely or less likely to end up with the DK/R response? If not (and I'd be pretty surprised to find out you did), including this predictor in the model w/o excluding these cases will result in noise. That is, you'll end up with less precision i...
null
CC BY-SA 3.0
null
2011-04-16T18:57:16.713
2011-04-16T18:57:16.713
null
null
11954
null
9619
2
null
9614
2
null
First you have to think over if the missing data are missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR) as deletion (in other words complete-case analysis) may lead to biased results. Alternatives are inverse probability weighting, multiple imputation, the full-likelihood metho...
null
CC BY-SA 3.0
null
2011-04-16T18:58:14.193
2011-04-16T18:58:14.193
null
null
3911
null
9620
2
null
9617
4
null
The purpose of characteristic functions is that they can be used to derive the properties of distributions in probability theory. If you're not interested in such derivations you do not need to learn about characteristic functions.
null
CC BY-SA 3.0
null
2011-04-16T19:24:55.683
2011-04-16T19:24:55.683
null
null
449
null
9621
2
null
9617
2
null
The characteristic function is the Fourier transform of the density function of the distribution. If you have any intuition regarding Fourier transforms, this fact may be enlightening. The common story about Fourier transforms is that they describe the function 'in frequency space.' Since a probability density is usua...
null
CC BY-SA 3.0
null
2011-04-16T19:36:20.890
2011-04-16T19:36:20.890
null
null
795
null
9622
2
null
9610
7
null
This sounds like a ['moment-matching' approach](http://www.johndcook.com/blog/2010/09/20/skewness-andkurtosis/) to fitting a distribution to data. It is generally regarded as not a great idea (the title of John Cook's blog post is 'a statistical dead end').
null
CC BY-SA 3.0
null
2011-04-16T19:39:11.997
2011-04-16T19:39:11.997
null
null
795
null
9623
1
null
null
3
30095
I've read the sampling error examples in Wikipedia, but I still don't understand. Could you give me a simple and characteristic example for sampling error?
Sampling error example
CC BY-SA 3.0
null
2011-04-16T19:47:10.053
2015-08-06T13:05:40.750
2011-05-20T09:04:49.110
930
4176
[ "sampling" ]
9624
2
null
9614
6
null
I was just wondering about exactly the same question when analyzing the latest [National Hospital Discharge Survey](http://www.cdc.gov/nchs/injury/injury_hospital.htm) data. Several variables have substantial missing values, such as marital status and type of procedure. This issue came to my attention because these c...
null
CC BY-SA 3.0
null
2011-04-16T20:11:08.790
2011-04-16T20:11:08.790
null
null
919
null
9625
1
9630
null
7
2575
Suppose you wish to test the hypothesis that the mean of a distribution equals the median, given some samples drawn from the distribution. How would this be done? I am guessing that the test statistic would be (the absolute value of) the sample mean minus the sample median, but am not sure about the standard error of t...
How to test if the mean equals the median?
CC BY-SA 3.0
null
2011-04-16T20:11:45.357
2011-04-18T03:43:18.880
null
null
795
[ "hypothesis-testing", "mean", "median" ]
9626
1
null
null
6
2046
I believe that for ANOVA unbalanced means unequal groups. But for randomised controlled trials unbalanced seems to mean something like groups of different characteristics despite randomisation. So in case of RCTs does unbalanced simply mean unlucky randomisation? Nothing to do with group sizes? What's the definition of...
When is a randomised controlled trial (RCT) balanced?
CC BY-SA 3.0
null
2011-04-16T20:16:25.510
2011-08-15T09:36:58.240
2011-04-18T08:36:35.570
183
4176
[ "sample-size", "clinical-trials" ]
9627
1
9720
null
9
4440
First of all, I realize multiple regression does not really give actually "causal" inferences about the data. Let me explain my current case: I have four independent variables which I hope (but am not sure) are involved in driving the thing I'm measuring. I wanted to use multiple regression to see how much each of thes...
What should I be aware of when using multiple regression to find "causal" relationships in my data?
CC BY-SA 3.0
null
2011-04-16T20:36:49.650
2011-04-20T04:35:36.783
2011-04-20T04:35:36.783
4139
4139
[ "multivariate-analysis", "multiple-regression" ]
9628
2
null
9623
1
null
When you take a sample you do so because you want to know what is happening in the wider population but unless you take a census and ask everyone there will always be a difference between the sample and the population. There is a good definition below taken from [here](http://www.socialresearchmethods.net/kb/sampstat....
null
CC BY-SA 3.0
null
2011-04-16T20:46:32.990
2011-04-16T22:24:59.253
2011-04-16T22:24:59.253
3597
3597
null
9629
1
9641
null
14
31138
I've read that the chi square test is useful to see if a sample is significantly different from a set of expected values. For example, here is a table of results of a survey regarding people's favourite colours (n=15+13+10+17=55 total respondents): ``` red, blue, green, yellow 15, 13, 10, 17 ``` A chi square test can...
Can chi square be used to compare proportions?
CC BY-SA 4.0
null
2011-04-16T21:08:05.087
2022-01-03T17:57:08.743
2022-01-02T13:29:49.523
11887
2830
[ "chi-squared-test", "hypothesis-testing", "proportion" ]
9630
2
null
9625
4
null
This is a bootstrap confidence interval for the (median - mean) difference in R: ``` z = function() {s = sample(women$weight, replace=TRUE); median(s)-mean(s)} k = replicate(10000, z()) c(quantile(k, c(.025, .5, .975)), mean=mean(k), sd=sd(k), qgte0=mean(k>=0)) 2.5% 50% 97.5% mean sd qgt...
null
CC BY-SA 3.0
null
2011-04-16T21:10:55.900
2011-04-16T21:10:55.900
null
null
3911
null
9631
2
null
9629
3
null
Yes, you can test the null hypothesis: ``` "H0: prop(red)=prop(blue)=prop(green)=prop(yellow)=1/4" ``` using a chi square test that compares the proportions of the survey (0.273, ...) to the expected proportions (1/4, 1/4, 1/4, 1/4)
null
CC BY-SA 4.0
null
2011-04-16T21:58:42.240
2022-01-02T09:47:16.443
2022-01-02T09:47:16.443
56211
null
null
9632
2
null
9627
5
null
If you want to see if the independent variables are correlated, that's easy - just test the correlations e.g. with PROC CORR in SAS, or cor in R, or whatever in whatever package you use. You might, though, want to test collinearity instead, or in addition. But that's only part of the problem for causation. More probl...
null
CC BY-SA 3.0
null
2011-04-16T22:01:47.947
2011-04-16T22:01:47.947
null
null
686
null
9633
2
null
9590
4
null
If you have only 3 IVs, why do you want to reduce them? That is, is your sample very small (so that 3 IVs risks overfitting)? In this case, consider partial least squares Or are the measurements very expensive (so, in future, you'd like to measure only one IV)? In this case, I'd consider looking at the different regr...
null
CC BY-SA 3.0
null
2011-04-16T22:06:58.427
2011-04-16T22:06:58.427
null
null
686
null
9634
2
null
9623
4
null
Imagine that you want to know the average height of men on earth. This average height exists but obviously you will never be able to know it (unless you're able to measure several millions men...). What you can do is measure hundreds or thousands of people and calculate the average height of these people. The average h...
null
CC BY-SA 3.0
null
2011-04-16T22:15:11.883
2011-04-16T22:15:11.883
null
null
3377
null
9635
2
null
9617
61
null
Back in the day, people used logarithm tables to multiply numbers faster. Why is this? Logarithms convert multiplication to addition, since $\log(ab) = \log(a) + \log(b)$. So in order to multiply two large numbers $a$ and $b$, you found their logarithms, added the logarithms, $z = \log(a) + \log(b)$, and then looked...
null
CC BY-SA 3.0
null
2011-04-17T00:40:55.120
2013-08-19T14:57:12.920
2013-08-19T14:57:12.920
7290
3567
null
9636
2
null
9629
5
null
The chi-square test is good as long as the expected counts are large, usually above 10 is fine. below this the $\frac{1}{E(x_{i})}$ part tends to dominate the test. An exact test statistic is given by: $$\psi=\sum_{i}x_{i}\log\left(\frac{x_{i}}{np_{i}}\right)$$ Where $x_{i}$ is the observed count in category $i$. $i...
null
CC BY-SA 3.0
null
2011-04-17T00:57:53.990
2011-04-17T02:04:47.963
2011-04-17T02:04:47.963
2392
2392
null
9637
1
null
null
5
2091
standard deviation (std) can be used when arithmetic mean is the right statistic. What is the equivalent of std when geometric mean is the right statistic?
Geometric mean and standard deviation
CC BY-SA 3.0
null
2011-04-17T03:23:52.840
2011-04-17T05:38:56.727
2011-04-17T04:42:11.300
2116
null
[ "hypothesis-testing", "confidence-interval" ]
9638
2
null
9627
2
null
The relationship between causation and association is basically in answering the following question: What else, besides the hypothesised causal relationship, could have caused $X$ and $Y$ to be related to each other? As long as the answer to this question is not "nothing" then you can only talk definitively about assoc...
null
CC BY-SA 3.0
null
2011-04-17T03:46:02.657
2011-04-17T03:46:02.657
null
null
2392
null
9639
2
null
9637
2
null
The geometric mean can be motivated by noting that it is the exponent of the arithmetic mean of the logarithm: $$\overline{x}_{geo}=\left(\prod_{i}x_{i}\right)^{\frac{1}{n}}=exp\left[\frac{1}{n}\sum_{i}log(x_{i})\right]=exp\left[\overline{log(x)}\right]$$ So it makes sense to take the exponent of the standard deviation...
null
CC BY-SA 3.0
null
2011-04-17T05:38:56.727
2011-04-17T05:38:56.727
null
null
2392
null
9640
2
null
9627
1
null
I'm not sure what field your work is in, so this may or may not be of any help- but I'm most familiar with using SPSS with psychological constructs. In my experience, if I have a few variables predicting an outcome variable (or dependent variable) in a regression, and I have one or more independent variables show up as...
null
CC BY-SA 3.0
null
2011-04-17T06:15:50.957
2011-04-17T06:15:50.957
null
null
4198
null
9641
2
null
9629
7
null
Correct me if I'm wrong, but I think this can be done in R using this command ``` chisq.test(c(15, 13, 10, 17)) Chi-squared test for given probabilities data: c(15, 13, 10, 17) X-squared = 1.9455, df = 3, p-value = 0.5838 ``` This assumes proportions of 1/4 each. You can modify expected val...
null
CC BY-SA 4.0
null
2011-04-17T08:16:50.087
2022-01-02T13:31:55.033
2022-01-02T13:31:55.033
11887
144
null
9642
2
null
9629
2
null
The test statistic for Pearson's chi-square test is $$\sum_{i=1}^{n} \frac{(O_i - E_i)^2}{E_i}$$ If you write $o_i = \dfrac{O_i}{n}$ and $e_i = \dfrac{E_i}{n}$ to have proportions, where $n=\sum_{i=1}^{n} O_i$ is the sample size and $\sum_{i=1}^{n} e_i =1$, then the test statistic is is equal to $$n \sum_{i=1}^{n} \f...
null
CC BY-SA 3.0
null
2011-04-17T11:21:53.427
2011-04-17T11:21:53.427
null
null
2958
null
9643
1
null
null
1
1566
I am using R software (R commander) to cluster my data. I have a smaller subset of my data containing 200 rows and about 800 columns. I am getting the following error when trying kmeans cluster and plot on a graph: > 'princomp' can only be used with more units than variables I then created a test doc of 10 row and 1...
Clustering can be plotted only with more units than variables?
CC BY-SA 3.0
null
2011-04-17T12:42:40.607
2011-04-17T13:10:59.397
2011-04-17T12:56:15.330
null
4020
[ "r", "clustering" ]
9644
2
null
9643
1
null
The clustering itself has no problems with the p>n situation, however the visualization internally uses `princomp` (which is incapable of handling p>n) to plot the similarity space projection. You can't fix that, at most try to reproduce similar graph by obtaining similarity space projection with `cmdscale(dist(...))` ...
null
CC BY-SA 3.0
null
2011-04-17T13:03:21.863
2011-04-17T13:10:59.397
2011-04-17T13:10:59.397
null
null
null
9645
1
9646
null
3
2301
I'm kind of new doing data mining, so sorry if my question is not very clear. I'm working in a project that is aiming to do data mining over the interactions of the students with a e-learning platform. So, I'm trying to generate decision trees with some data that I collected (number of times that student use a resourc...
Minimum number of instances to create a decision tree
CC BY-SA 3.0
0
2011-04-17T14:01:40.170
2011-05-17T07:51:12.127
2011-04-17T14:50:36.583
null
4203
[ "cart", "weka" ]
9646
2
null
9645
2
null
{I'm guessing that for each person and each variable you have a single value covering the 2 months--i.e., you don't have repeated measures.} 44 sounds like an awfully small number. Is it a random sample of a larger population? The answer to that, for one thing, would affect your confidence in the findings. I won't ...
null
CC BY-SA 3.0
null
2011-04-17T14:45:36.953
2011-04-17T14:45:36.953
null
null
2669
null
9647
1
null
null
3
247
Sometimes they ask questions in different orders, or use different prompts. Or datasets with instruments (with at least one variable randomized)? I would like to use at least one of them for my causal modelling course (Stat 566), whose syllabus is at [https://www.stat.washington.edu/tsr/s566/syllabus566.pdf](https://ww...
What are some examples of public datasets that have randomized instruments?
CC BY-SA 3.0
null
2011-04-17T17:16:26.730
2011-04-17T18:41:11.000
2011-04-17T18:11:52.157
919
null
[ "dataset" ]
9650
2
null
9647
3
null
Donald Green in Yale's political science department has posted the replication data for many of his experiments. You can find them here: - Donald Green's Replication Data Green is also the director for the Yale Institution for Social and Policy Studies. They have a replication data archive here: - ISPS Data Archive...
null
CC BY-SA 3.0
null
2011-04-17T18:41:11.000
2011-04-17T18:41:11.000
null
null
3265
null
9653
1
9655
null
23
46636
I've learnt that small sample size may lead to insufficient power and type 2 error. However, I have the feeling that small samples just may be generally unreliable and may lead to any kind of result by chance. Is that true?
Can a small sample size cause type 1 error?
CC BY-SA 3.0
null
2011-04-17T21:55:55.793
2013-10-15T11:43:49.583
2011-04-18T07:45:15.140
null
4176
[ "hypothesis-testing", "small-sample" ]
9654
1
9660
null
11
344
Many randomised controlled trial (RCT) papers report significance tests on baseline parameters just after/before randomisation to show that the groups are indeed similar. This is often part of a "baseline characteristics" table. However, significance tests measure the probability of getting the observed (or a stronger)...
Does significance test make sense to compare randomised groups at baseline?
CC BY-SA 3.0
null
2011-04-17T22:31:33.500
2011-04-18T10:52:12.323
2011-04-18T10:52:12.323
183
4176
[ "statistical-significance", "clinical-trials" ]
9655
2
null
9653
27
null
As a general principle, small sample size will not increase the Type I error rate for the simple reason that the test is arranged to control the Type I rate. (There are minor technical exceptions associated with discrete outcomes, which can cause the nominal Type I rate not to be achieved exactly especially with small...
null
CC BY-SA 3.0
null
2011-04-17T22:41:17.137
2011-04-17T22:41:17.137
null
null
919
null
9656
1
null
null
3
2309
am writing a simple R script to test the spectral clustering algorithm but for the eigenvalues I don't get them all positive and lambda0 is different from 0. here is my script ``` Dsqrt<-matrix(0,length(V(g)),length(V(g))) # The D^-0.5 matrix for(i in 1:(length(V(g))-1)) Dsqrt[i,i]<-1/sqrt(degree(g,V(g)[i-...
Problem with R code for spectral clustering
CC BY-SA 3.0
null
2011-04-18T00:43:44.917
2011-04-18T07:01:02.667
2011-04-18T07:01:02.667
2116
2325
[ "r", "clustering" ]
9657
2
null
8371
7
null
As whuber says, the short answer is that quota samples are the "poster child for outmoded, known-bad sampling methods" and "have long been discredited." The longer answer is that there may be conditions under which "quota-like" samples can work reasonably well. Exhibit A here is recent work on reconstructing represent...
null
CC BY-SA 4.0
null
2011-04-18T01:45:03.810
2019-07-17T12:03:09.373
2019-07-17T12:03:09.373
142322
4110
null
9659
1
null
null
6
1050
I wish to infer the posterior distribution on the probability of success $\theta$ in some binomial process, the twist being that I know that $\theta$ lies in the interval [0.5, 1]. The trouble is that a Beta distribution that is supported on [0.5, 1] is no longer conjugate. In particular, the prior looks like this ($p...
Fast integration of a posterior distribution
CC BY-SA 3.0
null
2011-04-18T02:52:39.853
2014-03-02T17:40:49.110
2011-04-18T07:40:42.710
null
4209
[ "bayesian", "beta-binomial-distribution" ]
9660
2
null
9654
6
null
A hypothesis test would be nonsensical, but a significance test may be useful. The hypothesis test would be testing a null hypothesis that is already known to be true, as your question makes clear. It is silly to apply a statistical test to any hypothesis that has a truth value already known via completely reliable inf...
null
CC BY-SA 3.0
null
2011-04-18T03:25:38.537
2011-04-18T03:25:38.537
null
null
1679
null
9661
2
null
9625
0
null
A permutations test can easily be set up to use the (mean - mode difference) as its test statistic. That would give you an exact P value for the difference.
null
CC BY-SA 3.0
null
2011-04-18T03:43:18.880
2011-04-18T03:43:18.880
null
null
1679
null
9662
1
9703
null
4
257
I have 3 different groups: A, B, and C: - A (has a medical condition) has 30 entries - B (another medical condition) has 31 entries - C (control group) has 55 entries All participants have information on the same set of variables. I want to assess whether there is a statistically significant difference in risk o...
How to assess differential risk of disease across three groups after adjusting for other risk factors?
CC BY-SA 3.0
null
2011-04-18T04:37:50.350
2011-04-18T19:55:39.293
2011-04-18T12:19:04.447
4210
4210
[ "correlation", "statistical-significance", "spss" ]
9663
1
9665
null
12
1162
If an item follows normal distribution, average also follows normal distribution. What about minimum and maximum?
Distribution of extremal values
CC BY-SA 3.0
null
2011-04-18T05:01:08.790
2011-10-30T22:02:55.253
2011-10-30T22:02:55.253
null
4211
[ "normal-distribution", "order-statistics" ]
9664
1
9722
null
106
19334
Suppose I have a set of sample data from an unknown or complex distribution, and I want to perform some inference on a statistic $T$ of the data. My default inclination is to just generate a bunch of bootstrap samples with replacement, and calculate my statistic $T$ on each bootstrap sample to create an estimated distr...
What are examples where a "naive bootstrap" fails?
CC BY-SA 3.0
null
2011-04-18T05:44:33.810
2013-12-30T13:46:24.387
2011-04-19T13:03:21.823
2970
1106
[ "hypothesis-testing", "confidence-interval", "bootstrap" ]
9665
2
null
9663
13
null
You should have a look at the [order statistics](http://mathworld.wolfram.com/OrderStatistic.html). Here is a very brief overview. Let $X_{1}, \ldots X_{n}$ be an i.i.d. sample of size $n$ drawn from a population with distribution function $F$ and probability density function $f$. Define $Y_{1}=X_{(1)}, \ldots, Y_{r} ...
null
CC BY-SA 3.0
null
2011-04-18T05:46:01.393
2011-04-18T06:59:14.667
2011-04-18T06:59:14.667
2116
3019
null
9666
1
null
null
5
1423
My new computer clock runs at a rate that changes in odd steps over time, even after I tuned it via the Linux adjtimex software. Here is a plot of the change in the cumulative clock drift for each of about 1700 samples taken every 10000 seconds, with a bunch of missed points and outliers when I was off the network and...
Identifying modes in floating point data
CC BY-SA 4.0
null
2011-04-18T06:10:33.577
2019-01-16T10:28:23.557
2019-01-16T10:28:23.557
79696
2434
[ "mode" ]
9667
1
null
null
12
2691
> Possible Duplicate: Books for self-studying time series analysis? I am new to time series modelling altogether. But I am aware about regression modelling and some data mining algorithms like decision trees. I want to learn time series from scratch. My background is Mathematics. Please suggest me any good book/mat...
Learning material about time series
CC BY-SA 3.0
null
2011-04-18T07:44:31.833
2011-04-19T15:57:14.973
2017-04-13T12:44:27.570
-1
861
[ "time-series", "references" ]
9668
2
null
9617
7
null
@charles.y.zheng and @cardinal gave very good answers, I will add my two cents. Yes the characteristic function might look like unnecessary complication, but it is a powerful tool which can get you results. If you are trying to prove something with cumulative distribution function it is always advisable to check whethe...
null
CC BY-SA 3.0
null
2011-04-18T07:47:28.053
2011-04-18T07:47:28.053
null
null
2116
null
9669
2
null
9280
4
null
Note that @whuber adresses all the points raised in the question, I will provide only the mathematical details. The regression with spatial error assumes that model is the following: $$y=X\beta+u$$ where $Euu'=\Omega$. The efficient estimate of $\beta$ then is $$\hat\beta=(X'\Omega X)^{-1}X'\Omega y$$ When you have ne...
null
CC BY-SA 3.0
null
2011-04-18T09:08:31.047
2011-04-18T13:52:57.690
2011-04-18T13:52:57.690
2116
2116
null
9670
2
null
6989
20
null
No need to leave the lme4 package to account for overdispersion; just include a random effect for observation number. The BUGS/JAGS solutions mentioned are probably overkill for you, and if they aren't, you should have the easy to fit lme4 results for comparison. ``` data$obs_effect<-1:nrow(data) overdisp.fit<-lmer(y~1...
null
CC BY-SA 3.0
null
2011-04-18T09:09:04.673
2015-06-22T11:38:13.537
2015-06-22T11:38:13.537
179
1893
null
9671
1
11196
null
4
2925
I am assessing how good different features are for unsupervised classification of a set of objects. For each different feature I test, I have computed a feature vector that describes the object. I then want to get a metric out for how 'good' this vector is at separating the objects into their respective classes. My cur...
How can I assess how descriptive feature vectors are?
CC BY-SA 3.0
null
2011-04-18T09:15:14.207
2011-05-24T15:05:40.330
null
null
4213
[ "clustering", "classification", "feature-selection", "unsupervised-learning" ]
9672
2
null
9667
4
null
I have yet still not found the time series book which I like. Here is the list of books which I found very useful: - Time Series Analysis by J. D. Hamilton. This is the book which contains practically everything. - Applied econometric time series by W. Enders. Classical reference - Introductory econometrics for fina...
null
CC BY-SA 3.0
null
2011-04-18T09:17:26.670
2011-04-18T09:17:26.670
null
null
2116
null
9673
2
null
9587
2
null
No, that isn't really it. One side point is you should consider looking into multi-modal inference a la Anderson and Burnham. However, there are plenty of resources, many of which also refer to the P+B book; such as this one, with code: [http://glmm.wikidot.com/basic-glmm-simulation](http://glmm.wikidot.com/basic-glmm-...
null
CC BY-SA 3.0
null
2011-04-18T09:28:42.100
2011-04-18T09:28:42.100
null
null
1893
null
9674
1
null
null
2
2861
I have a bit of a problem with the [tm](http://cran.r-project.org/web/packages/tm/index.html) R package for cleaning text documents. Here is how my code looks like: ``` library("tm") # import text files in corpus text – ok c_txt <- Corpus((DirSource(directory = ".", pattern ="txt", encoding = "UTF-8")...
How to remove stopwords with Russian documents?
CC BY-SA 3.0
null
2011-04-18T09:37:37.580
2018-05-21T12:37:46.633
2011-04-18T09:46:25.323
930
4212
[ "r", "text-mining" ]
9675
2
null
9508
1
null
A Likelihood ratio test on an lme object is probably fine to test a certain hypothesis; but that is not an appropriate way to build or choose a model. You would do that with REMLoff and: ``` anova(fit1, fit2) ``` AICc is a well developed criterion for model selection that directly implies and estimates from the data...
null
CC BY-SA 3.0
null
2011-04-18T09:38:45.867
2011-04-18T09:38:45.867
null
null
1893
null
9676
2
null
9327
1
null
Try the following packages on cran: Rcapture and mra. The easiest method to use in R for a log linear model, open closed or robust, M0, Mh, Mt, or Mth is well detailed here: [http://www.jstor.org/pss/3695557](http://www.jstor.org/pss/3695557) and that is what Rcapture is based on. You forgot to specify in your lmer cal...
null
CC BY-SA 3.0
null
2011-04-18T09:50:16.247
2011-04-18T09:50:16.247
null
null
1893
null
9677
2
null
8501
1
null
You could always just calculate try to calculate R^2 from the squared covariance of Ypred and Ynew over the product of their variances: [http://www.stator-afm.com/image-files/r-squared.gif](http://www.stator-afm.com/image-files/r-squared.gif) This works for any continuous model, regardless of how the parameters are est...
null
CC BY-SA 3.0
null
2011-04-18T10:01:20.853
2011-04-18T10:01:20.853
null
null
1893
null
9678
2
null
9664
2
null
The naive bootstrap depends on the sample size being large, so that the empirical CDF for the data are a good approximation to the "true" CDF. This ensures that sampling from the empirical CDF is very much like sampling from the "true" CDF. The extreme case is when you have only sampled one data point - bootstrapping...
null
CC BY-SA 3.0
null
2011-04-18T10:14:17.253
2011-04-19T08:24:30.707
2011-04-19T08:24:30.707
2116
2392
null
9679
2
null
7675
3
null
I disagree with the other responder, you shouldn't just fit varying intercept, fixed slope by default. y~1+condition*distractor*direction+(1+condition*distractor*direction|subject) should at least be fit for model testing. Otherwise, you are just assuming the subject effect is only on the intercept and you are assuming...
null
CC BY-SA 3.0
null
2011-04-18T10:22:26.577
2011-04-18T10:22:26.577
null
null
1893
null
9680
2
null
5517
4
null
It looks like your error message isn't about varying slopes, it is about correlated random effects. You can fit the uncorrelated as well; that is, a mixed-effects model with independent random effects: ``` Linear mixed model fit by REML Formula: Reaction ~ Days + (1 | Subject) + (0 + Days | Subject) Data: sleepstudy ...
null
CC BY-SA 3.0
null
2011-04-18T10:35:40.950
2013-08-24T14:58:15.637
2013-08-24T14:58:15.637
7290
1893
null
9681
2
null
9659
0
null
You can always use Monte Carlo Integration or the Midpoint method. With Monte Carlo, you simply generate a bunch of points in your parameter space and see if they are in the area or volume or hyper-dimensional space you are trying to integrate. From: [http://farside.ph.utexas.edu/teaching/329/lectures/node109.html](htt...
null
CC BY-SA 3.0
null
2011-04-18T11:41:02.280
2011-04-18T11:41:02.280
null
null
1893
null
9682
2
null
9674
5
null
I've just downloaded the Windows binary version of `tm` from CRAN: [http://cran.r-project.org/web/packages/tm/index.html](http://cran.r-project.org/web/packages/tm/index.html) The `russian.dat` file that's included there isn't UTF-8, but is encoded using [KOI-8](http://en.wikipedia.org/wiki/KOI8-R). I am unfamiliar wit...
null
CC BY-SA 3.0
null
2011-04-18T11:46:17.800
2011-04-18T12:04:01.667
2011-04-18T12:04:01.667
439
439
null
9683
2
null
9607
2
null
Just go ahead and calculate a random uniform, then use the inverse cdf method (http://en.wikipedia.org/wiki/Inverse_transform_sampling) to get a random Beta. Here is the formula for the inverse beta cdf: [http://www.mathworks.com/help/toolbox/stats/betainv.html](http://www.mathworks.com/help/toolbox/stats/betainv.html)...
null
CC BY-SA 3.0
null
2011-04-18T11:47:34.240
2011-04-18T11:54:48.510
2011-04-18T11:54:48.510
1893
1893
null
9684
2
null
7236
3
null
Yeah, the sampling package handles this, you can do cluster sampling or stratified or a few others: [http://cran.r-project.org/web/packages/sampling/sampling.pdf](http://cran.r-project.org/web/packages/sampling/sampling.pdf) It can then also handle a lot of the special variance estimation techniques you'll have to do ...
null
CC BY-SA 3.0
null
2011-04-18T12:02:13.153
2011-04-18T12:02:13.153
null
null
1893
null
9685
1
null
null
9
12640
My data set is comprised of either total mortality or survival of an organism at three site types, inshore, midchannel and offshore. The numbers in the table below represent the number of sites. ``` 100% Mortality 100% Survival Inshore 30 31 Midchannel ...
How to carry out multiple post-hoc chi-square tests on a 2 X 3 table?
CC BY-SA 3.0
null
2011-04-18T13:50:07.170
2022-01-02T09:40:58.107
2011-04-18T19:26:00.267
930
null
[ "logistic", "multiple-comparisons", "chi-squared-test" ]
9686
2
null
9685
7
null
A contingency table should contain all the mutually exclusive categories on both axes. Inshore/Midchannel/Offshore look fine, however unless "less than 100% mortality" means "100% survival" in this biological setting you may need to construct tables that account for all the cases observed or explain why you restrict yo...
null
CC BY-SA 3.0
null
2011-04-18T14:20:42.363
2011-04-19T15:42:39.223
2011-04-19T15:42:39.223
3911
3911
null
9687
2
null
9663
5
null
You might also want to read up on the [generalized extreme value (GEV) distribution](http://en.wikipedia.org/wiki/Generalized_extreme_value_distribution). It turns out that as $n\rightarrow\infty$, the (shifted and scaled) distribution of the maximal value of the sample converges to one of the three special cases of th...
null
CC BY-SA 3.0
null
2011-04-18T14:37:04.670
2011-04-18T14:37:04.670
null
null
279
null
9688
1
9689
null
1
461
Even simple models in probability theory can be quite confusing (e.g. drawing something with or without returning it, conditional probabilities, one and only one outcome, at least one outcome asoasf...) In other areas of mathematical modelling (e.g. differential equations) you often have powerful and easy to use modell...
Generator and/or interpreter of probability models
CC BY-SA 3.0
null
2011-04-18T14:56:54.450
2011-05-18T18:44:21.447
2011-05-18T18:44:21.447
null
230
[ "probability", "modeling" ]
9689
2
null
9688
0
null
I would recommend downloading R and then following a good R book on Statistics R download: [http://cran.r-project.org/bin/windows/base/](http://cran.r-project.org/bin/windows/base/) Here's a reasonable R/Stats book: [http://www.amazon.com/Introductory-Statistics-R-Peter-Dalgaard/dp/0387954759](http://rads.stackoverflow...
null
CC BY-SA 3.0
null
2011-04-18T15:42:57.210
2011-04-18T15:42:57.210
null
null
2775
null
9690
2
null
8371
2
null
- In most non-compulsory survey contexts, there is a substantial problem with nonresponse. This from 2002: "the recently reported estimate of survey cooperation rates from CMOR, the Council for Market and Opinion Research [USA], averaged only 14.7 percent." and from Paul Gerhold, "I believe that it is still possible t...
null
CC BY-SA 3.0
null
2011-04-18T16:21:07.000
2011-04-18T16:21:07.000
null
null
3919
null
9691
1
null
null
5
3473
As a follow up to my [previous question](https://stats.stackexchange.com/questions/9629/can-chi-square-be-used-to-compare-proportions), I learned that the chi square test can be used to compare expected and observed frequency distributions. But ... Suppose I have the following data table in CSV, which surveys people on...
Equivalent of Tukey test for chi-square?
CC BY-SA 4.0
null
2011-04-18T16:56:18.330
2023-02-12T02:44:22.600
2021-02-06T18:09:59.713
11887
2830
[ "distributions", "chi-squared-test", "multiple-comparisons", "tukey-hsd-test" ]
9692
1
9698
null
4
7286
In a (one or multi) way anova model, once a new individual is assigned to a treatment, the predicted value for him is calculated using the coefficients of the ANOVA model (simply assigning the treatment mean value to the individual). How should I construct a confidence (or prediction) interval for that predicted value...
Prediction in simple and multiple ANOVA
CC BY-SA 3.0
null
2011-04-18T17:01:07.550
2011-04-19T03:30:54.897
2011-04-19T03:30:54.897
3582
632
[ "r", "anova", "confidence-interval" ]
9693
1
14379
null
7
3485
What are some hot topics that mathematical statistics researchers are studying now?
Hot topics in mathematical statistics
CC BY-SA 3.0
null
2011-04-18T17:20:16.697
2016-10-28T09:51:48.300
null
null
4111
[ "mathematical-statistics" ]
9695
1
null
null
23
768
In [Statistical Modeling: The Two Cultures](https://projecteuclid.org/journals/statistical-science/volume-16/issue-3/Statistical-Modeling--The-Two-Cultures-with-comments-and-a/10.1214/ss/1009213726.full) Leo Breiman writes > Current applied practice is to check the data model fit using goodness-of-fit tests and residu...
Difficulty of testing linearity in regression
CC BY-SA 4.0
null
2011-04-18T18:24:55.707
2022-07-04T10:57:01.637
2022-07-04T10:57:01.637
79696
319
[ "regression", "goodness-of-fit" ]
9696
2
null
9691
5
null
With this many questions to ask of the data, you are approaching the border between a "test" and a "model" (not that such a sharp distinction exists except in the conceptualization of the problem). A [Poisson regression model](https://secure.wikimedia.org/wikipedia/en/wiki/Poisson_regression), aka log-linear model, can...
null
CC BY-SA 4.0
null
2011-04-18T19:00:36.163
2023-02-12T02:44:22.600
2023-02-12T02:44:22.600
345611
2975
null