Re: [R] ANOVA non-sphericity test and corrections (eg, Greenhouse-Geisser)
DarrenWeber wrote: I'm an experimental psychologist and when I run ANOVA analysis in SPSS, I normally ask for a test of non-sphericity (Box's M-test). I also ask for output of the corrections for non-sphericity, such as Greenhouse-Geisser and Huhn-Feldt. These tests and correction factors are commonly used in the journals for experimental and other psychology reports. I have been switching from SPSS to R for over a year now, but I realize now that I don't have the non-sphericity test and correction factors. This can be done using anova.mlm() and mauchly.test() which work on mlm objects, i.e., lm() output where the response is a matrix. There is no theory, to my knowledge, to support it for general aov() models, the catch being that you need to have a within-subject covariance matrix. __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] ANOVA non-sphericity test and corrections (eg, Greenhouse-Geisser)
On Mon, 2007-06-25 at 17:53 +1000, Simon Blomberg wrote: If you use lme, you can fit a general correlation structure to the within-subject data, and compare the fit to a model assuming uncorrelated within-subjects errors. That should tell you whether your data are ... correlated... (damn email gremlins.) Aren't the G-G and H-F corrections only approximate fixes? Surely it is better to work with a model that actually fits your data, rather than using ad hoc adjustments towards a model that doesn't quite fit. But I'm no psychologist. :-) Cheers, Simon. On Mon, 2007-06-25 at 08:22 +0200, Peter Dalgaard wrote: DarrenWeber wrote: I'm an experimental psychologist and when I run ANOVA analysis in SPSS, I normally ask for a test of non-sphericity (Box's M-test). I also ask for output of the corrections for non-sphericity, such as Greenhouse-Geisser and Huhn-Feldt. These tests and correction factors are commonly used in the journals for experimental and other psychology reports. I have been switching from SPSS to R for over a year now, but I realize now that I don't have the non-sphericity test and correction factors. This can be done using anova.mlm() and mauchly.test() which work on mlm objects, i.e., lm() output where the response is a matrix. There is no theory, to my knowledge, to support it for general aov() models, the catch being that you need to have a within-subject covariance matrix. __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -- Simon Blomberg, BSc (Hons), PhD, MAppStat. Lecturer and Consultant Statistician Faculty of Biological and Chemical Sciences The University of Queensland St. Lucia Queensland 4072 Australia Room 320, Goddard Building (8) T: +61 7 3365 2506 email: S.Blomberg1_at_uq.edu.au The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. - John Tukey. __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] ANOVA non-sphericity test and corrections (eg, Greenhouse-Geisser)
If you use lme, you can fit a general correlation structure to the within-subject data, and compare the fit to a model assuming uncorrelated within-subjects errors. That should tell you whether your data are Aren't the G-G and H-F corrections only approximate fixes? Surely it is better to work with a model that actually fits your data, rather than using ad hoc adjustments towards a model that doesn't quite fit. But I'm no psychologist. :-) Cheers, Simon. On Mon, 2007-06-25 at 08:22 +0200, Peter Dalgaard wrote: DarrenWeber wrote: I'm an experimental psychologist and when I run ANOVA analysis in SPSS, I normally ask for a test of non-sphericity (Box's M-test). I also ask for output of the corrections for non-sphericity, such as Greenhouse-Geisser and Huhn-Feldt. These tests and correction factors are commonly used in the journals for experimental and other psychology reports. I have been switching from SPSS to R for over a year now, but I realize now that I don't have the non-sphericity test and correction factors. This can be done using anova.mlm() and mauchly.test() which work on mlm objects, i.e., lm() output where the response is a matrix. There is no theory, to my knowledge, to support it for general aov() models, the catch being that you need to have a within-subject covariance matrix. __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -- Simon Blomberg, BSc (Hons), PhD, MAppStat. Lecturer and Consultant Statistician Faculty of Biological and Chemical Sciences The University of Queensland St. Lucia Queensland 4072 Australia Room 320, Goddard Building (8) T: +61 7 3365 2506 email: S.Blomberg1_at_uq.edu.au The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. - John Tukey. __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] ANOVA non-sphericity test and corrections (eg, Greenhouse-Geisser)
Darren, Further to Peter Dalgaard's help; Take a look at the example in --- library(car) ?Anova # note upper case 'A' The example in the Anova help page following the --- ## a multivariate linear model for repeated-measures data ## See ?OBrienKaiser for a description of the data set used in this example gives a workings for -- ## Greenhouse-Geisser and Huynh-Feldt Corrections ## for Departure from Compound Symmetry You might find that example helpful. John __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] ANOVA non-sphericity test and corrections (eg, Greenhouse-Geisser)
I'm an experimental psychologist and when I run ANOVA analysis in SPSS, I normally ask for a test of non-sphericity (Box's M-test). I also ask for output of the corrections for non-sphericity, such as Greenhouse-Geisser and Huhn-Feldt. These tests and correction factors are commonly used in the journals for experimental and other psychology reports. I have been switching from SPSS to R for over a year now, but I realize now that I don't have the non-sphericity test and correction factors. The backgroud to this question is that I'm doing a psychophysics experiment and the data analysis uses an aov model that looks like this: roiAOV - aov( roi ~ (Cue*Hemisphere) + Error(Subject/ (Cue*Hemisphere)), data=roiDataframe) where Cue is 2 levels (an arrow on a screen that points left or right) and Hemisphere is 2 levels (brain activity in the left or right cerebral hemisphere). There are 8 subjects and they all have one observation for all levels of Cue * Hemisphere (ie, a within-subjects design). I need some functions for calculation of Box's M and the Greenhouse- Geisser correction factor. Below is some code example that I have for the latter, but I don't know how to adapt it so it can take the aov object. # BEGIN CODE BLOCK # see pp. 45-47 of # http://www.psych.upenn.edu/~baron/rpsych.pdf # --- # create some data x0 - rnorm(30) x2 - rnorm(30) x4 - rnorm(30) data - cbind(x0,x2,x4) # n is the number of 'subjects' or rows; while # k is the number of levels in the factor (columns), # which is the number of repeated measures n - dim(data)[1] k - dim(data)[2] # if k = 2, the epsilon correction is not required. # When the data are perfectly spherical, epsilon = 1. # The minimum value possible for epsilon is epsi = 1 / (k - 1) # if epsi == 1 and k == 2, quit now... # --- # calculate variance-covariance matrix # diagonal entries are variance, # off-diagonal are covariance S - var(data) # --- # Now estimate Epsilon D - k^2 * ( mean(diag(S)) - mean(S) )^2 N1 - sum(S^2) N2 - 2 * k * sum( apply(S,1,mean)^2 ) N3 - k^2 * mean(S)^2 epsi - D / ( (k-1) * (N1 - N2 + N3) ) # e is used to modify the degrees of freedom for the # F test, so we have (k-1) becomes epsi(k-1) and also # (k - 1)(n - 1) becomes epsi(k - 1)(n - 1). The new # p-value for the F statistic is found with the # pf() function. For example, if we have # df1 = k - 1 = 3 - 1 = 2 # df2 = (k - 1)(n - 1) = (3 - 1)(10 - 1) = 18 # F = 40.719 # then the adjusted 2-tailed p-value is given by: # Fvalue - 40.719 Pepsi - 2 * (1 - pf(Fvalue, df1=epsi*(k-1), df2=epsi*(k-1)*(n-1) ) ) # Huynh-Feldt correction # The Greenhouse-Geisser epsilon tends to underestimate # epsilon when epsilon is greater than 0.70 (Stevens, 1990). # An estimated e=0.96 may be actually 1. Huynh-Feldt # correction is less conservative. The Huynh-Feldt # epsilon is calculated from the Greenhouse-Geisser epsilon, epsiHF - (n * (k-1) * epsi - 2) / ((k-1) * ((n-1) - (k-1)*epsi)) PepsiHF - 2 * (1 - pf(Fvalue, df1=epsiHF*(k-1), df2=epsiHF*(k-1)*(n-1) ) ) # MANOVA (and multivariate tests) may be better if the # Greenhouse-Geisser and the Huynh-Feldt corrections do not agree, # which may happen when epsilon drops below 0.70. When epsilon # drops below 0.40, both the G-G and H-F corrections may indicate # that the violation of sphericity is affecting the adjusted p-values. # MANOVA is not always appropriate, though. MANOVA usually requires # a larger sample size. Maxwell and Delaney (1990, p. 602) suggest # a rough rule of thumb that the sample size n should be greater # than k+10. # END CODE BLOCK __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
