Re: [R] Looking for transformation to overcome heterogeneity of variances
Thanks to all contributors for the fruitfulness of this discussion. I am speculating about a simpler solution: to use a non-parametric approach. To avoid the requirement of having normal residuals, Frank Harrell has suggested here the following non-parametric procedure: library(Design) # also requires library(Hmisc) f - lrm(y ~ a*b*c*d) f anova(f) Could someone please tell me whether that also works when there is no homoscedasticity? What are the assumptions of that method? Paul __ 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] Looking for transformation to overcome heterogeneity of variances
Dear All My data consists in 96 groups, each one with 10 observations. Levene's test suggests that the variances are not equal, and therefore I have tried to apply the classical transformations to have homocedasticity in order to be able to use ANOVA. Unfortunately, no transformation that I have used transforms my data into data with homocedasticity. The histogram of variances is at http://phhs80.googlepages.com/hist1.png Is someone able to suggest to me a transformation to overcome the problem of heterocedasticity? Thanks in advance, Paul __ 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] Looking for transformation to overcome heterogeneity of variances
Paul Smith [EMAIL PROTECTED] writes: Dear All My data consists in 96 groups, each one with 10 observations. Levene's test suggests that the variances are not equal, and therefore I have tried to apply the classical transformations to have homocedasticity in order to be able to use ANOVA. Unfortunately, no transformation that I have used transforms my data into data with homocedasticity. The histogram of variances is at http://phhs80.googlepages.com/hist1.png Is someone able to suggest to me a transformation to overcome the problem of heterocedasticity? Not based on that information. Try the following instead: fit - lm(y~g) par(mfrow=c(2,2)); plot(fit) -- O__ Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 __ 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] Looking for transformation to overcome heterogeneity of variances
On 03 Aug 2006 15:45:10 +0200, Peter Dalgaard [EMAIL PROTECTED] wrote: My data consists in 96 groups, each one with 10 observations. Levene's test suggests that the variances are not equal, and therefore I have tried to apply the classical transformations to have homocedasticity in order to be able to use ANOVA. Unfortunately, no transformation that I have used transforms my data into data with homocedasticity. The histogram of variances is at http://phhs80.googlepages.com/hist1.png Is someone able to suggest to me a transformation to overcome the problem of heterocedasticity? Not based on that information. Try the following instead: fit - lm(y~g) par(mfrow=c(2,2)); plot(fit) Thanks, Peter. By 'g', you mean factor1* factor2*factor3*factor4 ? Paul __ 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] Looking for transformation to overcome heterogeneity of variances
On 03 Aug 2006 16:32:38 +0200, Peter Dalgaard [EMAIL PROTECTED] wrote: My data consists in 96 groups, each one with 10 observations. Levene's test suggests that the variances are not equal, and therefore I have tried to apply the classical transformations to have homocedasticity in order to be able to use ANOVA. Unfortunately, no transformation that I have used transforms my data into data with homocedasticity. The histogram of variances is at http://phhs80.googlepages.com/hist1.png Is someone able to suggest to me a transformation to overcome the problem of heterocedasticity? Not based on that information. Try the following instead: fit - lm(y~g) par(mfrow=c(2,2)); plot(fit) Thanks, Peter. By 'g', you mean factor1* factor2*factor3*factor4 If that defines your 96 groups, yes. Thanks, Peter. The result of fit - lm(tardiness ~ interaction(factor1,factor2,factor3,factor4)) par(mfrow=c(2,2)); plot(fit) Warning message: X11 used font size 8 when 7 was requested is at http://phhs80.googlepages.com/2transform1.png Paul __ 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] Looking for transformation to overcome heterogeneity of variances
Paul Smith [EMAIL PROTECTED] writes: On 03 Aug 2006 15:45:10 +0200, Peter Dalgaard [EMAIL PROTECTED] wrote: My data consists in 96 groups, each one with 10 observations. Levene's test suggests that the variances are not equal, and therefore I have tried to apply the classical transformations to have homocedasticity in order to be able to use ANOVA. Unfortunately, no transformation that I have used transforms my data into data with homocedasticity. The histogram of variances is at http://phhs80.googlepages.com/hist1.png Is someone able to suggest to me a transformation to overcome the problem of heterocedasticity? Not based on that information. Try the following instead: fit - lm(y~g) par(mfrow=c(2,2)); plot(fit) Thanks, Peter. By 'g', you mean factor1* factor2*factor3*factor4 If that defines your 96 groups, yes. -- O__ Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 __ 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] Looking for transformation to overcome heterogeneity of variances
Paul: It is too bad that most peoples statistical thought processes lead them to thinking heterogeneity is something to overcome so that a simple test of differences in means with ANOVA can be made. If you have that much heterogeneity among 96 groups (hard for me to imagine otherwise), perhaps the distributional heterogeneity rather than simple shifts in means is the more important effect. You might try using omnibus tests of distributional differences (eg., MRPP, coverage tests, etc.) or compare multiple quantiles (e.g., with quantile regression) since you've already admitted that the group distributions differ by more than just a shift in means. Heterogeneous variances among groups immediately implies that there is not a single parameter describing changes in distributions among groups. Focusing on just a comparison of means, while traditional and analytically expedient, is unlikely to be very enlightening. You could of course, weight each group inversely by its variance to achieve a weighted comparison of means. But doing this just makes it so that you've made a valid test on only one of the parameters characterizing distributional differences. A better analysis but still not as enlightening as possible. My 2 pence. Brian Brian S. Cade U. S. Geological Survey Fort Collins Science Center 2150 Centre Ave., Bldg. C Fort Collins, CO 80526-8818 email: [EMAIL PROTECTED] tel: 970 226-9326 Paul Smith [EMAIL PROTECTED] Sent by: [EMAIL PROTECTED] 08/03/2006 07:33 AM To r-help@stat.math.ethz.ch cc Subject [R] Looking for transformation to overcome heterogeneity of variances Dear All My data consists in 96 groups, each one with 10 observations. Levene's test suggests that the variances are not equal, and therefore I have tried to apply the classical transformations to have homocedasticity in order to be able to use ANOVA. Unfortunately, no transformation that I have used transforms my data into data with homocedasticity. The histogram of variances is at http://phhs80.googlepages.com/hist1.png Is someone able to suggest to me a transformation to overcome the problem of heterocedasticity? Thanks in advance, Paul __ 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. [[alternative HTML version deleted]] __ 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.
