Re: [R] Non-parametric four-way interactions?
On 7/27/06, Frank E Harrell Jr [EMAIL PROTECTED] wrote: Tony Lachenbruch has written some about this, also see my book (it's web page is biostat.mc.vanderbilt.edu/rms). I don't know about the power of interaction tests, but for main effect tests in the absence of interaction, the Wilcoxon test (a special case of PO model) has efficiency of 3/pi compared to the t-test if normality holds. Other approaches: Cox PH model, avas, ace. My book covers these too. Thanks, Frank, for the useful information. 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] Non-parametric four-way interactions?
On 7/27/06, Frank E Harrell Jr [EMAIL PROTECTED] wrote: I am trying to study four-way interactions in an ANOVA problem. However, qqnorm+qqline result (at http://phhs80.googlepages.com/qqnorm.png) is not promising regarding the normality of data (960 observations). The result of Shapiro-Wilk test is also not encouraging: W = 0.9174, p-value 2.2e-16 (I am aware of the fact that normality tests tend to reject normality for large samples.) By the way, the histogram is at: http://phhs80.googlepages.com/hist.png To circumvent the problem, I looked for non-parametric tests, but I found nothing, but the article: http://www.pgia.ac.lk/socs/asasl/journal_papers/PDFformat/g.bakeerathanpaper-2.pdf Finally, my question is: has R got implemented functions to use non-parametric tests to avoid the fulfillment of the normality assumption required to study four-way interactions? Yes, although I seldom want to look at 4th order interactions. You can fit a proportional odds model for an ordinal response which is a generalization of the Wilcoxon/Kruskal-Wallis approach, and allows one to have N-1 intercepts in the model when there are N data points (i.e., it works even with no ties in the data). However if N is large the matrix operations will be prohibitive and you might reduce Y to 100-tile groups. The PO model uses only the ranks of Y so is monotonic transformation invariant. library(Design) # also requires library(Hmisc) f - lrm(y ~ a*b*c*d) f anova(f) Also see the polr function in VR Thanks, Frank. It is very encouraging to learn that, even without normality, I can still study my four-way interactions. I am also aware of transformations that may work in some non-normal cases, and I have tried some of them, but with no success. I am not familiar with the solutions that you suggest, and I would like to learn how they work theoretically, in some book or on the Internet. In particular, I would like to see, regarding power, how the non-parametric suggested approach compares with the classical ANOVA approach. Could you please indicate some references to help me with that? Again, 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] Non-parametric four-way interactions?
Paul Smith wrote: On 7/27/06, Frank E Harrell Jr [EMAIL PROTECTED] wrote: I am trying to study four-way interactions in an ANOVA problem. However, qqnorm+qqline result (at http://phhs80.googlepages.com/qqnorm.png) is not promising regarding the normality of data (960 observations). The result of Shapiro-Wilk test is also not encouraging: W = 0.9174, p-value 2.2e-16 (I am aware of the fact that normality tests tend to reject normality for large samples.) By the way, the histogram is at: http://phhs80.googlepages.com/hist.png To circumvent the problem, I looked for non-parametric tests, but I found nothing, but the article: http://www.pgia.ac.lk/socs/asasl/journal_papers/PDFformat/g.bakeerathanpaper-2.pdf Finally, my question is: has R got implemented functions to use non-parametric tests to avoid the fulfillment of the normality assumption required to study four-way interactions? Yes, although I seldom want to look at 4th order interactions. You can fit a proportional odds model for an ordinal response which is a generalization of the Wilcoxon/Kruskal-Wallis approach, and allows one to have N-1 intercepts in the model when there are N data points (i.e., it works even with no ties in the data). However if N is large the matrix operations will be prohibitive and you might reduce Y to 100-tile groups. The PO model uses only the ranks of Y so is monotonic transformation invariant. library(Design) # also requires library(Hmisc) f - lrm(y ~ a*b*c*d) f anova(f) Also see the polr function in VR Thanks, Frank. It is very encouraging to learn that, even without normality, I can still study my four-way interactions. I am also aware of transformations that may work in some non-normal cases, and I have tried some of them, but with no success. I am not familiar with the solutions that you suggest, and I would like to learn how they work theoretically, in some book or on the Internet. In particular, I would like to see, regarding power, how the non-parametric suggested approach compares with the classical ANOVA approach. Could you please indicate some references to help me with that? Again, thanks in advance. Paul Tony Lachenbruch has written some about this, also see my book (it's web page is biostat.mc.vanderbilt.edu/rms). I don't know about the power of interaction tests, but for main effect tests in the absence of interaction, the Wilcoxon test (a special case of PO model) has efficiency of 3/pi compared to the t-test if normality holds. Other approaches: Cox PH model, avas, ace. My book covers these too. Frank -- Frank E Harrell Jr Professor and Chair School of Medicine Department of Biostatistics Vanderbilt University __ 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] Non-parametric four-way interactions?
Dear All I am trying to study four-way interactions in an ANOVA problem. However, qqnorm+qqline result (at http://phhs80.googlepages.com/qqnorm.png) is not promising regarding the normality of data (960 observations). The result of Shapiro-Wilk test is also not encouraging: W = 0.9174, p-value 2.2e-16 (I am aware of the fact that normality tests tend to reject normality for large samples.) By the way, the histogram is at: http://phhs80.googlepages.com/hist.png To circumvent the problem, I looked for non-parametric tests, but I found nothing, but the article: http://www.pgia.ac.lk/socs/asasl/journal_papers/PDFformat/g.bakeerathanpaper-2.pdf Finally, my question is: has R got implemented functions to use non-parametric tests to avoid the fulfillment of the normality assumption required to study four-way interactions? 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] Non-parametric four-way interactions?
Paul Smith wrote: Dear All I am trying to study four-way interactions in an ANOVA problem. However, qqnorm+qqline result (at http://phhs80.googlepages.com/qqnorm.png) is not promising regarding the normality of data (960 observations). The result of Shapiro-Wilk test is also not encouraging: W = 0.9174, p-value 2.2e-16 (I am aware of the fact that normality tests tend to reject normality for large samples.) By the way, the histogram is at: http://phhs80.googlepages.com/hist.png To circumvent the problem, I looked for non-parametric tests, but I found nothing, but the article: http://www.pgia.ac.lk/socs/asasl/journal_papers/PDFformat/g.bakeerathanpaper-2.pdf Finally, my question is: has R got implemented functions to use non-parametric tests to avoid the fulfillment of the normality assumption required to study four-way interactions? Thanks in advance, Paul Yes, although I seldom want to look at 4th order interactions. You can fit a proportional odds model for an ordinal response which is a generalization of the Wilcoxon/Kruskal-Wallis approach, and allows one to have N-1 intercepts in the model when there are N data points (i.e., it works even with no ties in the data). However if N is large the matrix operations will be prohibitive and you might reduce Y to 100-tile groups. The PO model uses only the ranks of Y so is monotonic transformation invariant. library(Design) # also requires library(Hmisc) f - lrm(y ~ a*b*c*d) f anova(f) Also see the polr function in VR -- Frank E Harrell Jr Professor and Chair School of Medicine Department of Biostatistics Vanderbilt University __ 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.
