Re: [R] Non-parametric four-way interactions?

From: Frank E Harrell Jr <f.harrell_at_vanderbilt.edu>
Date: Thu 27 Jul 2006 - 13:42:58 EST

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.
Received on Thu Jul 27 13:36:25 2006

Archive maintained by Robert King, hosted by the discipline of statistics at the University of Newcastle, Australia.
Archive generated by hypermail 2.1.8, at Thu 27 Jul 2006 - 22:16:32 EST.

Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help. Please read the posting guide before posting to the list.