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

From: Paul Smith <>
Date: Thu 27 Jul 2006 - 20:52:05 EST

On 7/27/06, Frank E Harrell Jr <> wrote:
> > I am trying to study four-way interactions in an ANOVA problem.
> > However, qqnorm+qqline result
> >
> > (at
> >
> > 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:
> >
> >
> >
> > To circumvent the problem, I looked for non-parametric tests, but I
> > found nothing, but the article:
> >
> >
> >
> > 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 mailing list PLEASE do read the posting guide and provide commented, minimal, self-contained, reproducible code. Received on Thu Jul 27 20:58:17 2006

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