[R] Rank transformation and the linear mixed model

[Frank E Harrell Jr]

Bruno L. Giordano wrote:
> ----- Original Message ----- From: "Frank E Harrell Jr" 
> <f.harrell at vanderbilt.edu>
> To: "Bruno L. Giordano" <bruno.giordano at music.mcgill.ca>
> Cc: <r-help at stat.math.ethz.ch>
> Sent: Friday, November 03, 2006 8:22 AM
> Subject: Re: [R] Rank transformation and the linear mixed model
> 
> 
>> Bruno L. Giordano wrote:
>>> Hello,
>>> I am looking for references about mixed models built on rank transformed
>>> data.
>>> Did anybody ever consider this topic?
>>>
>>> Thank you,
>>>     Bruno
>>
>> If you are speaking about the response variable, it's better to use a
>> formal model such as the proportional odds model (generalization of the
>> Wilcoxon test).  That way you can do meaningful interaction tests and 
>> much
>> more, plus handle ties elegantly with likelihood ratio tests.  Some
>> researchers have developed mixed effects prop. odds models (which I
>> haven't used yet).
>>
>> Frank
>>
> 
> That's a nice start indeed!!
> 
> However, I am referring both to rank transformation of response variables
> and covariates.
> 
> The reference to this idea is the work by Conover and Iman (e.g., Conover
> and Iman - 1981 - Rank transformations as a bridge between parametric and
> nonparametric statistics).

That has largely been replaced by flexible right-hand-side regression 
modeling (regression splines, gams, etc).  These will handle any smooth 
shape and allow for modeling interactions.  The problem with Conover and 
Iman's method is that when more than one X-variable is being ranked, 
interpretation of partial effects is difficult, and interpretation of 
interactions is nearly impossible.

Frank

> 
> The need would be to handle robustly monotone and nonlinear 
> response-covariates relationships.
> 
>    Bruno
> 
>>>
>>>
>>> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>>> Bruno L. Giordano, Ph.D.
>>> CIRMMT
>>> Schulich School of Music, McGill University
>>> 555 Sherbrooke Street West
>>> Montréal, QC H3A 1E3
>>> Canada
>>> http://www.music.mcgill.ca/~bruno/
>>>
>>> ______________________________________________
>>> R-help at 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.
>>>
>>
>>
>> -- 
>> Frank E Harrell Jr   Professor and Chair           School of Medicine
>>                      Department of Biostatistics   Vanderbilt University
>>
> 
> 
> 


-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University