[R] keeping interaction terms

[Frank E Harrell Jr]

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Christian Jones wrote:
> 
> Hello,<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p>
> 
> while doing my thesis in habitat modelling I´ve come across a problem with interaction terms. My question concerns the usage of interaction terms for linear regression modelling with R. If an interaction-term (predictor) is chosen for a multiple model, then, according to <?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:office:smarttags" /><st1:place w:st="on">Crawley</st1:place> its single term has to be added to the multiple model: lrm(N~a*b+a+b).<o:p></o:p>
> 
> This nearly always leads to high correlation rates between the interaction term a*b and its single term a or b. With regards to the law of colinearity modelling should not include correlated variables with an Spearman index >0,7. Does this mean that the interaction term has to be discarded or can the variables stay within the model when correlated? I do not necessarily want to do a PCA on this issue.<o:p></o:p>
> 
> Thanks for helping<o:p></o:p>
> 
> Christian<o:p></o:p>

Your query opens up many issues.  First, the statement that a main 
effect has to be added if an interaction term is chosen assumes that an 
interaction has meaning without adjustment for main effects.  This is 
not the case.  The hierarchy principle needs to be executed in a forward 
manner.  Second, you are implying that you are not fitting a single 
pre-specified model but are doing variable selection based on p-values. 
  This creates a host of problems.  Third, you imply that correlations 
between main effects and interactions are not to be tolerated.  Again 
this is not the case.  It is a fact of life that we must accomodate. 
[Some people like to center main effects to reduce this correlation but 
that is an artificial and not helpful approach.]

Frank


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