keeping interaction terms
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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