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When I build my most parsimonious model using a backward selection approach, do I have to worry about multicollinearity. I mean, do I first check for multicollnearity and drop the variables which has highly collinear and then put only those independent variables in my model that are not correlated and then run a backward selection approach to build the most parsimonious model.

Or should I just put all variables in the model irrespective of whether there is multicollnearity issue since anyway I will end up with the most parsimonious model using a backward selection appraoch.

mdl<-lm(y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7)
drop1(mdl, test="F") 

Please let me know if the question is not clear and I will try to change it.

Thanks

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  • $\begingroup$ backward elimination is really terrible $\endgroup$ – bdeonovic Feb 2 '15 at 13:32
  • $\begingroup$ Ya, but this question is just to teach someone the backward elimination (not telling them it is the best) $\endgroup$ – user53020 Feb 2 '15 at 14:07
  • $\begingroup$ Its like asking whats the best way to dig a hole with a feather; no matter how you do it, you won't get the result you want. $\endgroup$ – bdeonovic Feb 2 '15 at 22:34
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I might avoid absolute statements. Every methods has its limitations.

(1) Often multicolinear terms are included in a model. Or alternatives to dropping one of the variables are found. The multicolinear term results in unstable parameter/coefficient estimates.
(2) Backward elimination has many limitation. One of those is unstable variable/model selection. Collinear terms may well increase this instability. Usually backward elimination is coupled with some form of bootstrap to evaluate model stability. I thought this might be built into the rms package, but couldn't find it on a quick look.

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