[R] Insignificant variable improves AIC (multinom)?

[Werner Wernersen]

> >Hi,

> >
> >I am trying to specify a multinomial logit model using the multinom function 
> from the nnet package. Now I add another independent variable and it halves the 
> AIC as given by summary(multinom()). But when I call Anova(multinom()) from the 
> car package, it tells me that this added variable is insignificant 
> (Pr(>Chisq)=0.39). Thus, the improved AIC suggests to keep the variable but the 
> Anova suggests to drop it.
> >
> >I am sure this is due to my lack of understanding of these models but could 
> someone help me out with a pointer what my mistake is?
> 
> 
> I am not sure why you  would expect the same answer from AIC and p-value.  They 
> are different questions.  AIC attempts to answer a question about overall model 
> fit.  p-value for a particular variable attempts to answer whether that 
> particular coefficient could be due to chance if the population value of the 
> parameter was 0.
> 
> One way these could give different answers is if the new variable affected the 
> parameter estimates for the other parameters.
> 
> It's yet another exemplar of the problems with using p-values for model 
> selection
> 
> HTH
> 
> Peter
> 
> Peter L. Flom, PhD
> Statistical Consultant
> www DOT peterflomconsulting DOT com

Many thanks for the answers, Peter and Krzysztof!

That was very enlightening. I have to read up on model selection. The thought I have to get my head around is that the added variable helps explaining the observed variability in the data and thus should be retained in the model. But since the coefficient is insignificant, I cannot interpret it and if I use this equation for predictions then I add a "random" value since I cannot reject that the coefficient is actually zero instead of what I estimated.

One just never sees someone presenting regression coefficients which are not significant although model selection procedures are often based on the AIC...

Have a good weekend,
  Werner