alexander russell-2 wrote:
Hello,
I'd like to say that it's clear when an independent variable can be ruled
out generally speaking; on the other hand in R's AIC with bbmle, if one
finds a better AIC value for a model without the given independent variable,
versus the same model with, can we say that the independent variable is not
likely to be significant(in the ordinary sense!)?
That is, having made a lot of models from a data set, then the best two are
say 78.2 and 79.3 without and with (a second independent variable
respectively) should we say it's better to judge the influence of the 2nd IV
as insignificant?
regards,
-shfets
_____________________________________
Without meaning to sound snarky, it's best not to consider hypothesis
testing (statistical significance) and AIC in the same analysis.
If you want to decide whether predictor variables have a significant
effect on a response, you should consider their effect in the full model,
via Wald test, likelihood ratio test, etc.. If you want to find the model
with the best expected predictive capability (i.e. lowest expected
Kullback-Leibler distance), you should use AIC.
Burnham and Anderson, among others, say this repeatedly.
In general, for a one-parameter difference, hypothesis testing
is "more conservative" than AIC (e.g., critical log-likelihood difference
for a p-value of 0.05 under the LRT test is 1.92, while the log-likelihood
difference required to say that a model is expected to have better
predictive capability/lower AIC is 1) -- but since they are designed to answer
such different questions, it's not even a fair comparison.
Ben Bolker
