I am running a Generalized Linear Mixed Model analysis in SPSS 25, and have gotten to the point where I would like to justify the selection of my final model based on information criteria.

However, there is one thing I do not understand. SPSS reports p-values for individual parameters based on the Wald-statistic, and this tells me whether the effect of some IV is significant or not. I assume the general way to proceed about doing this is estimating AIC/BIC for the largest candidate model first, then removing variables one by one, recalculating AIC/BIC, and comparing them for fit. I started by removing my non-significant variables from the model first,one by one, and as expected, AIC/BIC both favored the new, simpler models. So far, so good. I noticed however, than even if I remove my significant IVs, AIC/BIC still become smaller, the simpler the model becomes, regardless of whether the removed variable had a significant effect or not. This is not entirely unexpected, as (if I understand correctly) AIC/BIC are basically adjusted versions of -2LL, penalized for model complexity. Nonetheless, I still don't understand how I can use them for model selection if they always favor the simplest possible model, that is, the one with zero parameters. Is there something I am missing?

EDIT: After some further testing, it appears that AIC favors the model with only fixed effects and their interactions retained, without random slopes. Even though I have two random slopes which are significant. Is it okay, to remove such random parameters, based on AIC?

  • $\begingroup$ See this discussion on AIC and BIC... stats.stackexchange.com/questions/577/… $\endgroup$ – Erik Ruzek Jun 8 '19 at 21:04
  • $\begingroup$ A second general comment is that, particularly if you are modeling for explanation, use theory to help you decide on what should be in the model. If prediction is your goal, then AIC and BIC become more relevant as discussed in the link above. With that in mind, I generally use likelihood ratio testing to help me determine whether to keep a random slope. $\endgroup$ – Erik Ruzek Jun 8 '19 at 21:07

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