Model Selection Using AIC with Equally Weighted Models

aiclikelihood-ratiomodelmodel selection

I am using AIC (Akaike information criterion) for model selection. There are 2 models. The first model has 2 parameters with log likelihood of -10182.0284 and the second model has 3 parameters with the same likelihood when tried on a specific dataset that displays the need for only two parameters. The weighting I get with AIC is equal for both models. The equality seems to come from the fact that not all significant figures are taken into account and with such low log likelihood the number of parameter penalization is insignificant. The results:

AICmodelSelect(-10182.0284,-10182.0284)
AIC_min
null model min AIC
relprob_null
     1
relprob_alt
     1
weight_null
    0.5000
weight_alt
    0.5000

AIC equally favours both models. I am also doing likelihood ratio test cause the models are nested and the p-value is below 0.01 for the null model (simpler constrained model). But how do I justify choosing the simpler model with AIC when there is equal weighting given here?

Best Answer

There was a fairly good commentary in the Journal of Wildlife Management concerning uninformative parameters within the AIC framework.

Arnold, T. W. 2010. Uninformative parameters and model selection using Akaike’s Information Criterion. Journal of Wildlife Management 74:1175–1178. [Link].

We usually consider models within 2 delta AIC as competitive. However, if a model has an addition of only one parameter to its competitor and that parameter is not significant, that parameter is likely spurious. AIC = –2LL + 2K so the penalty for adding one parameter is +2 AIC. If only one parameter is added but the AIC is within 2 delta AIC, the model fit was not improved enough to overcome the penalty. Therefore, that parameter is uninformative and should not be included in the model or interpreted as having an effect.

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