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?