Understanding AIC Values for Best Model

Hello, I am trying to understand how to interpret my AIC outputs for three comparison models. I computed the AIC values using either the cumulative negative log likelihoods (nLL) or cumulative deviance for each model.

In my code, how I assess the two AIC values are as follows:

AIC_nLL = -2 * (cum_nLL) + 4; %4 because it is 2k and I have 2 free parameters in each model

AIC_dev = cum_dev + 4; %4 because it is 2k and I have 2 free parameters in each model

For AIC_nLL I get negative results, (i.e., -15585.2; -15821.7; -35015.2 ) and for AIC_dev I get positive results (i.e., 1.57E+04 ; 1.59E+04; 3.51E+04 ).

While the actual positve/negative values aren't relevant, the decision for which model is best differs between the two calculations, as for AIC_nLL it suggests Model 3 is best and with AIC_dev it suggests Model 1/2 are best.

I have already gone through to double check that my cum_nLL calclulations and cum_deviance calculations are correct. I'm not sure how to move forward with interpreting my results.

Answer 1

[William Rose]

@Alyssa,

Those negative AICs should be positive.

Simple interpretation is to take the model with the lowest (positive) AIC.

[William Rose]

@Alyssa, since you took the negative log likelihood, you don't wan't to multiply by -1. That is why you got negative AIC values when you should have had positive.

So both ways of calculating AIC indicate models 1 and 2 are a lot better than model 3.