Mixtools package is used to fit mixtures of normal/regressions. The package documentation is given here
regmixmodel.sel fits the mixture model for varying number of components and returns the AIC/BIC/CAIC for each. It also returns the "winner" model, the model with the highest of each of these selection critera. Example output:
> regmixmodel.sel(X,y,k=4,type="fixed") number of iterations= 352 number of iterations= 566 Need new starting values due to singularity... number of iterations= 615 1 2 3 4 Winner AIC Inf 7247.358 7319.812 7341.830 1 BIC Inf 7192.434 7233.992 7225.115 1 CAIC Inf 7184.434 7221.492 7208.115 1 ICL Inf 7193.024 7234.943 7226.069 1
What has me confused is why the "winner" returned is the highest AIC, and not the lowest? After all, the best fit is determined by the model with the lowest AIC?
The reason I am asking is that no explanation is given in the documentation, so I'm curious if there's something I misunderstand about AIC model selection for mixture models.
Given the output above, wouldn't we select the 2-component mixture model since it has the lowest AIC among the 4 considered?