How are the AIC and BIC in the output computed?

The AIC and BIC are penalized log-likelihood (LL) information criteria. The penalty for the AIC is two times the number of estimated parameters, and the penalty for the BIC is log(N) times the number of estimated parameters. In PROC LCA, the G2 statistic is penalized. The G2 equals -2(LL overall model – LL saturated model). Because the LL for the saturated model is a constant for a given data set, basing the AIC and BIC on this statistic is equivalent to basing it on -2LL of the overall model. Because the AIC and BIC are based on the G2 statistic, they will not necessarily match those from other software packages if they are based on the LL.


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