A model fit statistic considers goodness-of-fit
and parsimony. Select models that minimize AIC.

When comparing multiple model fits, additional model parameters
often yield larger, optimized loglikelihood values. Unlike the optimized
loglikelihood value, AIC penalizes for more complex models, i.e.,
models with additional parameters.

The formula for AIC, which provides insight into its relationship
to the optimized loglikelihood and its penalty for complexity, is:

$$aic=-2\left(logL\right)+2\left(numParam\right).$$

A model fit statistic considers goodness-of-fit
and parsimony. Select models that minimize BIC.

Like AIC, BIC uses the optimal loglikelihood function value
and penalizes for more complex models, i.e., models with additional
parameters. The penalty of BIC is a function of the sample size, and
so is typically more severe than that of AIC.

The formula for BIC is:

$$bic=-2\left(logL\right)+numParam*\mathrm{log}\left(numObs\right).$$