Goodness of model fit was assessed using four criteria: Bayesian Information Criteria (BIC), sample-size adjusted BIC, Akaike Information Criteria (AIC), and −2 Log Likelihood. The BIC is a fit statistic that extends the traditional maximum-likelihood-based model fit statistics in several ways including penalization for complexity of the model (i.e., number of parameters) (Etzioni and Kadane, 1995). The AIC is closely related but imposes a relatively lighter penalty for model complexity, when compared with BIC (Akaike, 1978). The −2 Log Likelihood is a standard maximum likelihood statistic for evaluating model fit. Note that absolute goodness-of-fit measures used in EFA analyses described earlier (e.g., CFI, TLI) are not available for maximum likelihood estimated IRT models fit to response patterns; thus relative measures BIC, sample size adjusted BIC, and AIC are estimated. Model fits were examined by comparing fit indices with all existing DSM-IV criteria plus craving to a model in which the craving parameter was constrained to be zero.
