  Watanabe-Akaike information criterion (WAIC; Watanabe, 2010) and
leave-one-out cross validation (LOO) are two fully Bayesian model selection
methods that have been shown to perform better than other traditional
information-criterion based model selection methods such as AIC, BIC, and DIC
in the context of dichotomous IRT model selection. In this paper, we
investigated whether such superior performances of WAIC and LOO can be
generalized to scenarios of polytomous IRT model selection. Specifically, we
conducted a simulation study to compare the statistical power rates of WAIC and
LOO with those of AIC, BIC, AICc, SABIC, and DIC in selecting the optimal model
among a group of polytomous IRT ones. We also used a real data set to
demonstrate the use of LOO and WAIC for polytomous IRT model selection. The
findings suggest that while all seven methods have excellent statistical power
(greater than 0.93) to identify the true polytomous IRT model, WAIC and LOO
seem to have slightly lower statistical power than DIC, the performance of
which is marginally inferior to those of the other four frequentist methods.
Keywords: polytomous IRT, Bayesian, MCMC, model comparison.
