Table 4.

Model Comparison Criteria to M2PL-Q Model Fitted to the Proficiency in English Data.

Models	DIC	WAIC	LOO
PL	$82742.26$	$82951.90$	$82975.57$
M2PL-Q custom	$83286.46$	$83909.16$	$83970.52$
M2PL-Q custom-global	$82295.00$	$82765.12$	$82841.41$

Note. M2PL-Q = multidimensional two-parameter logistic model with a Q-matrix; DIC = deviance information criterion; WAIC = widely available information criterion; LOO = leave-one-out cross-validation.