Table 4.

Model Comparison Indices for TIMSS 2007 Eighth-Grade Math and Science Items, U.S. Students: TIMSS Math (N = 7377).

Model	Log-likelihood	Log-prior	Log-posterior	#pars	BIC	AIC	AIC3	CAIC
1D-ordinal, equal CR item	−120,369.4	−159.6	−120,528.9	429	244,559.5	241,596.7	242,025.7	244,988.5
1D-ordinal	−120,181.2	−160.2	−120,341.5	450	2,443,702	241,262.5	241,712.5	244,820.3
2D-ordinal, equal CR itema	−119,702.9	−168.5	−119,871.4	506	243,912.3	240,417.8	240,923.8	244,418.3
2D-ordinala	−119,367.8	−170.5	−119,538.3	544	243,580.5	239,823.6	240,367.6	244,124.5
1D-nominal, equal CR item	−120,369.1	−159.5	−120,528.6	430	244,567.8	241,598.2	242,028.2	244,997.8
1D-nominal	−120,133.6	−160.3	−120,293.9	472	244,470.8	241,211.1	241,863.1	244,942.8
2D-nominal, equal CR itema	−119,709.8	−168.9	−119,878.7	507	243,935.1	240,433.7	240,940.7	244,442.1
2D-nominala	−119,311.2	−171.0	−119,482.2	583	243,814.7	239,788.4	240,371.4	244,397.7

Note. Boldfaced values indicate best model. TIMSS = Trends in Mathematics and Science Study; BIC = Bayesian Information Criterion; AIC = Akaike Information Criterion; CAIC = Consistent version of the AIC; CR = constructed response.

^aWith monotonicity constraints applied.