Table 5.
Model Comparison Indices for TIMSS 2007 Eighth-Grade Math and Science Items, U.S. Students: TIMSS Science (N = 7377).
| Model | Log-likelihood | Log-prior | Log-posterior | #pars | BIC | AIC | AIC3 | CAIC |
|---|---|---|---|---|---|---|---|---|
| 1D-ordinal, equal CR item | −132,753.8 | −164.0 | −132,917.7 | 448 | 267,497.5 | 266,403.5 | 266,851.5 | 269,945.5 |
| 1D-ordinal | −132,505.2 | −168.2 | −132,673.5 | 468 | 269,178.5 | 265,946.5 | 266,414.5 | 269,646.5 |
| 2D-ordinal, equal CR itema | −132,345.5 | −171.2 | −132,516.7 | 543 | 269,527.1 | 265,777.1 | 266,320.1 | 270,070.1 |
| 2D-ordinala | −131,084.2 | −197.6 | −131,281.8 | 581 | 267,342.9 | 263,330.5 | 263,911.5 | 267,923.9 |
| 1D-nominal, equal item | −132,679.7 | −163.9 | −132,933.6 | 447 | 269,520.4 | 266,433.3 | 266,880.3 | 269,967.4 |
| 1D-nominal | −134,194.2 | −167.1 | −134,361.3 | 482 | 272,681.1 | 269,352.4 | 269,834.4 | 273,163.1 |
| 2D-nominal, equal CR itema | −132,332.9 | −171.8 | −132,504.6 | 547 | 269,537.4 | 265,759.7 | 266,306.7 | 270,084.4 |
| 2D-nominala | −130,993.6 | −200.6 | −131,194.2 | 613 | 267,446.7 | 263,213.2 | 263,826.2 | 268,059.7 |
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.
a
With monotonicity constraints applied.