Table 1.

Model comparisons based on information criteria for the three ability domains—mathematics, reading and science—in PISA 2009.

	Mathematics			Reading			Science
Model	AIC	BIC	ΔGHP	AIC	BIC	ΔGHP	AIC	BIC	ΔGHP
1PL	217510	217779	0.0059	413555	414317	0.0055	347819	348222	0.0062
1PCL	220022	220291	0.0122	414757	415519	0.0070	348756	349160	0.0077
1PLL	216882	217151	0.0043	416988	417751	0.0098	348984	349388	0.0081
1PGL	216784	217068	0.0041	413369	414146	0.0053	347804	348223	0.0062
2PL	215621	216144	0.0012	410032	411541	0.0011	344597	345389	0.0009
4PGL	215142	216188	0.0000	409163	412182	0.0000	344064	345648	0.0000
3PLQ	215153	215938	0.0000	409327	411591	0.0002	344097	345285	0.0001
3PLRH	215174	215959	0.0001	409275	411539	0.0001	344083	345271	0.0000
3PL	215486	216099	0.0009	409767	411605	0.0008	344420	345362	0.0006
4PL	215179	216060	0.0001	409296	411852	0.0002	344105	345368	0.0001
4PLQ	215168	216102	0.0001	409245	411913	0.0001	344089	345464	0.0000

Note. AIC = Akaike information criterion; BIC = Bayesian information criteria; DGHP = difference in Gilula–Haberman penalty (GHP) between a particular model and the best-fitting model in terms of GHP; For model descriptions see Section 2.1 and Equations (3) to (14). For AIC and BIC, the best-fitting model and models whose information criteria did not deviate from the minimum value by more than 100 are printed in bold. For DGHP, the model with the smallest value and models with DGHP values smaller than 0.0005 are printed in bold.