Table 2.

Model fit comparisons of factor analysis, latent class analysis and factor mixture models of alcohol consumption, dependence and abuse indicators for wave 1 NESARC data^a

Model	Log-likelihood value	No. of parameters	BIC	VLMR p value	Entropy
Factor analysis
One factor	−109116.889	30	218546.49	–	–
Latent class analysis
Two classes	−114054.56	33	228453.11	< 0.001	0.88
Three classes	−109215.68	50	218952.54	< 0.001	0.85
Four classes	−108209.18	67	217116.74	< 0.001	0.82
Five classes	−108003.83	84	216883.24	< 0.001	0.77
Six classes	−107835.06	101	216722.91	< 0.01	0.75
Seven classesb	−107716.72	118	216663.42	< 0.01	0.76
Eight classes	−107650.61	135	216708.41	n.s.	0.78
Nine classes	−107603.70	152	216791.79	n.s.	0.78
Factor mixture analysis
Two classes, one factor
FMM1 (LCFA)	−114688.81	31	229700.74	< 0.001	0.87
FMM2	−108044.50	47	216578.90	< 0.001	0.65
FMM3	−107885.50	61	216406.84	< 0.001	0.67
Three classes, one factor
FMM1 (LCFA)	−109860.91	33	220065.79	< 0.001	0.84
FMM2	−107795.53	64	216258.17	< 0.001	0.57
FMM3	−107723.88	92	216406.74	n.s.	0.66
Four classes, one factor
FMM1 (LCFA)	−108802.50	35	217969.83	< 0.001	0.79
FMM2c	−107676.76	81	216197.83	< 0.001	0.66
FMM3	−107672.35	123	216626.80	n.s.	0.47

NESARC, National Epidemiologic Survey of Alcohol and Related Conditions; BIC, Bayesian Information Criterion; VLMR, Vuong–Lo–Mendell–Rubin test of relative improvement in fit; n.s., non-significant; FMM, factor mixture model; LCFA, latent class factor analysis.

^an=33644.

^bThe seven-class solution was best according to both the BIC and the VLMR test.

^cThe four-class second model (FMM2) was the best-fitting model according to the BIC.