Table 4.

Model fit comparisons of factor analysis, latent class analysis, and factor mixture models of alcohol consumption, dependence, and abuse indicators for wave 2 NESARC data^a

Model	Log-likelihood value	No. of parameters	BIC	VLMR p value	Entropy
Factor analysis
One factor	−93466.76	30	187237.56	–	–
Latent class analysis
Two classes	−97631.96	33	195598.35	< 0.001	0.86
Three classes	−93709.89	50	187926.50	< 0.001	0.85
Four classes	−92871.84	67	186422.68	< 0.001	0.80
Five classes	−92512.90	84	185877.09	< 0.001	0.74
Six classes	−92316.43	101	185656.45	< 0.001	0.75
Seven classesb	−92224.25	118	185644.37	n.s.	0.71
Eight classes	−92159.53	135	185687.22	n.s.	0.73
Nine classes	−92120.32	152	185781.09	n.s.	0.73
Factor mixture analysis
Two classes, one factor
FMM1 (LCFA)	−98057.37	31	196428.91	< 0.001	0.85
FMM2	−92550.87	47	185578.06	< 0.001	0.60
FMM3	−92338.04	61	185294.29	< 0.001	0.45
Three classes, one factor
FMM1 (LCFA)	−94239.06	33	188812.56	< 0.001	0.84
FMM2	−92289.00	64	185226.61	< 0.001	0.55
FMM3	−92180.81	92	185293.98	n.s.	0.52
Four classes, one factor
FMM1 (LCFA)	−93428.30	35	187211.30	< 0.001	0.78
FMM2c	−92193.93	81	185208.75	< 0.05	0.58
FMM3	−92099.48	123	185445.51d	< 0.05	0.53

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=25186.

^bThe seven-class solution was best according to the BIC; however, the six-class model was best fitting according to the VLMR test.

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

^dFailed to converge due to a non-positive definite first-order derivative product matrix.