Table 3.

Fit statistics from bivariate Cholesky models of Vocabulary and three separate alcohol problem measures

				Model comparison
	Model fit			Compared to
Model	−2LL	df	AIC		χ2 change	df	p value
Vocabulary – RAPI
1 ACE	8538.847	1155	6228.847
2 AE	8538.847	1158	6222.847	1	0	3	1
3 AE, no genetic covariance	8554.081	1159	6236.081	2	15.234	1	<0.001
4 AE, no environmental covariancea	8539.092	1159	6221.092	2	0.245	1	0.621
5 E	8678.712	1161	6356.712	2	139.865	3	<0.001
Vocabulary – Max drinks
1 ACE	8706.577	1176	6354.577
2 AE	8706.577	1179	6348.577	1	0	3	1
3 AE, no genetic covariance	8723.180	1180	6363.180	2	16.603	1	<0.001
4 AE, no environmental covariancea	8707.736	1180	6347.736	2	1.159	1	0.282
5E	8854.814	1182	6490.814	2	148.237	3	<0.001
Vocabulary – AD symptoms
1 ACE	8698.297	1181	6336.297
2 AE	8698.297	1184	6330.297	1	0	3	1
3 AE, no genetic covariance	8701.824	1185	6331.824	2	3.527	1	0.060
4 AE, no environmental covariancea	8698.745	1185	6328.745	2	0.448	1	0.503
5 AE, no covariance	8706.792	1186	6334.792	2	8.495	2	0.014
6 E	8834.855	1187	6460.855	2	136.558	3	<0.001

LL, Log likelihood ; df, degrees of freedom; AIC, Akaike’s Information Criterion ; RAPI, Rutgers Alcohol Problem Index ; Max drinks, maximum number of drinks consumed in a 24-h period ; AD, alcohol dependence.

To reduce skewness, RAPI and AD symptoms were Box–Cox transformed and Max drinks square root transformed.

In all models, different means for monozygotic (MZ) and dizygotic (DZ) twins were estimated and sex was included as a covariate.

^aBest-fitting model.