Mx Output from Two Factor Genetic Model

PARAMETER SPECIFICATIONS
MATRIX F
             1         2         3         4
   1        13         0         0         0
   2         0        14         0         0
   3         0         0        15         0
   4         0         0         0        16
MATRIX X
             1         2
   1         1         0
   2         2         5
   3         3         5
   4         4         5
MATRIX Z
             1
   1         9
   2        10
   3        11
   4        12

MX PARAMETER ESTIMATES
MATRIX F
             1         2         3         4
   1     6.674      .000      .000      .000
   2      .000     6.277      .000      .000
   3      .000      .000     5.644      .000
   4      .000      .000      .000     5.928
MATRIX X
             1         2
   1    15.067      .000
   2    13.701     4.270
   3    13.518     4.270
   4    13.832     4.270
MATRIX Z
             1
   1     4.408
   2     6.091
   3     6.800
   4     5.695

 Chi-squared fit of model >>>>>>>    47.52 
 Degrees of freedom >>>>>>>>>>>>>       59
 Probability >>>>>>>>>>>>>>>>>>>>     .858
 Akaike's Information Criterion >

The estimated genetic factor loading for the alcohol variables ($4.27$) is reasonably large, but much smaller than the loadings on the general genetic factor. This difference is more apparent when we consider proportions of genetic variance accounted for by these two factors, being ${4.27^2}/( 13.70^2+4.27)$ or 9% for the alcohol factor, and $100-9=91\%$ for the general genetic factor. The model yields a $\chi^{2}_{59} = 47.52$ ( = .86), indicating a good fit to the data. The chi-squared test for the significance of the alcohol factor loadings is $51.08 - 47.52 = 3.56$, which is not quite significant at the .05 level. Thus, while the hypothesis of there being genetic effects on the alcohol measures additional to those influencing arithmetic skills fits the observed data better, the increase in fit obtained by adding the alcohol factor does not reach statistical significance.