4 Fitting a Second Genetic Factor

The genetic common factor model we introduced in Sections 10.3.3 and 10.3.2 may be extended to address more specific questions about the data. In the arithmetic computation measures, for example, it is reasonable to hypothesize two genetic factors: one general factor contributing to all measurements of arithmetic computation, and a second ``alcohol'' factor which influences the measures taken after the challenge dose of alcohol. The most parsimonious extension of our common factor model may involve the addition of only 1 free parameter which represents each of the factor loadings on the alcohol factor (that is, the alcohol loadings may be equated for all alcohol measurements). We present a Mx script for this model in Appendix .

The Mx script in Appendix  corresponds very closely to that used in section 10.3.2, using the X for the genetic common factors We add the latent alcohol factors for twins 1 and 2 as a second column with the following specification statement:

Specify X
1 0 
2 5
3 5
4 5

The addition of the single parameter for all alcohol loadings reflects a model having 13 parameters and $2\times 8(8+1)/2 - 13 = 59$ degrees of freedom. We can, therefore, test the significance of the alcohol factor by comparing the goodness-of-fit chi-squared value for this model with that obtained from the model of Section 10.3.2 for a $60-59=1$ d.f. test.

The edited Mx output from the two-factor multivariate genetic model is as follows: