3 Fitting the Multivariate Genetic Model

Table 10.2: Observed female MZ (above diagonal) and DZ (below diagonal) correlations for arithmetic computation variables and variances.

	Twin 1				Twin 2
	T0	T1	T2	T3	T0	T1	T2	T3
T0	1.0	.81	.83	.87	.78	.65	.71	.68
T1	.89	1.0	.87	.87	.74	.74	.74	.71
T2	.85	.90	1.0	.90	.73	.66	.72	.70
T3	.83	.86	.86	1.0	.74	.71	.74	.75
T0	.23	.31	.36	.34	1.0	.73	.78	.79
T1	.22	.32	.34	.38	.81	1.0	.86	.87
T2	.16	.23	.27	.35	.79	.86	1.0	.87
T3	.23	.31	.34	.37	.81	.86	.87	1.0
MZ	297.92	229.41	247.42	274.94	281.96	359.70	326.93	281.09
DZ	259.66	259.94	245.24	249.30	283.80	249.49	262.09	270.93

To illustrate the genetic common factor model we fit it to the arithmetic computation data, but now using both members of the female twin pairs and specifying two groups for the MZ and DZ twins. The observed variances and correlations examined in this analysis are presented in Table 10.2. Appendix  shows the full Mx script for this model.

The Mx output from this common factor model is shown below (after editing). The PARAMETER SPECIFICATIONS section illustrates the assignment of parameter numbers to matrices declared Free in the matrices section. Consecutive parameter numbers are given to free elements in matrices in the order in which they appear.

The parameter estimates in the MX PARAMETER ESTIMATES section indicate a substantial genetic basis for the observed arithmetic covariances, as the genetic loadings are much higher than either the shared and non-shared environmental effects. The unique variances in F also appear substantial but these do not contribute to covariances among the measures, only to the variance of each observed variable. The $\chi^{2}_{56}$ value of 46.77 suggests that this single factor model provides a reasonable explanation of the data. (Note that the 56 degrees of freedom are obtained from $2\times 8(8+1)/2$ free statistics minus 16 estimated parameters).