3 Fitting the Multivariate Genetic Model

Twin 1 | Twin 2 | ||||||||

T0 | T1 | T2 | T3 | T0 | T1 | T2 | T3 | ||

T1 | 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 | |

T2 | 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 | 297.9 | 229.4 | 247.4 | 274.9 | 281.9 | 359.7 | 326.9 | 281.1 | |

DZ | 259.7 | 259.9 | 245.2 | 249.3 | 283.8 | 249.5 | 262.1 | 270.9 |

The results from this common factor model are shown in Table 10.3.3 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 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
free
statistics minus 16 estimated parameters).
Earlier in this chapter we alluded to the fact that confirmatory factor models allow one to statistically test the significance of model parameters. We can perform such a test on the present multivariate genetic model. The Mx output above shows that the shared environment factor loadings are much smaller than either the genetic or non-shared environment loadings. We can test whether these loadings are significantly different from zero by modifying slightly the Mx script to fix these parameters and then re-estimating the other model parameters. There are several possible ways in which one might modify the script to accomplish this task, but one of the easiest methods is simply to change the

`Matrices= Group 1`

statement in
the second and third group equates its loadings to those in the first.
Thus, the modified script represents a model in which common factors are
hypothesized for genetic and non-shared environmental effects to account
for covariances among the observed variables, and unique effects are
allowed to contribute to measurement variances. All shared environmental
effects are omitted from the model.
Since the modified multivariate model is a sub- or nested model of
the full common factor specification, comparison of the goodness-of-fit
chi-squared values provides a test of the significance of the deleted
factor loadings (see Chapter ). The full model has 56 degrees
of freedom and the reduced one:
d.f. Thus,
the difference chi-squared statistic for the test of loadings has degrees of freedom. As may be seen in the output fragment
below, the of the reduced model is 51.08, and, therefore,
the difference is
, which is
non-significant at the .05 level. This non-significant chi-squared
indicates that the shared environmental loadings can be dropped from the
multivariate genetic model without significant loss of fit; that is, the
arithmetic data are not influenced by environmental effects shared by
twins. Parameter estimates from this reduced model are given below in
Table 10.3.3
The estimates for the genetic and non-shared environment parameters differ somewhat between the reduced model and those estimated in the full common factor model. Such differences often appear when fitting nested models, and are not necessarily indicative of misspecification (of course, one would not expect the estimates to change in the case where parameters to be omitted are estimated as 0.0 in the full model). The fitting functions used in Mx (see Chapter ) are designed to produce parameter estimates that yield the closest match between the observed and estimated covariance matrices. Omission of selected parameters, for example, the loadings in the present model, generates a different model and thus may be expected to yield slightly different parameter estimates in order to best approximate the observed matrix.