4 Model for Age-Correction of Twin Data

`Cons_t1`

) and twin 2
(`Cons_t2`

). Since in this specification we have 3 indicator variables, we adjust
`NInput_vars=3`

. If we initially ignore age, as an exploratory
analysis, we can select only the conservatism scores for analysis,
using the `Select`

command (note that the list of variables
selected must end with a semicolon ``;`

').
The script fits the ACE model. The results of this model
are presented in the fourth line of the standardized results of Table 6.11, which
shows that the squares of parameters estimated from the model sum to
one, because these correspond to the proportions of variance
associated with each source (A, C, and E).
Parameter Estimates | Fit statistics | ||||||

Model | df | ||||||

-- | -- | 1.000 | -- | 823.76 | 5 | .000 | |

-- | 0.804 | 0.595 | -- | 19.41 | 4 | .001 | |

0.836 | -- | 0.549 | -- | 56.87 | 4 | .000 | |

0.464 | 0.687 | 0.559 | -- | 3.07 | 3 | .380 | |

0.836 | -- | 0.549 | 0.000 | 56.87 | 3 | .000 |

The significance of common environmental contributions to variance in conservatism may be tested by dropping (AE model) but this leads to a worsening of by 53.8 for 1 d.f., confirming its importance. Similarly, the poor fit of the CE model confirms that genetic factors also contribute to individual differences (significance of is for 1 df, which is highly significant). The model, which hypothesizes that there is no family resemblance for conservatism, is overwhelmingly rejected, illustrating of the great power of this data set to discriminate between competing hypotheses. For interest, we also present the results of the ADE model. Since we have already noted that is appreciably greater than half the MZ correlation, it is clear that this model is inappropriate. Symmetric with the results of fitting an ACE model to the BMI data (where was still less than , indicating dominance), we now find that the estimate of gets ``stuck" on its lower bound of zero. The BMI and conservatism examples illustrate in a practical way the perfect reciprocal dependence of and in the classical twin design of which only one may be estimated. The issue of the reciprocal confounding of shared environment and genetic non-additivity (dominance or epistasis) in the classical twin design has been discussed in detail in papers by Martin

`Select`

statement is dropped from the previous job). We
estimate simultaneously the contributions of additive genetic, shared
and unique environmental factors on conservatism, the variance of
age `V*V`

, and the contribution of age to conservatism `S*V`

.
Group 2: female MZ twin pairs Data NInput_vars=3 NOberservations=941 Labels age cons_t1 cons_t2 CMatrix Symmetric File=ozconmzf.cov Matrices= Group 1 Covariances V*V' | V*S' | V*S' _ S*V' | A+C+E+G | A+C+G _ S*V' | A+C+G | A+C+E+G;The matrix algebra here is more complex than usual, and for univariate analysis it would be easier to draw the diagram with the GUI. However, the algebraic approach has the advantage that it is much easier to generalize to the multivariate case. Results of fitting the ACE model with age correction are in the first row of Table 6.12. Standardized results are presented, from which we see that the standardized regression of conservatism on age (constrained equal in twins 1 and 2) is 0.422. In the unstandardized solution, the first loading on the age factor is the standard deviation of the sample for age, in this case 13.2 years. The latter is an estimated parameter, making five free parameters in total. In each group we have statistics, where

Parameter Estimates | Fit statistics | ||||||

Model | df | ||||||

0.474 | 0.534 | 0.558 | 0.422 | 7.41 | 7 | .388 | |

0.720 | -- | 0.547 | 0.426 | 31.56 | 8 | .000 | |

-- | 0.685 | 0.595 | 0.421 | 25.49 | 8 | .001 | |

0.464 | 0.687 | 0.559 | -- | 370.17 | 8 | .000 |

It is interesting to compare the results of the ACE model in Table 6.11 with those of the ACES model in Table 6.12. We see that the estimates of and are identical in the two tables, accounting for % and % of the total variance, respectively. However, in the first table the estimate of , accounting for 47% of the variance. In the analysis with age however, and accounts for 29% of variance, and age accounts for . Thus, we have partitioned our original estimate of 47% due to shared environment into 18% due to age regression and the remaining 29% due to `genuine' cultural differences. If we choose, we may recalculate the proportions of variance due to , and , as if we were estimating them from a sample of uniform age -- assuming of course that the causes of variation do not vary with age (see Chapter 9). Thus, genetic variance now accounts for % and shared environment variance is estimated to be %. Our analysis suggests that cultural differences are indeed important in determining individual differences in social attitudes. However, before accepting this result too readily, we should reflect that estimates of shared environment may not only be inflated by age regression, but also by the effects of assortative mating -- the tendency of like to marry like. Since there is known to be considerable assortative mating for conservatism (spouse correlations are typically greater than 0.6), it is possible that a substantial part of our estimate of may arise from this source (Martin