Maximum likelihood correlations were calculated for the five groups of twins (monozygotic male [MZM], dizygotic male [DZM], monozygotic female [MZF], dizygotic female [DZF], and opposite sex dizygotic [OSDZ] twins) and model-fitting analyses were performed with a special software package (Mx; Statistical Modeling, Richmond, VA).
20
In classic twin studies, variation of a trait can be decomposed into sources of additive genetic (A), common environmental (C), and unique environmental (E) effects.
21 MZ twins are derived from one fertilized egg and share 100% of their genes. DZ twins are derived from two distinct fertilized eggs and share, on average, 50% of their genes. Because the twins in our sample were reared together, both MZ and DZ twins shared 100% of common family environmental effects. Heritability is defined as the proportion of the total variance attributable to genetic variance.
The use of opposite-sex DZ twin pairs in twin studies provides an opportunity to detect sex-specific effects as well as gender difference in genetic and environmental influences on the phenotype under study.
21 In the present study, opposite-sex DZ correlation was lower than same-sex DZ correlation, suggesting that sex-specific effects may play a role in CCT variation. Thus, sex-limitation models were fit to the data using the model-fitting analysis software (Mx; Statistical Modeling).
Figure 1depicts the general sex-limitation model we used for the data. In the full general sex-limitation model (model 1), the A, C, and E parameters were assumed to differ between the boys and the girls (A
m ≠ A
f, C
m ≠ C
f, and E
m ≠ E
f). The full general sex-limitation model also assumed the existence of sex-specific genes by allowing the additive genetic correlation for opposite-sex twins (
r aO) to vary between 0 and 0.5. Variations of the full sex-limitation model were made to identify the best-fitting model. Four steps were taken specifically. First, to determine whether the full general sex-limitation model is acceptable, we compared the fit in that model with that in a saturated model where means and variances of CCT were allowed to differ across zygosity as well as between the first- and the second-born twins. Second, we fixed
r aO at 0.5, to detect effects of sex-specific genes. Third, we constrained the A, C, and E parameters to be equal across the two sexes, to determine the difference in the magnitude of genetic and environmental influences between the two sexes. Finally, either or both A and C parameters were eliminated from the full model and from the two sets of reduced sex-limitation models to test the significance of its effects.
For model-fitting analyses, the raw data option in the Mx software was used, which generates −2× log likelihood (−2LL) of the data. Difference in −2LL between the full and reduced model is itself approximately distributed as χ2, with the degree of freedom equal to the difference in degree of freedom between the two models. The selection of the best-fitting model was made using the log-likelihood ratio test (LRT): A significant change in χ2 between the full and reduced models suggested that the reduction was not acceptable, whereas a nonsignificant change in χ2 indicated that the reduced model was better than the full model.