In , we present twin correlations and covariances showing the basic relationships between cognitive ability, education, and AFB (measured both across the twin pairs and within twin individuals). The COG-AFB correlations are marked with one asterisk, and the ED-AFB correlations are marked with two. Studying these patterns shows that education correlates slightly more than cognitive ability with AFB.
Overall Twin Correlations, Variances, and Covariances for Twin 1 and Twin 2 in Female Danish Twin Pairs in MADT Sample
, which has already been described, contains the coefficients estimated by fitting the phenotypic regression model. The zero-order estimated coefficient between COG and AFB (without including education in the model) was a regression coefficient of .20. In a simple multiple regression form of this model (the top portion of ), bCOG→AFB
= .08, and bED→AFB
= .33. But when the mediation model was defined (the bottom portion of ), the original coefficient of bCOG→AFB
= .08 went to 0, bCOG→ED
= .66, and bED→AFB
= .31. We note that these results are very similar to those from the Neiss et al. (2002)
study from the United States. MacKinnon, Lockwood, and Williams (2004)
provide statistical tests and confidence intervals to test whether bCOG→AFB
is still significant after introducing a mediator, although there is no point in testing whether a sample coefficient of zero is different from a population parameter of zero. The links from COG to ED and ED to AFB are both statistically significant.
Next we report the results of reversing cognitive ability and schooling within this framework. The simple zero-order relationship between ED and AFB is bED→AFB = .66. When we fit a mediation model, with COG mediating this large relationship between ED and AFB, there was no mediation effect. The bCOG→AFB was estimated to be exactly zero (and this is actually the same model estimated above, shown in the bottom portion of ). Thus, the two mediation analyses suggest that ED fully mediates the COG→AFB link, but COG does not mediate the ED→AFB link.
If we stopped at this point, we would conclude that education mediates all of the apparent relationship between cognitive ability and AFB in this sample (and is the more likely causal variable). However, this result can be illusory, masking the broader family effects contained in a behavior genetic model. The illusion is the result of performing an analysis based solely on between-family variance. Our next analysis uses kinship information that accounts for variance both within and across families. This analytic approach, which is the basis for behavior genetic analysis, is itself based on the correlational structure shown in , except that it is separated into MZ and DZ categories.
In , we present the twin correlations and covariances partitioned into the two twin categories, MZ and DZ twins. The univariate COG-ED-AFB relationships are marked with one asterisk, and the multivariate COG-ED-AFB relationships are marked with two. A brief inspection of the univariate patterns across the twin categories shows obvious genetic variance underlying COG and ED and shared environmental variance in AFB.
Twin Correlations, Variances, and Covariances for MZ and DZ Twin Pairs
In the multivariate patterns in , the COG-ED link is strongly suggestive of shared genetic variance (compare the MZ correlation of .38 between the cognitive ability of one twin and the education of the other to the corresponding DZ correlation of .19). The ED-AFB link, however, shows obvious shared common environmental variance and no shared genetic variance (note the sizable cross-twin correlations of .15 and .24 for MZ and DZ twins, respectively, both of moderate size but not positively related to genetic relatedness).
When we fit the overall model in , the direct links between the measured variables (COG, ED, and AFB) were also evaluated, in the context of this overall model. By refitting the overall model in and evaluating the various paths for their contribution to the fit of the model, we identified the best-fitting reduced model. This model is shown in , where one-half of the model (for one type of twin pair, DZ twins) is shown; estimated parameter values in the MZ half of the model are constrained to be identical. Within this model, no link can be dropped without significantly reducing the fit of the model, and no link from the original model in can be added that significantly improves the fit. The confidence intervals are presented, and none of these contain zero within the interval. The maximum likelihood chi-square value for the model in is 39.4 (df = 21; there are 30 independent correlations—15 for the MZ twins and 15 for the DZ twins—that are used to estimate the nine free parameters shown in ). This chi-square statistic can be used to reject the fit of this model at the .05 level. However, the AIC = −26.6, and the RMSEA = .020, results both strongly supportive of the quality of the model’s fit (an RMSEA less than .05 is typically viewed as indicating excellent model fit, while an AIC less than 0.0 indicates that the reduced model fits better than the full model when parsimony is also taken into consideration). Within the presentation in , the parameter values are standardized, for ease of interpretation. One implication of standardizing is that the squared standardized parameter values of the links into each measured variable sum to 1.0, so that we can decompose these into percentage of variances.
Fig. 3 Best-fitting model from evaluation of the links in the model in . Note that only the half of the model for DZ twin pairs is shown here; the MZ half of the model is constrained to have identical path coefficients. That model differs from this one (more ...)
The joint additive genetic factor is shared only between our two primary independent variables, cognitive ability and education (not including AFB). The joint shared environmental factor is shared with all three of the measured variables. can be further inspected for the patterns among the specific latent variance sources for each measured variable, which are at the bottom of the diagram.
Of particular note is that, in addition to the model’s depiction of the behavior genetic relationships among these variables, there are no longer any significant links among the three measured variables. These links dropped out empirically; they were not constrained to be zero, but rather were estimated by the model to not contribute to the best-fitting model. Because of its interpretational importance, we note that even the link between education and AFB, which had a high coefficient in the phenotypic model, dropped out once the kinship structure was accounted for.
In addition to the results in , we also present statistics from this analysis in , which presents the univariate heritabilities (h2
) and shared environmental variance (c2
) estimated for each of our primary variables (and we add the Neiss et al. [2002
] results to show the similarity). AFB had no univariate heritability, so it had no genetic variance to overlap that of cognitive ability or education in (and note the absence of patterned correlations or covariances in relation to genetic category in ). But there is substantial c2
underlying AFB, and a large proportion of this has multivariate overlap with the variance from cognitive ability and education.
Fig. 4 Comparison of standardized parameter estimates from best-fitting models from this study and from Neiss et al. (2002). (Note that only one-quarter of the model is shown here, for only one member of a twin pair, and only one type of twin.) Neiss et al. (more ...)
Our ultimate outcome variable in this study is AFB among the female Danish twins. According to our best-fitting model in , the variance in that outcome can be attributed to two sources. Sixty-nine percent (.832) of its overall variance is unique nonshared or measurement error variance. The remaining 31% (.562) of it is shared common environmental variance shared with both education and cognitive ability. This is the most interesting source of variance, for scientific and policy-related purposes, because it suggests that education, cognitive ability, and AFB operate as a single factor, rather than being separated as previous research using simpler models implied.