Descriptive Statistics

presents mean, standard deviation, and number of participants at Wave-1 and Wave-2. No significant mean or variance differences were found between Twin-1 and Twin-2. Nor were there any mean or variance differences between zygosity groups for proactive or reactive aggression at either of the two time points. Significant mean differences were found between males and females, for reactive aggression at both time points (Wave-1: χ^{2} = 14.88, df = 3, *P*<.001; Wave-2: χ^{2} = 9.90, df = 3, *P* = .02), with males showing higher scores than females.

| **TABLE I**Number of Participants (*N*), Mean, and Standard Deviation (SD) for Reactive and Proactive Aggression, Ages 9–10 and 11–14, by Zygosity and Sex |

Twin Correlations

Intraclass and cross-twin cross-age correlations for the reactive and proactive aggression are presented in . All MZ intraclass correlations were higher than DZ intraclass correlations, suggesting genetic influences for both types of aggression. For example, the intraclass correlations for reactive aggression, Wave-1, were .48 for MZ males and .60 for MZ females. The corresponding numbers for DZ twins were lower, .35 and .46. There was no evidence for genetic nonadditivity (i.e., dominance or epistasis), as none of the MZ intraclass correlations exceeded twice the values of the DZ intraclass correlations for the same sex-twin pairs. All the DZ intraclass correlations were more than half the MZ intraclass correlations suggesting shared environmental effects, apart from proactive aggression Wave-1 in males. MZ intraclass correlations were all less than one, which suggest influence of nonshared environment.

| **TABLE II**Intraclass and Cross-Twin Cross-Age Correlations, by Sex and Zygosity |

Cross-twin cross-age correlations, as shown in , give a first indication of stability and change in genetic and environmental influences for reactive and proactive aggression across time. In most cases (except for MZ/DZ males’ reactive aggression), DZ correlations were greater than half MZ correlations, indicating that both genetic and shared environmental effects contribute to the stability in both forms of aggressive behavior. However, etiological patterns suggested by these twin correlations can be tested more formally using structural equations models.

Model-Fitting Analyses Within Each Wave

Model-fitting analyses for reactive and proactive aggression at age 9–10 have previously been carried out on these data [

Baker et al., 2008]. These results are summarized in , in order to facilitate comparisons to the analyses of Wave-2 and the longitudinal stability between the two waves. In brief, an ACE model constraining parameters to be equal across males and females fit the data best compared with the saturated model for both reactive and proactive aggression (reactive aggression: χ

^{2} = 16.76, df = 12,

*P* = .16; proactive aggression χ

^{2} = 14.84, df = 11,

*P* = .20). For reactive (proactive) aggression 26% (in males) and 32% (in females) of the variance was due to genetic influences, 27% (in males) and 21% (in females) was explained by shared environmental influences, and the remaining 46% (in males) and 47% (in females) was due to nonshared environment.

| **TABLE III**Model-Fitting Analyses Within Each Wave for Reactive and Proactive Aggression, at Ages 9–10 and 11–14 Years |

Model-fitting results for reactive and proactive aggression at age 11–14 (Wave-2) are also displayed in . For both reactive and proactive aggression a model constraining the relative influence of genetic and environmental factors to be equal in males and females fit the data best compared to the saturated model (reactive aggression: χ^{2} = 17.65, df = 12, *P* = .13; proactive aggression χ^{2} = 11.61, df = 11, *P* = .40). The model constraining variance components to be equal for males and females also had a smaller AIC, indicating that it is a more parsimonious model, and a smaller BIC, indicating a better fit.

Genetic effects accounted for 43% of the variance in reactive aggression at age 11–14 (*P*<.05); 15% of the variance was due to shared environmental effects (nonsignificant), and the nonshared environment accounted for the remaining 42% of variance in reactive aggression (*P*<.05). For proactive aggression, 48% of the variance was due to genetic effects (*P*<.05), 8% of the variance was due to shared environmental effects (nonsignificant), and the remaining 44% was due to the nonshared environment (*P*<.05). At a glance, genetic factors appeared slightly higher at the second time point compared with the first time point, whereas the shared environment effect slightly declined across age.

Longitudinal Model-Fitting Analyses

First, bivariate Cholesky decomposition models were used to assess the effects of stable and new genetic and environmental effects in reactive and proactive aggression from childhood to early adolescence. For both reactive and proactive aggression, a saturated model was used as a baseline to which the Cholesky decomposition was compared (see ). For reactive aggression, a Cholesky decomposition equating genetic and environmental estimates to be equal in males and females provided a better fit of the data based on AIC and BIC criteria (AIC = 1,245.84; BIC = −4,036.72), and did not significantly differ from the saturated model (Δχ^{2} = 73.01; Δdf = 57; *P* = .08). Similarly, for proactive aggression, a Cholesky decomposition equating genetic and environmental estimates to be equal in males and females fit the data better based on BIC (AIC = 1,396.74; BIC = −3,961.27), and did not significantly differ from the saturated model (Δχ^{2} = 72.96; Δdf = 57; *P* = .08). This model estimates fewer parameters and is therefore more parsimonious, although the AIC was slightly smaller for the model estimating different parameters in the two sexes (AIC = 1,394.52). Further, mean differences between reactive aggression scores across the two time points were found (χ^{2} = 54.80, df = 18, *P*<.001), with mean values being lower at Wave 2. No mean differences between proactive aggression scores across the two time points were found (χ^{2} = 14.64, df = 18, *P* = .69).

| **TABLE IV**Bivariate Longitudinal Model-Fitting Results for Reactive and Proactive Aggression, at Ages 9–10 and 11–14 Years |

The total estimated genetic and environmental effects for reactive and proactive aggression at each time point can be obtained by summing the contributions of common and unique components (see for reactive aggression and proactive aggression, respectively). For example, the estimated heritability in reactive aggression at Wave-1 is (*a*_{11})^{2} = .54^{2} = .29, and at Wave-2 (*a*_{21})^{2}+ (*a*_{22})^{2} = .48^{2}+.49^{2} = .47. In general, the total genetic and environmental effects estimated for each measure in the bivariate model are consistent with those derived in each univariate genetic models. Slight variation in the parameter estimates is a result of additional information available in cross-twin cross-age covariance.

For reactive aggression, the phenotypic stability correlation was derived to be *r* = .54 [i.e., (*a*_{11}**a*_{21})+ (*c*_{11}**c*_{21})+(*e*_{11}**e*_{21}) = (.54*.48)+(.50*.12)+(.68*.32)]. For proactive aggression this correlation was *r* = .50 = (.58*.73)+(.45*.00)+(.68*.11). From the estimates presented in , it is also possible to calculate how much the phenotypic stability correlation is due to genetic influences, shared environmental and nonshared environmental influences.

For reactive aggression, 48% of the phenotypic stability correlation was explained by genetic factors: (

*a*_{11}+

*a*_{21})/

*r* = (.54+.48)/.54 = .48. The shared environment explained 11% of the stability, though nonsignificant. The remaining 41% of the phenotypic stability was due to the nonshared environmental influences. Conversely, one can examine the extent to which longitudinal change in aggression may be due to genetic and environmental factors, by computing the ratio of each unique Wave-2 specific effect (i.e., new effects at Wave-2) to the total of the Wave-2 specific effects. For reactive aggression, the Wave-2 specific effects were due primarily (48%) to nonshared environmental influences [i.e.,

], whereas the genetic (38%) and shared environmental (14%) effects were nonsignificant.

For proactive aggression, 85% of the stability was due to genetic factors, with the remaining 15% due to the nonshared environment. Conversely, the Wave-2 specific effects were due primarily to nonshared environmental influences (93%). Again, the genetic (0%) and shared environmental (7%) Wave 2 specific effects were nonsignificant.

While the bivariate longitudinal analyses indicated strong genetic stability for both reactive and proactive aggression, the separate analyses of each form of aggression do not address the extent to which their etiologies may overlap. Thus, a series of multivariate models were fit simultaneously to the reactive and proactive aggression scales at both waves, to investigate this etiological overlap. Specifically, the model specified two latent factors, one for each form of aggression (reactive and proactive), with the respective subscales at both time points loading onto each factor. Thus, each latent factor represents one form of aggression as measured at different time points in the two waves of assessment. The scale-specific effects (i.e., for each form of aggression at a single time point) represent genetic and environmental effects unique to each form of aggression during a particular assessment (Wave 1 or 2). The extent to which there are genetic or environmental influences unique to a given time or form of aggression can be investigated by examining these subscale-specific parameters.

Given the lack of sex differences in all univariate and bivariate models, a multivariate Cholesky model constraining male and female estimates to be equal was used as a baseline to which the two-factor common pathway was compared. The two-factor common pathway model (with separate but correlated latent factors for reactive and proactive forms of aggression) provided a better fit to the data according to BIC and AIC criteria (AIC = 2,093.27; BIC = −8,270.43), and did not significantly differ from the Cholesky model (Δχ^{2} = 5.13; Δdf = 7; *P* = .64).

A series of reduced models were fit in order to simplify the two-factor common pathway model, see . A model in which the common genetic factor was dropped from the two latent aggression factors was first fit, although it failed miserably (Model 2a, Δχ^{2} = 18.77; df = 3; *P*<.001). Next, a model dropping the common shared environmental factor was fit (Model 2b, Δχ^{2} = 1.46; df = 3; *P* = .69), and a model dropping both the common genetic and shared environmental factors (Model 2c, Δχ^{2} = 131.53; df = 6; *P*<.001). Thus, the shared environmental factor common to both reactive and proactive aggression could be dropped without a significant reduction in fit (Model 2b). The two-factor common pathway model could be further reduced by dropping time and measurement-specific genetic influences (proactive and reactive aggression, Wave 1) and time and measurement specific shared environment influences (reactive and proactive aggression, Wave 2) (Model 2d, Δχ^{2} = 4.52; df = 7; *P* = .72). displays standardized parameter estimates from this reduced two-factor common pathway model.

| **TABLE V**Multivariate Longitudinal Model-Fitting Results for Reactive and Proactive Aggression, at Ages 9–10 and 11–14 Years |

Squaring the standardized parameter estimates presented in provides the relative contributions to the phenotypic variance for each form of aggression as derived from both waves of assessment. A common genetic factor explained 80% (*P*<.05) of variance in the first latent factor (labeled *Reactive Aggression*) and 63% (*P*<.05) of variance in the second latent factor (labeled *Proactive Aggression*). A nonshared environmental factor common to both Reactive and Proactive Aggression factors explained 20% (*P*<.05) of variance in the Reactive Aggression latent factor and 37% (*P*<.05) of variance in the Proactive Aggression latent factor.

There was a significant amount of time and measurement-specific variance for each of the variables (i.e., not all of the variance could be explained by the two latent aggression factors). For reactive and proactive aggression, Wave 1, there were time-specific shared environmental influences (reactive aggression: *C*_{s} = 13%; proactive aggression: *C*_{s} = 19%). There were also some time-specific genetic influences (*A*_{s}) for both types of aggression at Wave 2, explaining 26% in reactive aggression and 29% in proactive aggression. The residual variances also received contributions from non-shared environmental sources, explaining 38, 30, 25, and 18% of the variance in reactive aggression, Wave1 and Wave 2, and proactive aggression Wave 1 and Wave 2, respectively. It should be noted that nonshared environmental influences on the specific subscales also include measurement error.