General ACE structural equation twin model of a single behavioral measure. Individual differences in performance on a measure (depicted with rectangles to denote an observed variable) are modeled as due to three types of influences: additive genetic (A), shared environmental (C), and nonshared environmental (E). The Twin 1 with Twin 2 A correlation is set to 1.0 for monozygotic (MZ) twins because they share all of their genes, and 0.5 for dizygotic (DZ) twins because they share on average half of their genes by descent. The C correlation is set to 1.0 for both types of twins because both are raised together. The E correlations are set to zero because nonshared environment is uncorrelated, by definition.

Phenotypic confirmatory factor analysis model of the three executive functions. Task names are abbreviated. Numbers on arrows are standardized factor loadings, those next to the smaller arrows on the right are residual variances, and those on curved double-headed arrows are inter-factor correlations. All parameters were significant (p < .05).

Three executive functions’ ACE models. Numbers next to the executive functions’ ACEs (e.g., A_U) are the percentages of executive function latent variable variances due to genetic (A), shared environmental (C), and nonshared environmental (E) influences. Numbers under the lower ACEs are estimates for nonexecutive variances in individual tasks (names abbreviated). Numbers on top of the arrows from latent executive functions to tasks are standardized factor loadings. Boldface type and solid lines indicate p < .05.

Hierarchical multivariate executive function ACE model. Task names are abbreviated. Numbers above the top ACEs (A_C, C_C, and E_C) are the percentages of the Common Executive (Common EF) variance due to genetic and environmental influences. The numbers occluding arrows are standardized factor loadings. Numbers next to latent variable executive functions’ ACEs (e.g., A_I, A_U, and A_S) are their specific genetic and environmental variances independent of the Common EF factor. Numbers under the lower ACEs are estimates for the remaining nonexecutive variances in individual tasks. Boldface type and solid lines indicate p < .05. The italics type for stop-signal’s specific A variance indicates marginal significance (p = .052).

Nested factors multivariate executive function ACE model. All nine executive function tasks (names abbreviated) load on the first Common Executive (Common EF) factor; hence, this factor represents what is common to all executive functions. The updating and shifting task also load on Updating-specific and Shifting-specific factors, respectively; hence these factors represent what is specific to the updating and shifting tasks, once the influence of the Common EF factor is removed. Numbers above the top ACEs are the percentages of the Common EF, Updating-specific, and Shifting-specific factors’ variances due to genetic and environmental influences. The numbers occluding arrows are standardized factor loadings. Numbers under the lower ACEs are estimates for the remaining nonexecutive variances in individual tasks. Boldface type and solid lines indicate p < .05. The italics type for stop-signal’s specific A variance indicates marginal significance (p = .057).

Executive function ACE model with Perceptual Speed. Task names are abbreviated. Numbers above the ACEs for the latent variables are the percentages of those latent variables accounted for by genetic and environmental influences. Numbers occluding the double-headed arrows are correlation coefficients. Correlations for components with zero or near-zero variances were not estimated. The numbers occluding arrows are standardized factor loadings. Numbers under the lower ACEs are estimates for task-specific variances. Boldface type and solid lines indicate p < .05. The italics type for hidden patterns’s specific C variance indicates marginal significance (p = .055).

Nested factors executive function model with WAIS-IQ. Task names are abbreviated. Numbers above the ACEs for the latent variables and WAIS-IQ are the percentages of those variables accounted for by genetic and environmental influences. Numbers occluding the double-headed arrows are correlation coefficients. Correlations for components with zero or near-zero variance were not estimated. The numbers occluding arrows are standardized factor loadings. Numbers under the lower ACEs are estimates for task-specific variances. Boldface type and solid lines indicate p < .05.

Two multivariate ACE models for three tasks. In a common pathway model (panel A), the executive functions’ ACE variables influence the individual tasks through the executive function (EF) latent variable. In the less restrictive independent pathways model (panel B), the executive function’ ACEs influence the tasks directly through separate paths (i.e., there is no underlying latent variable postulated for the correlations among the measure).

Nested factors model of the WAIS-III subtests. The model depicts a “g” factor on which load all 11 subtests (names abbreviated), and 4 nested factors: Verbal Comprehension-(VC) specific, on which load vocabulary, similarities, information, and comprehension; Working Memory- (WM) specific, on which load arithmetic and digit span; Perceptual Organization- (PO) specific, on which load picture completion, block design, picture arrangement, and object assembly; and Perceptual Speed- (PS) specific, which has digit-symbol substitution as a single indicator. Because a two-indicator latent variable is not statistically identified when it does not correlate with any other variables in the model (Bollen, 1989), the loadings for the WM-specific variable were fixed at the values estimated in the full model that incorporated correlations with the executive function latent variables. Numbers above the ACEs for the latent variables are the percentages of those variables’ variances accounted for by genetic and environmental influences. The numbers occluding arrows are standardized factor loadings. Numbers under the lower ACEs are estimates for task-specific variances. Boldface type and solid lines indicate p < .05. Italic font indicates marginal significance for the .23 loading of the information subtest on the VC-specific variable (p = .066), the 18% specific C variance for the picture completion subtest (p = .055), and the 21% specific A variance for the picture arrangement subtest (p = .061).