Variance Components Models for Gene–Environment Interaction in Twin Analysis

“rural environments), or through a subsequent extension of the twin model (Dick, Rose, Viken, Kaprio, & Koskenvuo, 2001; Purcell, 2002) allowing one to test for changes in genetic and environmental influences as a function of a more continuous environmental measure (e.”

“These techniques apply both to continuous traits (Pletcher 1999; Pletcher and Geyer 1999; Jaffréic and Pletcher 2000; Pletcher and Jaffréic 2002; Purcell 2002; Purcell and Sham 2002; Meyer and Kirkpatrick 2005) and to categorical traits (Towne et al. 1997; Viel et al. 2005).”

“As shown in the study by Purcell (12), the between-pair component contributes to shared environment and/or gene shared environment interaction, whereas the within-pair component contributes to nonshared environment and/or gene nonshared environment interaction.”

“In the classical twin design, variance due to interactions between shared environmental risk factors and genotype is included in the estimate of the genetic variance component, if not modeled explicitly (Molenaar et al., 1990; Purcell, 2002).”

“In short, ArC interaction acts like A, and ArE interaction acts like E (Purcell, 2002).”

“We know exactly what kinds of effects violations of these assumptions have on model results, but we generally do not know which or to what degrees violations are present (Johnson 2007; Purcell 2002).”

“Age-related change in heritability was examined using a gene-environment interaction model (Purcell, 2002).”

“1; Turkheimer et al., 2017), which differs from the commonly used Purcell model (Purcell, 2002) in several important ways.”

“For a discussion of the uses of variance partitioning approaches in quantitative genetics, see Purcell (2002). rGE in the “Post-Genomics” Era The easy accessibility of full-genome sequences has revolutionized genetics, including rGE research.”

“Purcell (2002) recommended also plotting and presenting the results of the unstandardized variance components.”

“variate twin model in which age and marital status were included as moderating variables (Purcell 2002; Van der Sluis et al. 2008).”

“This first step served as a preliminary analysis to confirm the results of analyses in the second step where we performed model-fitting analyses incorporating age as a continuous moderator (Purcell 2002).”

“To further confirm that the specific genetic component (Ag) works regardless of the SLE level, we incorporated gene-environment interaction terms (Purcell 2002) into the bivariate model to examine the moderation effect of SLE on the paths from As ? depressive symptoms, and from Ag ? depressive symptoms (Fig.”

“Importantly, because the minor allele frequencies did not differ between the groups, the results described later cannot be explained by gene–environment correlations (Purcell, 2002; Scarr andMcCartney, 1983).”

“New analytic techniques have been developed to estimate these interactions (Purcell, 2002).”

“This was done using univariate interaction models specified in Purcell (2002).”

“Model (3) is the ‘Cholesky GxM’ model proposed by Purcell (2002), and model (4) is a special case of (3) proposed by Rathouz et al.”

“However, this constitutes a latent genetic– smoking correlation (rGE; Purcell, 2002; Scarr and McCartney, 1983)—our analyses control for rGE to some extent by allowing for smoking to mediate motive scores.”

“Perhaps more directly relevant to the issue of G · E, it is possible to examine whether estimated genetic influences interact with measured environmental influences on a trait using twin data [53].”

“A recent series of power analyses assuming a continuous dependent variable suggests that the method has reasonable power for sample sizes on the order of those studied in this report (Purcell, 2002).”

“This overlooks the possibility that genetic factors may correlate or interact with environmental factors in complex ways (Purcell, 2002).”

“…will be conducted as follows: We will first confirm that the etiologies of mindset, grit, locus of control, challenge-seeking behavior, and cognitive ability, respectively, do not vary across the two intervention groups de novo (i.e., Phase 1) via Purcell’s univariate G×E model (Purcell 2002).”

“Second, in order to investigate G × E, we combined the general sex-limitation model (Neale and Maes 2004) with the Purcell approach for the binary and continuous moderators (Purcell 2002), and applied them to lifetime and number of years smoking.”

“In order to estimate if the parameters describing the ACE model were stable over time we allowed the relative contributions of A, C and E to vary with offspring birth year (Purcell, 2002).”

“bivariate biometric moderation model (Purcell 2002) with relationship satisfaction as the moderator, for a total of 14 models with moderation parameters freely estimated.”

“Such studies model genetic influences as latent effects on the phenotype and test whether these genetic effects are moderated by the environmental variables (e.g., Boomsma, de Geus, van Baal, & Koopmans, 1999; Purcell, 2002).”

“These results also need to be interpreted taking into consideration that GxE may be biassed in the presence of unobserved rGE (Purcell, 2002; Rathouz, van Hulle, Rodgers, Wald-man, & Lahey, 2008; van der Sluis, Posthuma, & Dolan, 2012).”

“(A) Path diagram of the full linear moderation model (21).”

“Previous studies suggest that rGE can lead to overestimation of genetic variance in twin studies (Purcell, 2002) and spurious moderation effects in molecular genetic studies (Jaffee and Price, 2007).”

“For more details about MNLFA and its precursors, see Mehta and Neale (2005), Molenaar et al. (2010), Neale (1998), Neale et al. (2006), and Purcell (2002).”

“Min-max value from two studies are presented (BPA [17, 96]; phthalates [21, 118]; PCBs [17, 105]; PFAS [17, 195]; PBDEs [17, 23])”

“Difference scores therefore also remove the sort of passive rGE characterized by correlation between additive genetic effects and the shared environment, since correlation between A and C acts like C (Purcell 2002), and C factors (or shared environmental factors) are removed in difference scores.”

“To address the role of participants’ age moderating genetic and environmental influences, the same models (without controlling for personality) were extended by age as a moderator variable (model elements of Figure 1 with dashed lines; see also Purcell, 2002).”

“…the proportion of variance in phenotype due to shared environment (C) is the same for MZ and DZ twins (Grayson, 1989; Rijsdijk & Sham, 2002), and because it further assumes the absence of gene-environment interactions and correlations (Purcell, 2002; Rijsdijk & Sham, 2002).”

“When not explicitly incorporated in the model, positive interactions will be estimated as variance due to nonshared environment, whereas positive A × C interactions will be estimated as variance due to additive genetic effects (Purcell, 2002).”

“G×E model; a model testing whether genetic and/or environment influences on a trait/disorder differ by levels of a moderator) was examined (Purcell, 2002).”

“Next, a model specifying the genetic and environmental architecture of the liability to exercise behavior was fitted to the data, namely a moderation model with linear and quadratic effects of z-transformed age as moderators on the means and variance components (Medland et al. 2009; Purcell 2002; Purcell and Koenen 20…”

“Finally, although the findings suggested the presence of a G × E interaction between ADHD symptoms and dietary habits, they may be partly explained by G × E correlation, which reflects genetic differences in the exposure to particular environments [35,45].”

“…talented ones receive tests with very difficult items, future research should focus on the exact nature of the genotype-environment interaction, for example by using the parametrization introduced by Purcell (2002) that regresses measured environmental moderators directly on the genotypic value.”

“Controlling for such possible rGE is important when examining G E to avoid biased conclusions (Purcell, 2002).”

“Models for testing GxM The remainder of the models explores GxM interactions through various specifications for P. Purcell (2002) proposed an extension of the Cholesky model with GxM (CholGxM), P¼lPþðaCþaCMÞAMþðcCþjCMÞCMþðeCþeCMÞEM þðaUþaUMÞAUþðcUþjUMÞCUþðeUþeUMÞEU ; ð2Þ where lP is the intercept…”

“A standard univariate twin model incorporating age as a moderator (age-moderation model) was applied to the raw data (Figure 1; Purcell, 2002).”

“The model takes into account the phenotypic association between the two traits [27].”

“The effects of these violations on the resulting estimates of genetic and environmental influences are well known (Purcell, 2002).”

“Moreover, inclusion of interactions with latent environmental factors is crucial to examine whether the moderating effect of the measured environment variable is specific to the latent genetic variance components or whether it increases variation over the entire range of the phenotypic distribution (Purcell, 2002).”

“Because the main effect of CSA was non-significant, results suggest minimal bias resulting from confounded gene‐environment correlation ( Purcell 2002 ).”

“To minimize the false positive moderation of causal effects, we also specified moderation coefficients for the instrumental and pleiotropic paths, the A and E variance component paths and the A covariance path (Purcell, 2002).”

“…twin moderation models) to test potential genetic effects since these techniques require several hundred twin pairs for adequate statistical power (Purcell, 2002), but results from twin intraclass correlations (see post hoc analyses; Figure S1) provide tentative evidence that lower levels of…”

“Consistent with prior recommendations (Purcell, 2002), all reported parameter estimates from the G × E models are unstandardized so as not to obscure absolute changes with the moderator.”

“For instance, (unmodeled) covariance between A (additive genetic variable) and C (shared environmental variable) biases the estimate of the shared environmental variance (σC) in the classical twin ACE model (Eaves et al., 1977; Keller et al., 2010; Keller et al., 2009; Purcell, 2002).”

“As there were no significant shared genetic effects in FRA and PB, the univariate G × E interaction model (Figure 2; Purcell, 2002) was applied to the data to determine whether genetic and environmental contributions to PB vary as a function of the moderator, FRA.”

“This removed potential genetic effects shared between alcohol involvement and income/parental education (Purcell, 2002).”

“A standard twin model incorporating age as a moderator (Neale and Cardon, 1992; Purcell, 2002) was applied to the raw data for the CP and the HP, respectively.”

“To take such GE covariation into account, the statistical GxE interaction model used by Figlio et al. (1) included a main effect of SES on academic measures; as such, the genotype × SES interaction effect only moderated the variance in academic achievement that is independent from SES (14, 15).”

“We sought to further confirm these results using the bivariate gene-environment interaction model (Purcell, 2002), as recommended by van der Sluis et al.”

“A variety of SEM and MEML twin software is available (e.g. Neale and Cardon 1992; Williams et al. 1992; Neale 1997; Purcell 2002; Rijsdijk and Sham 2002; Rabe-Hesketh et al. 2008; Feng et al. 2009).”

“In this approach, the genetic and environmental path coefficients have a constant part and a variable part that depends linearly on the twin specific risk factors, which are modeled as definition variables in Mx (Figure 2; Purcell, 2002).”

“Figure 1 presents the bivariate G x E model (Purcell, 2002; van der Sluis, Posthuma, & Dolan, 2012), where PS interacts with “ A ” , “ C ” , and “ E ” effects common to PS and GA (A c , C c , and E c , respectively), and those effects unique to GA (A u , C u , & E u , respectively).”

“Because the genetic correlation between moderator and motor milestones was very low (R g = 0.06), a univariate model was deemed appropriate as it yields more power than a bivariate model that explicitly models the gene-by-moderator correlation (27,31).”

“Next, a series of six two-group gene-by-environment interaction models were run (Purcell 2002).”

“For example, if not explicitly modeled, GxE and rGE can present as main effects of G or E in twin research, leading to an overestimation of either effect (Purcell, 2002), and genetic association studies can pick up on environmental signal in the case of rGE (Selzam et al.”

“To investigate whether the quasi-causal effect of education on economic ideology is moderated by economic hardship in an individual’s local context, we estimate a gene–environment interaction model as outlined by Purcell (2002).”

“1993; Duffy and Martin 1994), the moderation of genetic and environmental effects (Purcell 2002), and the analysis of the dimensionality of psychological (psychometric) instruments (Franić et al.”

“That is, an interaction effect is difficult to interpret in the absence of its main effect (Nelder, 1994; Purcell, 2002).”

“This removes variance in alcohol involvement due to rural/urban residency and any potential genetic effects shared between alcohol involvement and rural/urban residency (Purcell 2002).”