Variance Components Models for Gene–Environment Interaction in Twin Analysis

“Second, multicollinearity arising from correlations between genetic effects on the ‘environment’ and those influencing depression may reduce the power of detecting interactions between the environmental factor and the remaining genetic component on the phenotype (Purcell, 2002).”

“Purcell’s [18] simulations suggest that this would also be the case when testing only moderation of the shared environment.”

“presentation of the gene–environment interaction model proposed by Purcell (2002). M symbolizes the moderator and y the Investment bias”

“Although other twin models can examine both concordant and discordant pairs (e.g., moderation models, see Purcell, 2002), we were unable to use these models due to relatively small sample sizes in the groups (see Table 1).”

“If S is correlated with genetics—for example, through parental genotypes—its effect in the twin model, where S is unmodelled, will be to increase the estimated proportion of C 43 and so to act to deflate estimates of genetic contributions.”

“As rGE may be present for some life events (see results section on rGE), the mean PAI-BOR score was corrected for the effect of the moderator by including it as a fixed effect in the mean model (Purcell, 2002).”

“In addressing the confounding effects of rGE in GE investigations, Purcell (2002) demonstrated using simulations that the inclusion of the moderator as a main effect in the means/threshold model (M in enclosed triangle; Fig. 2) removed any genetic effects that were common between the moderator and trait.”

“Ideally, we would have examined differences in the heritability of these scores by estradiol levels using twin moderation models (Purcell, 2002).”

“That is, rather than modeling physical health using the linear equation shown above, we used variance component models for gene–environment interactions described by Purcell (2002) to express the variance associated with each of the three components as a linear interaction with the moderators.”

“Although ADHD has substantial heritability, the search for biological targets is increasingly informed by interest in whether the disorder is shaped by interactions between genotypeandenvironmental factors (Nigg,Nikolas,&Burt, 2010; Purcell, 2002).”

“It is possible to develop models assessing the effects of such correlations and interactions (Purcell, 2002), but it is necessary to specify and measure the environmental moderators.”

“In addition to the constraint models, we also conducted moderation models (Purcell, 2002) to directly test sex and pubertal moderation of heritability for disordered eating.”

“, nichepicking; Scarr & McCartney, 1983) and Gene × Environment interaction (i.e., interaction between genetic and environmental effects shared by twins; Purcell, 2002) to some degree.”

“Such designs can be used to examine whether associations between music and mental health are magnified based on other exposures or psychological constructs (gene-by-environment interactions) [132], and whether parents engaged with music are more likely to pass down environments that are protective or hazardous for lat…”

“The CTD assumes no genotype–environment covariation and as a consequence, such effects mimic V ˆ C in the CTD (Eaves et al., 1989; Purcell, 2002; Tambs et al., 1992).”

“Second, we fitted a continuous moderator model (Purcell, 2002) using the program Mx (Neale et al.”

“Whether this relationship actually represents an interaction between environmental stressors and genetic vulnerabilities cannot be determined from the current analyses and requires the application of additional model-fitting techniques (e.g. Purcell, 2002 ).”

“Fortunately, behavioral genetic simulations have shown that G × E interactions can be detected even in the presence of G–E correlations (Purcell, 2002).”

“Purcell (2002) showed how such a model can be fitted in the freely available Mx program (Neale, Boker, Xie, & Maes, 2002).”

“We first evaluated the impact of age on the etiology of DEL and AGG via a series of nested moderation models (see Figure 1; Purcell, 2002) using the crosssectional Time 1 data.”

“This approach is essentially a longitudinal data extension of the genotype by environment interaction (GXE) model described by Purcell (2002) and van der Sluis et al. (2012), with the important addition that substance use can elicit new sources of genetic variance (increase values of a2 … a4) as…”

“Of note, these more recent studies have made use of major advances in the statistical modeling of G·E in twin studies; in effect, they have estimated heritability at every level of a continuously measured environment.(16)”

“Another explanation is that nonshared environmental variance may reflect effects of interactions between personality-relevant genotype and environments (Plomin, DeFries, & Loehlin, 1977) because interaction between additive genetic and nonshared environmental effects is confounded with nonshared environmental variance…”

“First, it allows us to statistically test GxE (see Purcell 2002 for technical details).”

“…to A, C, and E differ for children who attend preschool (preschool = 1) versus children who do not attend preschool (preschool = 0), as follows (cf. Purcell, 2002): Yt, p = µ + bpreschool × preschoolp + (a + a′ × preschoolp) × At, p + (c + c′ × preschoolp) × Ct,p + (e + e′ × preschoolp) × Et,p,…”

“Such a form of gene-by-environment interplay is consistent with a diathesis-stress model, and points towards gene-by-environment interactions [20,21] that, while rooted in early life, can exert their effect also in early adulthood.”

“…limitations of gene main-effect findings, as well as growing appreciation of epigenetics and gene-by-environment interplay (Goldsmith et al. 1997; Purcell 2002), have re-awakened interest in environmental influences on ADHD (Banerjee et al. 2007; SonugaBarke 2010) and consequently in G × E…”

“1c) described by Purcell (2002) was applied in which the effect of a moderator is introduced on the prevalence (i.”

“A frequently used method of testing for G E involves testing whether the proportion of var- iance attributable to genetic (and environmental) effects for a given phenotype, for example antisocial behavior, is moderated by environmental risk exposure (Purcell, 2002).”

“See Guo and Wang (2002) for examples of gene by environment interaction analyses via HLM, and Purcell (2002) for related analyses using SEM.”

“continuous V , including moderated factor models (Bauer and Hussong 2009; Molenaar, Dolan, Wicherts, and van der Mass 2010; Purcell 2002) and factor mixture models (Dolan and van der Maas 1998; Lubke and Muthén 2005).”

“4.4 Choice of variance decomposition In contrast to Purcell (2002), our proposal for obtaining statistically coherent variance decompositions in models such as (2) for phenotype P involves re-expressing the structural model as a sum of uncorrelated additive terms.”

“In contrast, interactions with shared environmental influences would be included in the A estimates (Purcell, 2002).”

“Finally, the externalizing behavior scale and the NLEs were somewhat skewed; skewed data may mimic GrE effects (Purcell, 2002), although the effects are reduced when the moderator is also included in the model.”

“To do so, we fit a series of nested moderator models (of note, twins are not required to be concordant on the value of the moderator).(33,34) The first model functioned as a baseline main effects model in which only the genetic, shared environmental, and nonshared environmental path estimates or intercepts were comput…”

“It is also of practical value in the specification of models of sexlimitation and genotype by environment interaction (Purcell 2002; Neale et al.”

“Although the single-level model has undergone considerable modifications ( Purcell 2002 ), it continues to be used to assess the genetic contribution to a trait’s overall variation (Rende et al. 2005; Slomkowski et al. 2005).”

“A model designed to test interactions of a latent genetic variable with a measured continuous moderator variable (Purcell, 2002) was used for the total sample (average age 15.”

“Step #2: Univariate interaction model—As described by Purcell (2002), the conventional univariate twin model can be easily expanded to test for gene-by-environment interaction.”

“To model the effects of continuous moderators in Mx, Purcell (http://statgen.iop.kcl.ac.uk/gxe/) has made available a series of moderation models, which are based on previous models by Martin and colleagues (1987) and Purcell (2002) .”

“, G-E correlation) in the presence of a G × E interaction (Purcell, 2002).”

“…health problems using the simple linear equation shown above, we made use of variance component models for gene-environment interaction described by Purcell (2002) to express the variance associated with each of the three components as a linear interaction with income, leading to the equation V p…”

“The increase in the genetic variance can be decomposed on basis of the mathematical formula for the contribution from one genetic locus which equals p(1-p)a(2), where ‘‘p’’ denotes the population prevalence of an arbitrary obesity-related allele and ‘‘a’’ is the effect of that allele [26].”

“Mean levels of ability associated with SES must be modeled to validly assess interactions in which the moderator (such as SES) may be heritable and correlated with the trait of interest (Purcell, 2002; van der Sluis et al., 2012).”

“Although the twin approach enables tests of gene x environment interaction, it is less suitable to address research questions on contextual moderation because of lack of power at the extremes of the moderator [40].”

“This process could include genotype–environment correlation or interaction; such effects are included within the proportion of variance explained by genetic influences in most twin studies (Purcell, 2002).”

“[PubMed: 15989750] Purcell S. Variance components models for gene-environment interaction in twin analysis.”

“The moderator can take the same value or different values for the two twins in a pair (Purcell, 2002).”

“Nevertheless, it should be noted that using simulated data, Purcell (2002) estimated that the presence of gene-environment correlation had little impact on the ability to detect gene · environment interactions.”

“The need for the addition of an interaction into biometric variance models has been considered by many other researchers (Cattell, 1963, 1982; Fulker, 1970; Hendersen, 1975; Mather and Jinks, 1977; Loehlin, 1978; Jinks and Martin et al., 1987; Purcell and Sham, 2002; Eaves and Erkanli, 2003).”

“We have examined whether small variations in the individual level variance can explain the negative correlations, potentially arising from unmodeled interactions (Purcell 2012), but this is not the case.”

“In the genetic model used in this study, both active gene–environment correlation and gene– environment interaction inflates the effect of additive genetic factors (Purcell 2002), and thus a part of the effect of additive genetic component may in reality be because of the interplay between environmental and genetic fa…”

“Although longitudinal data is obviously better suited to address Age*A questions, a novel extension of the ACE model allows for modeling age effects on phenotypic variance using cross-sectional data [Purcell, 2002].”

“…decomposition framework that focuses on the latent genetic effects at a population level, a “broad heritability-environment interaction” method (see Purcell 2002) can be used to explain how specific environmental influences alter the contributions of the genetic and environmental variation to a…”

“" The advantage of the model that we utilize is that it is possible to decompose the moderator variable into its genetic and environmental variance components and test for gene– environment interaction in the presence of gene– environment correlation (Purcell, 2002).”

“Correlation between genetic and shared environmental influences acts to increase estimates of shared environmental influence; correlation between genetic and nonshared environmental influences acts to increase estimates of genetic influence (Purcell, 2002).”

“Moderator effects on the means were included to allow for possible main effects of the moderator on the mean of the dependent variable (FSIQ), and to adjust for possible gene-environment correlation (rGE, Purcell 2002).”

“Interaction coefficients can be incorporated into this model by redefining each path as a linear function of a “moderator” variable (Purcell, 2002).”

“Similar analytic strategies have been suggested previously in relation to child-specific environments (Eaves et al., 2003; Purcell, 2002 ).”

“We implemented the quantitative genetic models in the computer program Mx (Neale, Boker, Xie, & Maes,1999), specifying them as recommended by Purcell (2002) .”

“Second, genetic nurturing causes a (passive) gene–environment correlation, and if this correlation is not modeled it contributes to common environmental variance (Purcell 2002).”

“The sample size of 1,000 same-sex twin pairs in each cohort provides increased statistical power for implementing G × E and rGE in our analyses (see Narusyte et al., 2008; Purcell, 2002).”

“Notably, GxE and rGE processes can co-occur, such that the same environmental factors may simultaneously be involved in both GxE and rGE with respect to a developmental outcome (Eaves, Silberg, & Erkanli, 2003; Purcell, 2002).”

“Gene-environment correlations also affect heritability estimates, specifically, passive gene-environment correlations result in higher estimates of shared environmental variance, while active gene-environment correlations result in higher estimates of additive genetic variance (Purcell, 2002).”

“Further, some factors that were previously considered to be purely environmental are now considered to have a heritable component, such as family life, parent–child interaction, divorce, and life events [72].”

“After providing an overview of the tests, we illustrate their general use via the R packages lavaan and strucchange.”

“Ignoring the correlation between genes and nonshared environmental factors may lead to an overestimation of the genetic effects (Purcell 2002).”

“A second set of analyses examined whether children’s temperament moderates genetic and environmental contributions to parenting (Figure 2; Button, Scourfield, Martin, Purcell, & McGuffin, 2005; Purcell, 2002).”

“For instance, recent research has addressed the extent to which differences in genetic, shared environmental, and nonshared environmental influences on child adjustment are moderated by varying levels of parenting behaviors, typically described as G × E (e.g., Purcell, 2002).”

“…school-level SES on genetic and environmental influences on reading comprehension achievement in the Florida Twin Project on Reading, Behavior, and Environment (Taylor, Hart, Mikolajewski, & Schatschneider, 2013) were explored using a univariate gene 9 environment interaction model (Purcell, 2002).”

“Furthermore, we adopted the classic ACE model in genetic analyses, which overlooks the possibility that genetic and environmental influences on individual differences may correlate or interact with each other (Purcell, 2002).”

“We used twin gene-environment interaction models (Purcell, 2002) to quantify the degree of additive genetic (A; the additive effects of multiple genes), shared environmental (C; factors that make members of a twin pair similar to one another), and non-shared environmental (E; factors that make…”

“In future research, twin model including gene x environmental interaction (Purcell, 2002) and family based studies (such as the twin-family design incorporating measures of parental psychopathology and the children of twins (CoT) design with genetic and environmental variation in family-level risk factors (D'Onofrio e…”

“In order to study how birth year modifies the genetic and environmental variances of height, we additionally conducted gene-environment interaction modeling using birth year as an environmental modification factor (Purcell, 2002).”

“Such moderation of heritability supports the presence of a GxE interaction (Purcell 2002).”

“life-history LDCs, representing disorganized groups of cognitive generalists, by the straightforward and inevitable operation of Ricardo's (1891) Law of Comparative Advantage.”