Developmental Psychology Copyright 2008 by the American Psychological Association
2008, Vol. 44, No. 2, 305 315 0012-1649/08/$12.00 DOI: 10.1037/0012-1649.44.2.305
Effects of the Family Environment: Gene Environment Interaction and
Passive Gene Environment Correlation
Thomas S. Price and Sara R. Jaffee
University of Pennsylvania
The classical twin study provides a useful resource for testing hypotheses about how the family
environment influences children s development, including how genes can influence sensitivity to
environmental effects. However, existing statistical models do not account for the possibility that
children can inherit exposure to family environments (i.e., passive gene environment correlation). The
authors introduce a method to simultaneously estimate the effects of passive gene environment corre-
lation and gene environment interaction and use it to investigate the relationship between chaos in the
home and verbal ability in a large sample of 4-year-old twins.
Keywords: twins, epidemiology, gene environment interaction, gene environment correlation
Supplemental materials: http://dx.doi.org/10.1037/0012-1649.44.2.305.supp
Developmental psychologists have long been interested in in- (Rutter, 2003). Gene environment interactions (G E) occur
vestigating whether and how children s family environments in- when genetic factors influence sensitivity to environmental effects.
fluence their cognitive and behavioral development. Researchers An alternative way of conceptualizing the interaction is to say that
have demonstrated that environmental factors measured at the
environmental exposure moderates the effect of genetic risk fac-
family level, such as socioeconomic status (SES) and geographical
tors. The existence of such moderating effects would suggest
location, are associated with children s outcomes independent of
greater scope for environmental intervention to alter heritable traits
individual-level parent or child factors (e.g., Duncan & Brooks-
such as cognitive abilities.
Gunn, 1997; Leventhal & Brooks-Gunn, 2000) and are often
However, many challenges remain to identify G E. It has
mediated by more proximal processes (Collins, Maccoby, Stein-
been demonstrated in animal experiments by researchers showing
berg, Hetherington, & Bornstein, 2000).
differential effects of environmental conditions in groups of ani-
Although many studies have demonstrated associations between
mals stratified by their genetic background (e.g., Bennett et al.,
family environmental factors and children s adjustment, it is
2002). For obvious reasons, it has been much harder to demon-
equally true that the effects of family environment can vary from
strate G E in humans. Whereas in animal studies both genotype
child to child, even for children raised in the same family. For
and environmental exposure can be manipulated for experimental
example, extreme privation in childhood can cause profound cog-
purposes, in human studies interactions must generally be sought
nitive deficits, but children raised under such conditions vary
between naturally occurring variations in genotype and environ-
widely in terms of their cognitive and socioemotional functioning
ment. Epidemiological approaches to G E can offer greater
(Rutter, O Connor, & the English and Romanian Adoptees Study
validity than experimental studies, but they do so at the expense of
Team, 2004). One possibility is that the effects of adversity are
statistical power and experimental control. One of the drawbacks
conditioned by individual differences in children s resilience or
of an epidemiological study of G E is the possibility of corre-
adaptivity to environmental risk, which may have a genetic basis
lation between genotype and environment: the phenomenon of
gene environment correlation (rGE). Statistical methods for de-
tecting G E in human populations need to allow for the possible
Thomas S. Price, Institute for Translational Medicine and Therapeutics,
lack of independence between genetic and environmental risk
University of Pennsylvania; Sara R. Jaffee, Department of Psychology,
factors (Etheredge, Christensen, Del Junco, Murray, & Mitchell,
University of Pennsylvania.
2005; Liu, Fallin, & Kao, 2004).
We have no financial interests or conflicts of interest related to the
Genotype and environment can correlate for various reasons
material reported in the article. This work was supported by Grant P50
HL81012 from the National Heart, Blood, and Lung Institute to Thomas S. (Jaffee & Price, 2007), but studies of the effects of family envi-
Price and Grant R01 HD050691 from the National Institute of Child Health
ronments on children s outcomes are particularly subject to con-
and Human Development to Sara R. Jaffee.
founding due to passive rGE (Kendler & Eaves, 1986; Plomin,
We thank the participants in the Twins Early Development Study
1986). Passive rGE occurs when the family environment depends
(TEDS), Robert Plomin, and the TEDS research team, especially Andy
on heritable parental characteristics, so that parents pass on to their
McMillan for providing data management support.
children an environment that correlates with the parental genotype.
Correspondence concerning this article should be addressed to Thomas
Biological parents also pass on the genotype to their children.
S. Price, Institute for Translational Medicine and Therapeutics, University
When this genotype also influences children s behavioral or cog-
of Pennsylvania, Room 807 BRB II/III, 421 Curie Boulevard, Philadelphia,
PA 19104. E-mail: [e-mail] nitive outcomes, the result is a spurious association between en-
305
PRICE AND JAFFEE
306
vironment and outcome (Plomin, DeFries, & Loehlin, 1977; Scarr in these studies that originate in their failure to account for possible
& McCartney, 1983). In this way, an association between a mea- effects of passive rGE and explain how the new statistical model
sure of the family environment and a childhood outcome can be may overcome these shortcomings. Finally, we apply the method
partially or totally accounted for by the effects of parental geno- to a large sample of twins and show for the first time that such data
type. In the absence of passive rGE this association is attributed to can be used to distinguish true environmental effects from passive
the influence of the family environment on the outcome. Failure to rGE.
rule out the possibility that passive rGE accounts for some portion
of the association may result in its misattribution to environmental
Studies of G E and Children s Cognitive Abilities
causes.
When the association between measured environment and out- A series of twin studies has attempted to quantify and test the
come is accounted for by unobserved genetic factors (namely, moderating effects of family environmental variables (e.g., paren-
parental genotype), then the association is said to be genetically tal education, SES) on genetic factors that influence individual
mediated. When the association is accounted for by unobserved differences in children s verbal or cognitive abilities (Asbury,
environmental factors, then it is said to be environmentally medi- Wachs, & Plomin, 2005; Fischbein, 1980; Guo & Stearns, 2002;
ated. This terminology is admittedly somewhat confusing. The Harden, Turkheimer, & Loehlin, 2007; Kremen et al., 2005; Rowe,
terms genetic mediation and environmental mediation as used by Jacobson, & Van den Oord, 1999; Scarr-Salapatek, 1971; Turkhei-
behavioral geneticists do not imply that genes or environments are mer, Haley, Waldron, D Onofrio, & Gottesman, 2003). The results
intervening variables in the association between the measured have been contradictory. An analysis of data from the National
environment and the outcome; clearly, parental genotype is caus- Longitudinal Study of Adolescent Health concluded that the her-
ally prior to both measured environment and childhood outcome. itability of verbal ability was greater in families with highly
Studies of twin children can exploit differences in genetic re- educated parents (Rowe et al., 1999), although a reanalysis as-
latedness between monozygotic (MZ) and dizygotic (DZ) pairs to cribed the moderating effect to employment status and race (Guo
quantify the degree to which the effects of environmental exposure & Stearns, 2002). Other studies have also found that the genetic
at the level of the individual are genetically mediated and envi- influences on cognitive abilities are stronger in families in which
ronmentally mediated, even in the presence of G E (Eaves, parents have more education (Kremen et al., 2005) or higher SES
Silberg, & Erkanli, 2003; Rathouz, Van Hulle, Rodgers, & Lahey, (Harden et al., 2007; Turkheimer et al., 2003). In contrast, a large
2007). However, current statistical methods for studies of twin study of 4-year-old twins did not find that heritability estimates
children are uninformative about whether the effects of family- varied as a function of SES (Asbury et al., 2005) but that herita-
wide environments are environmentally or genetically mediated bility estimates were higher in high-risk families characterized by
(Turkheimer, D Onofrio, Maes, & Eaves, 2005). In fact, the meth- high levels of chaos and poor parent child communication
ods that are currently in use implicitly assume the absence of aspects of the environment that typically correlate with low SES
passive rGE. This problem extends to studies that investigate (Asbury et al., 2005; Evans, 2004). Moreover, these reports of G
possible interactions between genetic influences and the family E have not been confirmed in studies of nontwin families (Nagoshi
environment. & Johnson, 2005; Van den Oord & Rowe, 1997).
The goal of the current article is to introduce an analytical The twin studies reviewed above used either a structural equa-
method for twin studies that simultaneously estimates G E and tion modeling framework (e.g., Turkheimer et al., 2003), a mixed
passive rGE for measures of the family environment. The motiva- model (Guo & Stearns, 2002), or a DeFries-Fulker regression
tions for developing this method are twofold. First, we have model (e.g., Rowe et al., 1999) to test hypotheses about the effects
identified a problem with the statistical methodology that is cur- of the family environment on cognitive outcomes. These methods
rently used to investigate the moderating effects of the family estimate the overall association between family environment and
environment, namely, the assumption that there is no passive rGE. the phenotype but do not distinguish between environmentally
Therefore, we wish to develop an alternative method that does not mediated effects and passive rGE (Turkheimer et al., 2005). In
suffer the consequences of violating this assumption. The second effect, the influences of latent genetic and environmental factors
motivation is the prospect that passive rGE can be estimated using are estimated from the variation in the phenotype that remains after
data from child twins under specific circumstances: namely, when estimating a main effect of the measured family environment
genetic influences on the phenotype both correlate with and are (Purcell & Koenen, 2005; Turkheimer et al., 2005). This is equiv-
moderated by a measure of the family environment. alent to assuming that the association between the measured family
In this study, we analyze simulated datasets to investigate environment and the child phenotype is mediated entirely through
whether these motivations are justifiable. First, we analyze the the shared environment. In the presence of passive rGE this im-
simulated datasets using the existing method for detecting G E plicit assumption is violated, so that these procedures not only
to quantify the problems that arise when passive rGE is present. misspecify the effect of the measured environment but also mis-
Second, we reanalyze the simulated data using the new model to specify the effects of the latent shared environmental factor. A
outline the range of circumstances under which the simulated further consequence of the presence of passive rGE is that the
parameter values are accurately recovered. phenotypic variance cannot be resolved into separate genetic and
We illustrate the model with an application to the trait of environmental components in the usual way (Rathouz et al., un-
childhood verbal ability. Below, we review twin studies that have published manuscript). Crucially, at least two studies have dem-
attempted to demonstrate how family-wide environments such as onstrated that rGEs are likely to account for part of the association
SES and parental education moderate genetic influences on chil- between SES or parental education and offspring cognitive abili-
dren s cognitive outcomes. We highlight methodological problems ties (Neiss, Rowe, & Rodgers, 2002; Tambs, Sundet, Magnus, &
SPECIAL SECTION: EFFECTS OF THE FAMILY ENVIRONMENT
307
Berg, 1989), suggesting that estimates of G E as predictors of
Method
cognitive abilities might be biased. The same problem may apply
Statistical Model
to twin studies of G E in other phenotypes: For example, the
relationship between family dysfunction and children s antisocial
In this section we first outline a model for the effects of a
behavior may be genetically rather than environmentally mediated
measured family environment on twin phenotypes that parameter-
(Button, Scourfield, Martin, Purcell, & McGuffin, 2005). On the
izes the effects of passive rGE and explains why it cannot be
other hand, studies that have been careful to measure environments
successfully estimated. Next, we extend the model to account for
that are not likely to be genetically correlated with the outcome,
the effects of both G E and passive rGE and show that the
such as geographical region, are less vulnerable to this criticism
existence of G E allows the main effect of the measured family
(e.g., Dick, Rose, Viken, Kaprio, & Koskenvuo, 2001).
environment to be distinguished from passive rGE.
Let us say that we are interested in understanding the sources of
variation in a phenotype like children s verbal ability. In the
Need for New Statistical Methods
standard biometric model for twin data, the phenotype Yij for twin
j in family i is determined by the population mean and the values
In this article we suggest a methodological innovation that
of the random variables Aij, Ci, and Eij that represent additive
addresses the problem we have identified. We introduce a statis-
genetics, shared environment, and nonshared environment, respec-
tical model for the classical twin design that estimates both the
tively. We assume that the latent variables A, C, and E are
environmentally mediated effects of the family environment and
independently normally distributed and load on the phenotype with
passive rGE in the presence of G E. The influence of the
coefficients a, c, and e, respectively. In order for the model to be
measured family environment is modeled as a random effect that
identified, it is necessary to provide an arbitrary location and scale for
may correlate with genotype rather than a fixed main effect, an
the latent genetic and environmental variables. In accordance with
approach that allows both the genetically mediated effects and the
convention, we scale these latent variables to zero mean and unit
environmentally mediated effects of the measured environment to
variance. Because MZ twins have the same genomic DNA, whereas
be estimated from the data. Similar analytic strategies have been
DZ twins share half their segregating genes, the genetic factors for
suggested previously in relation to child-specific environments
twins in the same family, Ai1 and Ai2, are correlated with Coefficient
(Eaves et al., 2003; Purcell, 2002). Simulation studies have been
1 for MZ twins and with Coefficient 0.5 for DZ twins. The nonshared
performed that quantify the deficiencies of the existing method and
environments Eij are uncorrelated within members of the same family.
validate the proposed analytical procedure.
We supplement this model with an additional random variable X
We illustrate the new method using data from a large twin study
representing a measured family environment that is, a variable
of early cognitive development. A previous report from this study
measured at the family level whose value differs between families
found evidence that chaos in the family home and features of
but not within families (e.g., family chaos). X is normally distrib-
parent child communication style moderated genetic influences
2
uted with zero mean and variance X, has a main effect x on the
on verbal ability at age 4 (Asbury et al., 2005). We selected family
phenotype, and is correlated with A due to a passive rGE, such that
chaos for our analysis to facilitate comparison with the existing
Cor(Xi, Ai1) Cor( Xi, Ai2) r. Under this model, the value of the
literature on the moderating effects of distal family environments
phenotype Yij for twin j in family i is given by
over genetic influences on cognitive development.
Chaos reflects the child s physical microenvironment, including
Yij aAij cCi eEij xXi . (1)
the child s exposure to noise, crowding, and patterns of environ-
mental traffic (Matheny, Wachs, Ludwig, & Phillips, 1995). Fam- Because we are interested in the effects of an environmental factor
that differs between families but not within families, it is illumi-
ily chaos may retard cognitive development by causing children to
nating to rearrange the model for the phenotypic scores into
filter out useful environmental stimuli along with unwanted noise
separate terms for the half sum (the within-family mean, corre-
(Evans, 2006). Parent child interactions in noisy or crowded
sponding to the component of the twins phenotypic scores that
homes are also less conducive to cognitive development because
differs between families) and the half difference (the component of
parents are less responsive to their children (Evans, 2006). Chaos
the twins phenotypic scores that varies within families):
correlates with SES and may function as a proximal mediator of its
effects (Asbury et al., 2005; Pike, Iervolino, Eley, Price, & Plomin,
1 1
2006). It has previously been shown that this measure of the family
Yi1 Yi2 a Ai1 Ai2
2 2
environment not only correlates with verbal ability (Petrill, Pike,
Price, & Plomin, 2004; Pike et al., 2006) but also moderates the
1
effect of genetic influences on verbal ability (Asbury et al., 2005).
cCi e Ei1 Ei2 xXi , (2)
2
Although these findings are premised on the assumption that chaos
has environmentally mediated effects on children s verbal ability,
1 1 1
Yi1 Yi2 a Ai1 Ai2 e Ei1 Ei2
an alternative hypothesis is that parents who raise their children in
2 2 2
chaotic home environments also pass along genetic variants that
are associated with poor verbal ability and that, in fact, the asso- Note that the sum of these terms is Yi1 (i.e., the score for Twin
ciation between chaos and children s verbal ability is partly ge- 1 in family i) and the difference between them is Yi2 (i.e., the score
netically mediated. In this study, we use a new statistical method for Twin 2 in family i). The variance in the phenotypic scores can
to show that a previously reported association between chaos at be partitioned into a component of variance due to differences
home and early verbal ability cannot be explained by passive rGE. between families, 2, accounted for by factors that differ between
b
PRICE AND JAFFEE
308
families such as the main effect of X, and a component of variance parameters (namely a, c, e, x and r) to be estimated (the variance
due to differences within families, 2 , which cannot be accounted X can be estimated directly from the data). This means that x and
w
for by the main effect of X because X takes the same value for all r are not identified: It is not possible to estimate unique values for
children in a family. Let us assume that the variables follow a these parameters from the data.
multivariate normal distribution and there are no systematic effects Let us now extend the model with additional terms describing
of birth order. The latter is not generally considered a controversial the moderating effects of the measured family environment. We
assumption for behavioral data simply because twins are so close can model G E by allowing a moderating effect of the measured
in age, although there is some evidence that perinatal risk is environment on the genotype so that the coefficient of genetic
elevated in second-born twins (Armson et al., 2006). Under these influence on the phenotype is given by a 1 mAX , where mA is
assumptions the following equality holds: a linear moderation term. Nonzero values for this term imply that
the genetic influences on the phenotype vary across levels of the
1
measured environmental variable. We can also allow linear mod-
Var Yi1 Var Yi2 b w Var Yi1 Yi2

2 eration of the paths for the shared environment, c 1 mCX , and
nonshared environment, e 1 mEX . The variances of the phe-
1
notypic sums and differences are now given by:
Var Yi1 Yi2 . (3)

2
2 a2 1 mAX 2 c2 1 mCX 2
bMZ
The variances of the half-sums and half-differences correspond,
1
respectively, to the between-family variance 2 and the within-
b
e2 1 mEX 2 x2 2 2a 1 mAX x Xr, (5)
X
2
family variance 2 , and are uncorrelated. The values of 2 and 2
w b w
depend on the zygosity of the twin pair, because genetic differences
1
between twins can contribute to within-pair differences for DZ pairs
2 e2 1 mEX 2,
wMZ
2
but not for MZ pairs. It can be shown that the between- and within-
family phenotypic variances for MZ and DZ pairs are given by:
3
2 a2 1 mAX 2 c2 1 mCX 2
bDZ
4
1
2 a2 c2 e2 2 2 2ax Xr, (4)
bMZ X
2
1
2
e2 1 mEX 2 x2 X 2a 1 mAX x Xr,
2
1
2 e2,
wMZ
2
1 1
2 a2 1 mAX 2 e2 1 mEX 2.
wDZ
4 2
3 1
2 a2 c2 e2 x2 2 2ax Xr,
bDZ X
4 2
The covariance between the measured environment X and the
phenotype Y, cXY, comprises terms relating to the environmentally
1 1
and genetically mediated effects of the measured environment:
2 a2 e2.
wDZ
4 2
cXY x 2 a 1 mAX Xr. (6)
X
We can see that a positive association between the measured
family environment and the phenotype increases the variance of The covariance between measured environment and phenotype
the phenotype between families. This association has two compo- due to passive rGE, a 1 mAX Xr, is a linear function of X,
nents: an environmental component that is mediated solely by the whereas the covariance due to the environmentally mediated ef-
latent environmental variable X, and a genetic component due to fect, x 2, is constant with respect to X. Consequently, if it is
X
the passive rGE between A and X. The phenotypic variance ac- known (or can be shown in advance) that there is moderation of the
counted for by the environmental component of the association is genetic variance such that mA and a are nonzero, then a model that
simply the square of the main effect of the environmental influence estimates the covariance between measured environment and phe-
on the phenotype, x2 2. The phenotypic variance due to passive notype as a linear function of X is identified and allows unique
X
rGE equals twice the covariance between A and X 2ax Xr . Note values for x and r to be estimated from the data. In other words, the
that the within-family phenotypic variance does not depend on existence of G E allows one to distinguish between the envi-
either x or r. The lack of dependence of within-family variance on ronmentally and genetically mediated effects of the measured
x is not surprising, because we model the effect of the family family environment. For example, if the environmental exposure X
environment the same way for both twins in a pair. The reason that is binary with values corresponding to exposure/nonexposure, then
passive rGE makes no contribution to within-family differences the equations in (5) will provide eight pieces of information four
can be understood intuitively as follows. Genetic differences variances for each value of X sufficient to estimate the eight
within DZ twin pairs arise from recombination during meiosis, a parameters in the model. Naturally, the power to discriminate
random process that is uncorrelated with the parental genotypes between the main effect of the environment and passive rGE will
and hence with the processes that cause passive rGE. As a final depend strongly on the values of the genetic path parameter a and
point, it is important to note that the environmentally and geneti- the genetic moderation parameter mA: Power will increase as the
cally mediated effects of the measured family environment on the magnitude of these parameters increases.
between-family and within-family variances are confounded in Because the covariance between X and Y is entirely due to the
this model. There are four pieces of information, and there are five covariance between X and the half-sums, which also equals cXY,
SPECIAL SECTION: EFFECTS OF THE FAMILY ENVIRONMENT
309
the covariances between the variables in our model can be de- A path diagram corresponding to this model of environmental
scribed completely by inserting the values from the equations in mediation and moderation is shown in Figure 1. For simplicity of
(5) and (6) into the following structural equations: presentation, the means model is omitted. The model can either be
implemented within a structural equation modeling paradigm and
1 1
estimated by maximum likelihood an example script is provided
MZ: Var Yi1 Yi2 ,2 Yi1 Yi2 ,Xi

2
as part of the supplementary materials online in Supplemental
Appendix I, for the freely distributed software package Mx (http://
2 0 cXY
bMZ
www.vcu.edu/mx/; Neale, Boker, Xie, & Maes, 1999) or imple-
0 2 0
, (7)
wMZ

mented as a Bayesian model and estimated by Markov chain
cXY 0 2
X
Monte Carlo methods. Bayesian models allow very flexible pa-
rameterization: A script for the freely distributed program win-
1 1
DZ: Var Yi1 Yi2 ,2 Yi1 Yi2 ,Xi
BUGS 1.4.1 (www.mrc-bsu.cam.ac.uk/bugs/; Spiegelhalter,
2
Thomas, Best, & Lunn, 2003) is provided online in Supplemental
2
Appendix II.
bDZ 0 cXY
0 2 0
.
wDZ

cXY 0 2
Data Analysis
X
The expected vector of means for, respectively, the half-sums, As mentioned previously, the statistical model described by the
half-differences, and measured environment is ( , 0, 0) for both equations in (7) can only be estimated when it is already known
zygosity groups. However, in practice it may be better to estimate that the measured family environment moderates the genetic vari-
the means for MZ and DZ groups without imposing any con- ance (i.e., mA 0). For this reason, the full model containing
straints to capture any mean effects due to zygosity and birth order. both r and mA parameters cannot, by itself, provide a test for the
(1+ mC X)2
r Cb
2
(1+ mAX)2 (1+ mE X)2 (1+ mE X)2
sX
X Ew
Ab Eb
c
a
1
"½ e "½ e
x
MZ ½(Y1 Y2)
½(Y1+Y2)
X ½(Y1+Y2)
(1+ mC X)2
2 " 4/3 r
(1+ mAX)2 Cb
sX
(1+ mE X)2 (1+ mE X)2
(1+ mAX)2
X Ew
Ab Eb
c
"¾ a
Aw
1
"½ e
"½ e
x
"ź a
½(Y1 Y2)
X ½(Y1+Y2)
½(Y1+Y2)
DZ
Figure 1. Path diagrams for monozygotic (MZ) and dizygotic (DZ) twin pairs, showing observed variables
(square boxes), latent variables (circles), regression paths (single-headed arrows) and correlations (double
headed arrows). The means model has been omitted. X measured family environment; x2 the variance of
1 1
the measured family environment; D 2 (Y1 Y2) half sum of twin phenotypes; D 2 (Y1 Y2) half difference
between twin phenotypes; A additive genetics; C shared environment; E nonshared environment; b
suffix between-family variance; w suffix within-family variance; mC linear moderation of shared
environmental path; r correlation due to passive rGE; mA linear moderation of genetic path; a additive
genetic path parameters; c shared environment path parameters; e nonshared environment path parameters;
x environmentally mediated effect of the measured environment.
PRICE AND JAFFEE
310
statistical significance of the genetic moderation parameter mA. uX rather than a(1 mA X), so that mA u/afor a 0. The model
The usual way to test whether or not a parameter in a structural did not falsely identify G E when it was absent and recovered
equation model is statistically significant is to estimate an alter- accurate estimates of mA. However, as noted previously, this
native model in which the parameter is fixed at zero. The param- model cannot distinguish between genetically mediated and envi-
eter is considered significant if the reduced model provides a ronmentally mediated effects of the measured family environment
significantly worse fit to the data, as measured using the likelihood (Purcell & Koenen, 2005; Turkheimer et al., 2005). As a result,
ratio test or by other methods of hypothesis testing such as the genetically mediated effects of the family environment (i.e., sim-
comparison of Akaike s information criterion fit statistics (Akaike, ulated values of r 0) were estimated as a main effect of the
1974). As we have shown, the alternative model with r freely measured environment (i.e., estimated values of x 0). In addi-
estimated and mA 0 is not identified. The existence of G E tion, estimates of the squared shared environmental path parameter
can, however, be established by testing the significance of mA in a c2 were increasingly biased down from the simulated value as the
reduced model in which r is fixed to zero. This reduced model is simulated strength of the passive rGE increased. Similar results
essentially a reparameterization of the existing structural equation can be obtained using augmented DeFries Fulker analysis (as used
model used in, for example, Turkheimer et al. (2003). by, e.g., Rowe et al., 1999), although because this model tests for
We therefore recommend a two-step strategy for data analysis. linear moderation of the standardized variance components h2 and
The first step is to test for genetic moderation by the measured c2 rather than the genetic and environmental path parameters, the
environment using the statistical model with r fixed to zero. If the datasets must be simulated in a slightly different way (data not
results of the first analysis indicate significant effects of genetics shown).
and G E, the model can be rerun with r freely estimated in order We reanalyzed these simulated datasets using the new structural
to estimate the effects of passive rGE in addition to the other equation model with r fixed to zero (Table 2). As for the previous
parameters. analyses, the model was constrained to estimate linear moderation
on the genetic path parameter only. The results were virtually
identical, indicating the near-equivalence between these two mod-
Simulation Studies
els: The only real difference between them is that the new model
A series of simulations was conducted to validate the statistical
estimates an additional parameter for the variance of the measured
methods that we have described. Four simulations were conducted,
environmental variable. It is important that the absence of bias in
each containing 500 datasets consisting of 500 pairs each of MZ
the test of G E provided justification for the proposed two-step
and DZ twins, using the parameter values a 0.5, c 0.25, e analytic strategy.
0.25, x 0, r k, and mA 0, indicating no G E for each Finally, we analyzed the simulated datasets with both geneti-
of the values k 0, 0.1, 0.2, 0.3. (The method by which the cally and environmentally mediated effects of the measured family
datasets were simulated is available from the corresponding author environment and G E using the full structural equation model.
on request.) These values correspond to a heritable phenotype with The mean, median, standard deviation, and 2.5% and 97.5% quan-
shared and nonshared environmental influences, with a measure of tiles (defining an empirical symmetric 95% confidence interval
the family environment that has no environmentally mediated [CI]) for the parameter estimates, as well as the proportion of
effects on the phenotype, correlates nonnegatively with genetic statistically significant estimates of mA, r, and x, are shown in
influences on the phenotype, and does not moderate the genetic Table 3. The mean parameter estimates were close to the simulated
effects. A further three sets of 500 datasets were simulated using value, demonstrating that in principle this model can accurately
estimate the effects of rGE, G E, and environmentally mediated
the parameter values a 0.5, c 0.25, e 0.25, x k, r
effects of the family environment. However, the variability around
k, and mA 0 for each of the values k 0.1, 0.2, 0.3. These values
these estimates, especially those for c2, r, and x in datasets with the
correspond to a heritable phenotype with shared and nonshared
environmental influences, with a measure of the family environ- smallest simulated values of mA, r, and x, emphasizes the need for
large sample sizes. It is no surprise that there is little power to
ment that is positively correlated with the phenotypes due to both
distinguish genetic from environmental mediation of the effects of
environmentally mediated and genetically mediated effects and
the measured environment when the true value of mA is close to
does not moderate the genetic effects. Finally, six sets of 500
zero. Indeed, in the absence of G E, r and x are completely
datasets were simulated, similar to the others but with x 0 or k,
confounded, as we have already noted.
r k, and mA k for k 0.1, 0.2, 0.3, corresponding to the
presence of both rGE and G E.
Twins Early Development Study
Results
Sample. We illustrate our analytical approach by using it to
The simulated data were first analyzed using an existing struc- estimate the moderating effects of family chaos on genetic influ-
tural equation model (http://www.psy.vu.nl/mxbib/mx_show_ ences on verbal ability at 4 years. The Twins Early Development
script.php?page rawVCmod1 as used in, e.g., Turkheimer et al., Study (TEDS) is a population-based study of twins born in the
2003) in which the absence of passive rGE is implicitly assumed United Kingdom between 1994 and 1996 (Trouton, Spinath, &
(Purcell & Koenen, 2005; Turkheimer et al., 2005; see Table 1). Plomin, 2002). The families participating in TEDS are represen-
This model was constrained to estimate linear moderation on the tative of the U.K. population of parents of young children in terms
genetic path parameter only and did not estimate moderation of the of parental education, ethnicity, and employment status, which
shared or nonshared environment paths. The results were reparam- were assessed from parental responses to questionnaire booklets
eterized slightly, because this model estimates a genetic path a sent to the families in the twins 2nd year (Trouton et al., 2002).
SPECIAL SECTION: EFFECTS OF THE FAMILY ENVIRONMENT
311
Table 1
Results of Simulation Study to Test for the Effects of G E With an Existing Structural Equation Model
Simulated value a2 c2 e2 mA x
2LL
mA x r M SD M SD M SD M SD M SD M SD p .05 (%) p .01 (%)
0 0 0 .50 .07 .24 .06 .25 .02 .00 .04 .00 .03 1.01 1.54 5.0 1.2
0 0 .1 .50 .07 .24 .06 .25 .02 .00 .04 .07 .03 1.01 1.54 5.0 1.2
0 0 .2 .49 .07 .23 .06 .25 .02 .00 .04 .14 .03 0.96 1.37 5.6 0.6
0 0 .3 .50 .07 .20 .07 .25 .02 .00 .03 .21 .03 0.98 1.27 3.4 0.6
0 .1 .1 .50 .07 .24 .07 .25 .02 .00 .03 .17 .03 1.00 1.35 5.4 0.8
0 .2 .2 .49 .07 .23 .07 .25 .02 .00 .04 .34 .03 1.03 1.36 5.4 0.8
0 .3 .3 .50 .07 .20 .07 .25 .02 .00 .03 .51 .03 1.03 1.38 5.8 0.8
.1 0 .1 .50 .07 .24 .06 .25 .02 .10 .04 .07 .03 9.13 5.79 80.8 62.0
.2 0 .2 .50 .07 .23 .07 .25 .02 .20 .05 .13 .03 31.8 11.2 100.0 100.0
.3 0 .3 .49 .07 .23 .06 .25 .02 .30 .07 .17 .03 63.8 16.3 100.0 100.0
.1 .1 .1 .49 .07 .25 .06 .25 .02 .10 .04 .17 .03 8.91 5.81 80.0 59.2
.2 .2 .2 .49 .07 .24 .06 .25 .02 .20 .05 .33 .03 31.3 11.3 100.0 99.6
.3 .3 .3 .48 .07 .23 .06 .25 .02 .30 .07 .48 .03 63.1 16.6 100.0 100.0
Note. Simulation study tested for the effects of G E by use of an existing structural equation model (Turkheimer et al., 2003), including maximum
likelihood estimates of squared additive genetic (a2), shared environment (c2), and nonshared environment (e2) path parameters; linear moderation of genetic
path (mA) and environmentally mediated effect of the measured environment (x); change in fit ( ) and proportion of models with statistically significant
2LL
changes in fit at p .05 and p .01 when the moderation term is dropped from the model. Each value is the result of analyzing 500 simulated datasets.
Simulated values of mA, x, and correlation due to passive rGE (r) are given in the first three columns on the left.
Parental ratings of physical similarity were used to determine the female MZ twins, 1,001 families with male DZ twins, and 1,042
zygosity of the twins, a method that assigns zygosity with more families with female DZ twins.
than 95% accuracy as validated by genotyping (Price et al., 2000). Verbal ability. Verbal ability was assessed at age 4 with the
Families were excluded if English was not the principal language Expressive Vocabulary and Grammatical Complexity subscales of
spoken in the home, if zygosity was uncertain, or if either twin had the MacArthur Communicative Development Inventory (MCDI;
severe medical, genetic, or perinatal problems. Data were also Fenson et al., 1994). These measures were parent administered.
excluded if the test booklets sent to parents when twins were 4 The MCDI is widely used and demonstrates excellent internal
years old were incomplete or were returned more than 6 months consistency, test retest reliability, and concurrent validity with
late. Opposite-sex twin pairs were excluded from the current tester-administered measures (Fenson et al., 1994). Expressive
investigation to simplify the statistical analysis. The final sample vocabulary is assessed with a multi-item checklist on which par-
consisted of 943 families with male MZ twins, 1,099 families with ents report on their children s production of root words. We
Table 2
Results of Simulation Study to Test for the Effects of G E With a Reduced Version of the New Structural Equation Model
Simulated value a2 c2 e2 mA x
2LL
mA x r M SD M SD M SD M SD M SD M SD p .05 (%) p .01 (%)
0 0 0 .50 .07 .24 .07 .25 .02 .00 .04 .00 .03 0.98 1.33 5.0 1.0
0 0 .1 .50 .07 .24 .06 .25 .02 .00 .04 .07 .03 1.05 1.63 5.8 1.8
0 0 .2 .49 .07 .23 .07 .25 .02 .00 .04 .14 .03 0.95 1.33 5.4 0.8
0 0 .3 .50 .07 .20 .07 .25 .02 .00 .04 .21 .03 0.98 1.29 4.2 0.6
0 .1 .1 .50 .07 .24 .07 .25 .02 .00 .04 .17 .03 0.98 1.31 5.2 0.6
0 .2 .2 .50 .07 .23 .07 .25 .02 .00 .04 .34 .03 0.97 1.29 4.8 0.4
0 .3 .3 .50 .07 .20 .07 .25 .02 .00 .04 .51 .03 0.97 1.31 4.4 0.8
.1 0 .1 .50 .07 .25 .06 .25 .02 .10 .04 .07 .03 7.69 5.20 76.6 50.6
.2 0 .2 .49 .07 .23 .07 .25 .02 .20 .05 .13 .03 26.7 10.3 99.8 99.6
.3 0 .3 .49 .07 .23 .06 .25 .02 .30 .07 .17 .03 53.3 15.2 100.0 100.0
.1 .1 .1 .49 .07 .25 .07 .25 .02 .10 .04 .17 .03 7.61 5.42 71.8 49.4
.2 .2 .2 .49 .07 .24 .06 .25 .02 .20 .05 .33 .03 26.2 10.1 99.6 98.8
.3 .3 .3 .48 .07 .23 .06 .25 .02 .30 .07 .48 .03 52.1 15.4 100.0 100.0
Note. Simulation study tested for the effects of G E by use of a reduced version of the new structural equation model, including maximum likelihood
estimates of squared additive genetic (a2), shared environment (c2), and nonshared environment (e2) path parameters; linear moderation of genetic path (mA)
and environmentally mediated effect of the measured environment (x); change in fit ( ); and proportion of models with statistically significant changes
2LL
in fit at p .05 and p .01 when the moderation term is dropped from the model. Each value is the result of analyzing 500 simulated datasets. Simulated
values of mA, x, and correlation due to passive rGE (r) are given in the first three columns on the left.
PRICE AND JAFFEE
312
Table 3
Results of Simulation Study to Quantify the Effects of G E in the Presence of Passive rGE
With the New Structural Equation Model
Variable a2 c2 e2 mA xr
mA, x, r .1
M .49 .29 .25 .11 .11 .09
SD .07 .09 .02 .04 .20 .29
2.5% .36 .14 .22 .04 .29 .50
50% .49 .28 .25 .11 .12 .09
97.5% .62 .48 .28 .20 .51 .64
p .05 (%) 86.6 5.6 6.8
mA, x, r .2
M .50 .26 .25 .21 .20 .19
SD .07 .06 .02 .05 .10 .14
2.5% .37 .13 .22 .13 .01 .06
50% .49 .26 .25 .21 .21 .19
97.5% .63 .38 .28 .31 .39 .47
p .05 (%) 100.0 57.4 28.8
mA, x, r .3
M .50 .25 .25 .31 .30 .29
SD .07 .06 .02 .06 .06 .09
2.5% .37 .13 .22 .21 .17 .13
50% .50 .25 .25 .30 .30 .29
97.5% .64 .35 .28 .43 .41 .46
p .05 (%) 100.0% 98.6 89.0
Note. Simulation study quantified the effects of G E in the presence of passive rGE by use of the new
structural equation model, including linear moderation of genetic path (mA) and environmentally mediated effect
of the measured environment (x); correlation due to passive rGE (r); maximum likelihood estimates of squared
additive genetic (a2), shared environment (c2), and nonshared environment (e2) path parameters; change in fit
( ); and proportion of models with statistically significant changes in fit at p .05 and p .01 when the
2LL
moderation term is dropped from the model. Statistics and the proportion of models in which dropping the
relevant term results in significant deterioration in fit according to the likelihood ratio test at p .05 are given
for each set of estimates resulting from the analysis of 500 simulated datasets.
calculated a composite score by summing the number of words
checked. The Grammatical Complexity subscale examines
whether and how children combine words. We calculated a total
verbal ability score by summing standardized scores on these two
measures (Spinath, Price, Dale, & Plomin, 2004).
Chaos. The degree of chaos in the home was assessed at the
same time by parental report using the short version of the Con-
fusion, Hubbub, and Order Scale (Matheny et al., 1995), which
includes items such as  You can t hear yourself think in our home
and  We are usually able to stay on top of things. The score is
derived by summing six items rated on a 5-point scale and has
been validated against direct observations (Matheny et al., 1995).
These items show acceptable internal consistency in the TEDS
sample (Cronbach s .63). To aid convergence of the analytic
model, we centered and scaled the variable to unit variance.
Descriptive statistics. Details of the distributions of these vari-
ables in the TEDS sample are available in previous publications on
the TEDS sample (Asbury et al., 2005; Petrill et al., 2004; Pike et
al., 2006; Spinath et al., 2004). The analyses of verbal ability and
chaos in the home presented here employ the standardized resid-
uals after removing the linear effects of age and sex.
Phenotypic and twin correlations. Chaos and verbal ability
correlated at  .19 ( p .01). The intraclass twin correlations are
presented in Figure 2 as a function of zygosity and degree of chaos
in the home. A trend was evident toward lower DZ correlations in
more chaotic homes. Sex differences in twin correlations for the
Figure 2. Intraclass twin correlations for verbal ability at age 4 by
4-year verbal measure were relatively small, as noted in a previous
zygosity and degree of chaos in the home. MZ monozygotic; DZ
analysis of this dataset (Spinath et al., 2004). dizygotic.
SPECIAL SECTION: EFFECTS OF THE FAMILY ENVIRONMENT
313
Test of G E. The data were first analyzed using a reduced poor verbal ability) is more strongly expressed in high risk envi-
version of the model described above, with the parameters for r, ronments (Rosenthal, 1963). The new method was sufficiently
mC, and mE fixed to zero. Previous explorations of these data have powerful to exclude the possibility that the association between
indicated only small differences in parameter estimates between
chaos in the home and children s verbal ability could be explained
males and females (Spinath et al., 2004); for this reason, the path
solely by passive rGE. Indeed, the estimate of passive rGE was
parameters for males and females were equated in these analyses,
nonsignificant, suggesting that the association between chaos and
except that different mean values were estimated for males and
verbal ability may be mediated wholly by the shared environment.
females. A second model, further constrained with mA fixed to
These analyses support the conclusions of a previous report, which
zero, provided significantly worse fit ( 71.7, df 1, p
2LL suggested that chaos is associated with poor verbal performance in
.0001), indicating substantial moderation of genetic effects by
3- to 4-year-olds but did not demonstrate environmental mediation
family chaos. The results suggested that genetic influences on
of the association (Petrill et al., 2004).
verbal ability were stronger in more chaotic households.
In this demonstration of our method, there is a possibility of
Estimation of model parameters. Having established the pres-
criterion contamination deriving from reliance on a single infor-
ence of significant G E, we estimated an enlarged model with
mant for both environmental and outcome variables. Despite ex-
the parameter r free to vary and mC and mE fixed to zero. This
tensive validation of the measures we employed, it could be that
model estimates the effect of G E while distinguishing geneti-
informant error in reporting chaos in the home is correlated with
cally from environmentally mediated effects of chaos on children s
error or bias in administering tests of offspring s verbal abilities.
verbal abilities. There was a moderate effect of additive genetics
Method variance due to correlated measurement errors would be
(a2 0.33; 95% CI 0.29, 0.37), a substantial component of shared
estimated as part of the main effect of the measured environment.
environment (c2 0.49; 95% CI 0.45, 0.54), and a small compo-
Given the overall lack of genetic correlation between chaos and
nent of nonshared environment (e2 0.12; 95% CI 0.11, 0.13),
verbal ability, we consider it unlikely that heritable factors con-
consistent with a previous analysis of this dataset (Spinath et al.,
tribute to this method variance to any significant degree. Hence,
2004). There was significant moderation of the genetic variance
our conclusion that the association between chaos and verbal
(mA 0.17; 95% CI 0.13, 0.22) by chaos. Each increment (or
ability is not mediated by passive rGE remains unchanged.
decrement) of one standard deviation in the chaos measure was
We have presented the simplest possible version of this tech-
associated with a 17% increase (or decrease) in the genetic path
nique, employing single measures for the environment and out-
parameter. Genetic influences were stronger on children growing
come. Further explorations of these data could be improved by
up in chaotic homes. Although the total variability was also greater
incorporating analyses of multiple phenotypic or environmental
in these children, the proportion of genetic variance (heritability)
measures, especially information from more than one informant.
was also greater in children from chaotic homes, consistent with
The model can in principle be adapted for multivariate measures of
the findings reported in Asbury et al. (2005). The 95% CI for the
the outcome and/or environment by substituting vector and matrix
standardized main effects of chaos on verbal ability, x, extended
quantities for the scalar variables in the structural equations. As is
from 0.03 to 0.29, with a point estimate of 0.16 that was
the case for the univariate model, the crucial issue is the size of the
statistically different from zero ( 6.16, df 1, p .01).
2LL
moderating effects that are necessary to estimate the mediation
The 95% CI for the estimate of passive rGE r spanned from 0.24
parameters accurately. We are currently developing extensions of
to 0.18, with a nonsignificant point estimate of 0.03 (
2LL
the method to address this issue in the multivariate case. In
0.089, df 1, p .77).
addition, the method can be used to investigate moderating effects
of the family environment on shared and nonshared environment
Discussion
influences, although the current article does not explore these
possibilities in detail.
Existing statistical methods for testing hypotheses about the
These findings reaffirm that the classical twin study is a useful
effects of the measured family environment on children s devel-
experimental design for investigating gene environment interplay.
opment using twin data implicitly assume the absence of passive
Although children-of-twins studies and other extended family re-
rGE. These include the methods that have been used to investigate
search designs have been advocated as the best methods for
the effects of G E, which in the presence of passive rGE are
distinguishing genetically mediated and environmentally mediated
liable to misspecify both the effects of the measured environment
effects of the family environment (Purcell & Koenen, 2005;
and the effects of the latent shared environmental factor, although
Turkheimer et al., 2005), the classical twin design has the double
it is important to note that estimates of the G E itself appear to
advantage that suitable datasets are both more readily available
be unaffected. We have demonstrated a new analytic strategy that
and easier to collect. Phenotypic data are only required for the
detects and quantifies the effects of passive rGE in the presence of
twins themselves, rather than for multiple generations in the fam-
G E. We have presented results from simulated datasets that
ily. This facilitates data collection, especially for phenotypes mea-
attest to the viability of this method over a range of parameter
sured in adulthood. In addition, the overwhelming majority of
values.
existing family studies have collected information only or predom-
To illustrate this novel statistical model, we have performed an
inantly for one generation. The methods we present are also
analysis that confirmed a previous finding that genetic influences
adaptable to other family study designs: The authors consider that
on children s abilities are stronger among children in the TEDS
sample who were raised in a chaotic home environment (Asbury et a balance of different research designs with complementary merits
al., 2005). These results are consistent with a diathesis stress and assumptions will prove optimally informative (Rutter, Moffitt,
model in which a genetic predisposition for some outcome (e.g., & Caspi, 2006).
PRICE AND JAFFEE
314
Finally, we recognize the limitations of all family study designs genotype and environment on liability to psychiatric illness. American
Journal of Psychiatry, 143, 279 289.
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ultimate significance of G E concerns the mechanistic interac-
Toomey, R., et al. (2005). Heritability of word recognition in middle-
tion between measured environments and specific genotypes, not
aged men varies as a function of parental education. Behavior Genetics,
statistical interactions with  black box variables representing
35, 417 433.
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Leventhal, T., & Brooks-Gunn, J. (2000). The neighborhoods they live in:
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The effects of neighborhood residence on child and adolescent out-
promote understanding of the causes of cognitive disability and
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psychopathology and may be important for preventative efforts
Liu, X., Fallin, M. D., & Kao, W. H. (2004). Genetic dissection methods:
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Please include with your letter your vita. In the letter, please identify which APA journal(s) you
are interested in, and describe your area of expertise. Be as specific as possible. For example,
 social psychology is not sufficient you would need to specify  social cognition or  attitude
change as well.
" Reviewing a manuscript takes time (1 4 hours per manuscript reviewed). If you are selected to
review a manuscript, be prepared to invest the necessary time to evaluate the manuscript
thoroughly.
Write to Journals Office, American Psychological Association, 750 First Street, NE, Washington,
DC 20002-4242.