FormalGXEtestJCPP2013

Full text

Confirmatory and competitive evaluation of
alternative gene-environment interaction hypotheses
Jay Belsky,
1,2,3
Michael Pluess,
4
and Keith F. Widaman
5
1
Department of Human Ecology, University of California, Davis, CA, USA;
2
Department of Special Education, King
Abdulaziz University, Jedda, Saudi Arabia, USA;
3
Department of Psychological Sciences, Birkbeck University of
London, London, UK;
4
Institute of Psychiatry, Kings College, London, UK;
5
Department of Psychology, University of
California, Davis, CA, USA
Background: Most gene-environment interaction (GXE) research, though based on clear, vulnerability-oriented
hypotheses, is carried out using exploratory rather than hypothesis-informed statistical tests, limiting power and
making formal evaluation of competing GXE propositions difficult. Method: We present and illustrate a new
regression technique which affords direct testing of theory-derived predictions, as well as competitive evaluation of
alternative diathesis-stress and differential-susceptibility propositions, using data on the moderating effect of DRD4
with regard to the effect of childcare quality on children’s social functioning. Results: Results show that (a) the new
approach detects interactions that the traditional one does not; (b) the discerned GXE fit the differential-
susceptibility model better than the diathesis-stress one; and (c) a strong rather than weak version of differential
susceptibility is empirically supported. Conclusion: The new method better fits the theoretical ‘glove’ to the empirical
‘hand,’ raising the prospect that some failures to replicate GXE results may derive from standard statistical
approaches being less than ideal. Keywords: Gene-environment interaction, diathesis-stress, differential
susceptibility, child care, DRD4.
Introduction
For the past decade virtually all psychiatric gene-
environment (GXE) interaction research has been
guided, implicitly if not explicitly, by the diathesis-
stress model of environmental action (Zubin &
Spring, 1977) which stipulates that some individuals
are more susceptible to the negative consequences of
adverse experiences than others (Burmeister, McIn-
nis & Zollner, 2008). The expectation, then, is that
individuals carrying ‘risk alleles’ or ‘vulnerability
genes’ (e.g., short 5-HTTPLR, DRD4-7 repeat) will
function more poorly than those with different geno-
types under conditions of contextual adversity (e.g.,
child maltreatment, negative life events).
Yet even in the face of guiding theory and strong
predictions, the statistical methods used to evaluate
GXE are exploratory in character. Using hierarchical
regression and/or ANOVA techniques, the interac-
tion of environmental factor and genetic moderator is
evaluated after taking into account the main effects
of each. Notably, this approach does not formally
evaluate whether a detected interaction is consistent
with the implicit or explicit diathesis-stress theoriz-
ing that motivated the research. This is why, follow-
ing the detection of a significant interaction,
investigators routinely (a) conduct additional regres-
sion analyses affording comparisons of simple slopes
linking predictor to outcome separately for the
putative vulnerable and resilient subgroups, or (b)
compare means of subgroups defined in terms of
genotype and environment (i.e., vulnerable geno-
type/risky environment, vulnerable genotype/
benign environment, non-vulnerable genotype/risky
environment, non-vulnerable genotype/benign envi-
ronment). To determine whether findings are consis-
tent with diathesis-stress, visual inspection of
plotted simple slopes with or without additional
comparison of group means is undertaken.
Being exploratory in nature, these approaches
completely disregard the a priori predictions on
which they are based. Given well-known statistical
challenges to testing interactions (Aiken & West,
1991; McClelland & Judd, 1993), including need for
larger sample sizes than when evaluating main
effects, statistical methodology should not further
undermine statistical power and thus the detection
of interactions. This would seem especially the case
in studies of GXE interaction given widespread
appreciation that even significant main effects of
candidate genes –in genotype-phenotype studies –
are likely to account for only a very small amount of
variance in almost all phenotypes of interest to
developmental and behavioral scientists.
A perhaps even more significant limitation of
standard exploratory approaches is that they do
not provide a direct means of testing competing
predictions derived from alternative theoretical
frameworks. This latter limitation is particularly
acute now that a theoretical alternative to the
diathesis-stress model has been proposed (Belsky
& Pluess, 2009; Ellis, Boyce, Belsky, Bakermans-
Conflict of interest statement: No conflicts declared.
©2013 The Authors Journal of Child Psychology and Psychiatry ©2013 Association for Child and Adolescent Mental Health.
Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA 02148, USA
Journal of Child Psychology and Psychiatry 54:10 (2013), pp 1135–1143 doi:10.1111/jcpp.12075

Kranenburg, and van IJzendoorn, 2011) and applied
to the study of GXE interactions (Belsky et al.,
2009), first by Bakermans-Kranenburg and van
IJzendoorn (2006), but more recently by many
others (for summary, see Belsky & Pluess, in press).
This differential-susceptibility framework stipulates
that some individuals are more susceptible not just
to negative environmental influences but to positive
ones as well (i.e., ‘for better and for worse’, Belsky,
Bakermans-Kranenburg, and van IJzendoorn,
2007). For this reason, Belsky et al. (2009) sug-
gested that some ‘vulnerability genes’ might be better
conceptualized as ‘plasticity genes.’
This alternative to the diathesis-stress model of
environmental action led Belsky et al. (Belsky, Bak-
ermans-Kranenburg, et al. 2007) to delineate statis-
tical criteria for distinguishing GXE (and other
person-X-environment) interactions that reflected
differential-susceptibility from ones reflecting diath-
esis-stress. Kochanska, Kim, Barry and Philibert
(2011) proposed adding to Belsky, Bakermans-Kran-
enburg, et al. (2007) more or less traditional regres-
sion approach (with some modifications) the
evaluation of regions of significance (Aiken & West,
1991; Preacher, Curran & Bauer, 2006). And more
recently Roisman et al. (2012)have advanced even
more rigorous statistical criteria for testing differen-
tial susceptibility. In all cases, however, these efforts
require that an exploratory test of GXE (or person-X-
environment) interaction prove significant and thus
function as a ‘screen’ before different forms of
interaction are evaluated.
To address limitations of such exploratory
approaches to testing GXE interactions, we present
a confirmatory method developed by Widaman et al.
(2012) that explicitly evaluates alternative theoreti-
cal models while maximizing statistical power by
aligning analyses with hypotheses of interest. Of
note is that the approach illustrated in this paper is
by no means restricted to testing either GXE, as it
will be here, or any other person-X-environment
interaction; indeed, it can be used in virtually any
and all tests of statistical interactions in which there
are competing hypotheses as to the form the inter-
action might take (e.g., father involvement X paternal
sensitivity in predicting infant-father attachment
security; Brown, Mangelsdorf & Neff, 2012). The
method systematically varies the number of param-
eters included in a regression equation in order to
contrast alternative conceptual frameworks, most
notably parameters specifying where on the contin-
uum of environmental measurement regression lines
reflecting the association between environmental
predictor and outcome for different genetic sub-
groups will cross. Whereas diathesis-stress theoriz-
ing predicts an ordinal interaction with regression
lines crossing at or above the most positive observed
value for the measured environment (Figure 1A),
differential-susceptibility theorizing predicts a disor-
dinal or cross-over interaction, with regression lines
crossing somewhere within the range of values of the
measured environment (Figure 1B). Comparisons of
proportion of variance explained by alternate regres-
sion models then determine whether one model
provides a better fit to the data and therefore a
better explanation for the observed phenomenon
than do other models.
The confirmatory approach to testing GXE inter-
actions is buttressed by prior work showing that
reliance on omnibus tests from exploratory methods
may often obscure significant findings aligned with a
priori hypotheses. Hale (1977), Rosnow and Rosen-
thal (1989), and Burchinal and Clarke-Stewart
(2007) offered cogent examples of the problematic
outcomes of omnibus tests. If an omnibus test has
more than one df, essentially nil values associated
with one or more df can combine with significant
values associated with other df to result in a nega-
tively biased omnibus test value. To avoid the
negative bias, a confirmatory approach to testing a
priori hypotheses is recommended, and the Wid-
aman et al. (2012) approach does so for GXE
research.
To illustrate this method, we present analyses of
children’s social competence and behavior problems
that test an interaction between a genetic polymor-
phism, the 7-repeat (7R) allele of the dopamine
receptor D4 (DRD4), and exposure to varying quality
of childcare, using data from the large-scale NICHD
Study of Early Child Care (NICHD Early Child Care
Research Network., 2005a). This is a particularly
interesting issue because (a) prior analyses of these
Environment
negave posive
Outcome
negave
posive
resilient
vulnerable
Environment
negave posive
Outcome
negave
posive
not malleable
malleable
(A) Diathesis-Stress GXE Interacon
(B) Differenal Suscepbility GXE Interacon
Figure 1 Plots of idealized results under (A) the diathesis-stress
GXE model and (B) the differential susceptibility GXE model
[figures based on Bakermans-Kranenburg and van IJzendoorn
(2007)]
©2013 The Authors Journal of Child Psychology and Psychiatry ©2013 Association for Child and Adolescent Mental Health.
1136 Jay Belsky, Michael Pluess, and Keith F. Widaman J Child Psychol Psychiatry 2013; 54(10): 1135–43

data failed to reveal main effects of childcare quality
(Belsky, Vandell, et al. 2007; NICHD Early Child
Care Research Network., 2005b); (b) a 10-study
meta-analysis showed that variation in genes related
to dopamine signaling in the brain influence chil-
dren’s sensitivity to both sensitive/responsive and
harsh/unresponsive parenting (Bakermans-Kranen-
burg & van IJzendoorn, 2011); (c) experimental
evidence indicated that children carrying the DRD4
-7R allele benefited more than others from an
intervention fostering skilled parenting (Baker-
mans-Kranenburg, van IJzendoorn, Pijlman, Mes-
man & Juffer, 2008); and (d) the measure of quality
of childcare used in the current inquiry is similar to
parenting measures in the just-cited work. We thus
predicted that the GXE interaction would take the
form of differential-susceptibility: children carrying
DRD4-7R would exhibit (a) the most social compe-
tence and fewest behavior problems under condi-
tions of high-quality childcare and (b) the least social
competence and most behavior problems under
conditions of low-quality childcare.
Therefore, we conducted a comparative analysis of
a number of alternative GXE models. These alter-
natives represent ‘weak’ and ‘strong’ versions of
diathesis-stress and differential-susceptibility prop-
ositions. The strong(er) version of each framework
presumes that children not carrying DRD4-7R are
not affected at all by quality of childcare, whereas the
weak(er) version of each presumes that those with-
out DRD4-7R are affected by childcare quality, but to
alesser degree than those carrying DRD4-7R. Based
on prior research (e.g., Bakermans-Kranenburg &
van IJzendoorn, 2011) and theoretical syntheses of
research (e.g., Belsky & Pluess, 2009), we predicted
that the strong differential-susceptibility model
would provide the best, most parsimonious repre-
sentation of the data for both social skills and
behavior problems. That is, we predicted that the
GXE interaction would resemble Figure 1B, with the
slope for the non-malleable group fixed at zero. We
would reject the strong differential-susceptibility
model if the weak differential-susceptibility model
provided improved fit to the data or if either the weak
or strong diathesis-stress models provided compa-
rable fit to the data with still fewer parameter
estimates.
Methods
Participants
The NICHD Study of Early Child Care recruited 1364
families through hospital visits shortly after the birth
of a child in 1991 at 10 US locations (for detailed
description of recruitment procedures and sample
characteristics see NICHD Early Child Care
Research Network., 2001). The current analysis
includes 441 cases on whom genetic data were
available. Informed consent was secured at each
data collection delineated below, with a special
consent form for the collection of saliva for purposes
of assaying genes.
Measures
Genetic analyses. DNA were obtained from buccal
cheek cells when children were 15 years of age.
Children with at least one 7R allele (n=95; 21.5%)
were distinguished from those with both alleles
shorter than 7R (n=346; 78.5%).
Childcare quality. Quality of care was measured
using observational assessments of caregiver behav-
ior conducted in childcare arrangement at ages 6,
15, 24, 36, and 54 months. Unconditional linear
growth curves were fit across repeated composite
ratings of caregiver behavior and individual inter-
cepts were estimated reflecting the degree to which
caregiving was sensitive, stimulating, positive and
neither neglectful nor negative in character. The
sample mean, M=2.83 (SD =0.24), and median,
Md =2.82, were near the middle of the range (2.10–
3.38) observed in the study.
Social competence. Teacher-reported social com-
petence in 1st grade (~6 years old) was assessed with
the Social Skills Questionnaire from the Social Skills
Rating System (Gresham & Elliott, 1990). Raw
scores were standardized. The sample mean,
M=104.23 (SD =13.19), and median, Md =104.00,
were near population values.
Behavior problems. The Child Behavior Checklist
Teacher Report Form (Achenbach, 1991) evaluated
externalizing behavior in 1st grade. Raw scores were
standardized, based on normative data for children
of the same age. The sample mean, M=49.96
(SD =8.40), and median, Md =49.00, were close to
population values.
Data analysis
Exploratory and confirmatory analytic approaches
were used.
Exploratory. Childcare quality was the environ-
mental variable X, and a dummy variable Ddemar-
cated gene group (0 =absence of 7R, and
1=presence of 7R). The standard multiple regres-
sion model can be written as:
Y¼B0þB1XþB2DþB3XDðÞþEð1Þ
where Y is the dependent variable, B
0
the inter-
cept, B
1
and B
2
regression slopes for main effects of
environment (X) and genes (D), respectively, B
3
the
regression coefficient for the product variable ðXDÞ
and represents the difference in slope on Xfor the
‘7R present’ group relative to the ‘7R absent’ group,
and Eis a stochastic error term.
©2013 The Authors Journal of Child Psychology and Psychiatry ©2013 Association for Child and Adolescent Mental Health.
doi:10.1111/jcpp.12075 Confirmatory testing of GXE 1137

Equation 1 is fit once excluding the product term
ðXDÞ, testing partial (or simultaneous) main effects
(Model 1). With the product term added (Model 2), a
significant increase in the squared multiple correla-
tion, R
2
, provides evidence for a GXE interaction. To
determine whether the GXE interaction is consistent
with diathesis-stress or differential-susceptibility
models, simple slopes for the two groups can be
computed and plotted, and a point estimate of the
cross-over point Ccan be calculated as ^
C¼
^
B2=^
B3
(Aiken & West, 1991).
Confirmatory. Following Widaman et al. (2012), we
re-parameterized the regression model for a dichot-
omous gene polymorphism, allowing a-priori testing
of alternative forms of the GXE interaction, as:
Y:D¼0Y¼B0þB1XCðÞþE
D¼1Y¼B0þB3XCðÞþE
ð2Þ
Here Cis the point on Xat which the slopes for the
two gene groups cross. If the point estimate of Cis
within the range of values on Xobserved in a study,
the interaction tested is disordinal, consistent with
differential-susceptibility. Conversely, if the point
estimate of Cis greater than or equal to the most
positive point on Xin the study, the interaction is
ordinal, reflecting diathesis-stress. Importantly,
because Cis a parameter in the model, the point
estimate of Cis accompanied by a SE, so a confi-
dence interval (CI) for the cross-over point can be
calculated, giving more information on the likely
range for the population value of this key parameter.
Equation 2 is a four-parameter equation (i.e., B
0
,
B
1
,B
3
, and C). Cis the point on Xat which predicted
values for the two groups cross-over or converge, and
B
0
is the estimated Yscore at the cross-over point. B
1
is the slope for the environmental variable Xfor the
non-7R group (D=0), and B
3
is the comparable
slope for the 7R group (D=1). If Cfalls within the
range of Xand the GXE interaction is disordinal and
if the slope for the non-7R group is fixed at zero (i.e.,
B
1
=0), the model in Equation 2 is consistent with
strong differential-susceptibility in which the non-
7R group is unaffected by the environment. This is
the model we hypothesized a priori would hold for
both child outcome variables we analyzed, and we
term this Model 3a.
But, patterns of fixed and free parameters in
Equation 2 can be re-specified to represent other a
priori models that might explain the data virtually as
well as or better than Model 3a. For example,
relaxing the constraint that B
1
=0 leads to Model
3b, the weak differential susceptibility model. If the
slope for the non-7R group differs significantly from
zero, Model 3b should explain significantly more
variance than does Model 3a. In such a situation,
one has a statistical justification to reject the more
parsimonious Model 3a in favor of the better fitting
Model 3b. Or, if one retained the constraint that the
non-7R group is unaffected by the environment and
added a constraint that the cross-over point fell at
the highest value for the environment observed in the
sample, or C=max(X), the model would be consis-
tent with predictions under the strong diathesis-
stress model (Model 3c). Finally, if one allowed both
B
1
and B
3
to differ from zero, but fixed the cross-over
point at the highest value observed in the sample, or
C=max(X), the model would conform to the weak
diathesis-stress model, Model 3d.
Models 3b and 3c represent models with one more
and one less parameter, respectively, than our
preferred Model 3a, so can be tested to determine
if these two models lead to a significant increase or
decrease in explained variance, respectively, when
compared to Model 3a. In addition, all three
restricted models (Models 3a, 3c, and 3d) are nested
within Model 3b, so can be compared against the fit
of Model 3b. Strong-differential-susceptibility and
weak-diathesis-stress models (3a, 3d) each have
three parameter estimates, so cannot be tested
statistically against one another. But, as competing
three-parameter models, the one with the higher R
2
is the one that provides a better representation of
the data. We also used the Akaike information
criterion (AIC) and Bayesian information criterion
(BIC) to evaluate model fit. For both the AIC and
BIC, lower values indicate better fit of a model to
data. AIC and BIC values are especially useful for
evaluating non-nested models (e.g., Models 3a and
3b), which cannot be compared using statistical
tests.
The use of the re-parameterized Equation 2 thus
affords direct determination of whether the GXE
interaction is disordinal, as posited by differential-
susceptibility, or ordinal, consistent with diathesis-
stress. If differential susceptibility best fits the data,
point and interval estimates of the cross-over point
are obtained. Further, it provides a means of deter-
mining whether a strong or weak version of a model
best fits the data. Widaman et al. (2012) provide
programming details regarding how to fit these
confirmatory models in SAS, SPSS, and R packages;
they are available upon request.
Results
First, we conduct tests of GXE interactions for social
competence and behavior problems using the stan-
dard exploratory approach to analyses. Then, we
contrast, for each outcome, strong and weak forms of
the differential-susceptibility and diathesis-stress
models to determine which provided the best, most
parsimonious fit to the data.
Standard exploratory analysis
Social competence. Table 1 shows that Model 1,
with main effects of environment and gene group,
©2013 The Authors Journal of Child Psychology and Psychiatry ©2013 Association for Child and Adolescent Mental Health.
1138 Jay Belsky, Michael Pluess, and Keith F. Widaman J Child Psychol Psychiatry 2013; 54(10): 1135–43

was fit to data on social competence and had an
R
2
=.023, with environment effect significant,
^
B1=7.12 (SE =2.57), p <.01, but not the gene
main effect, p =.17. Adding the GXE interaction to
the equation, Model 2, resulted in an increase in R
2
,
or DR
2
, of .0175, which was significant, p<.01, as
was the coefficient for the GXE product term itself,
^
B3=17.51 (SE =6.23) , p=.005. Critically, param-
eter estimates for Model 2 do not afford a direct
determination of the nature of the interaction (i.e.,
ordinal vs. disordinal), for which follow-up testing is
usually undertaken.
Behavior problems. Table 2 shows that Model 1
produced a non-significant R
2
of .0117, p=.08, with
neither partial main effect proving significant
(ps>.09). The GXE interaction produced a non-
significant DR
2
=of .0057, p=.11 (Model 2). These
results of the standard approach yield the conclu-
sion of ‘no significant GXE interaction,’ thereby
terminating consideration of genetic moderation of
an environmental effect.
Strong vs. weak differential susceptibility
Versions of Equation 2 reflecting strong and weak
differential susceptibility were next fit, first for social
competence and then for behavior problems.
Social competence. The strong differential-suscep-
tibility model (3a) stipulates that children without the
7R allele would be unaffected by quality of child care,
but that children with the 7R allele would be
positively affected by child care quality. As shown in
Table 1, Model 3a explained a significant amount of
variance in social competence, R
2
=.0374, p<.0005.
The estimated cross-over point Cfell close to the
sample mean on child care, ^
C¼2:75 ðSE ¼0:08Þ,
and the CI fell completely within the range of child
care, 95% CI of ^
C½2:59;2:91. Thus, Model 3a
provides strong support for the strong differential
susceptibility model for social competence.
Relaxing the constraint that B
1
=0 leads to Model
3b, the weak differential-susceptibility model. As
seen in Table 1, Model 3b explained a very small and
non-significant amount of additional variance over
that explained by Model 3a, DR
2
=.0032, p=.23.
Therefore, we find no statistical basis for rejecting
the parsimonious Model 3a in favor of the more
highly parameterized Model 3b, lending support in
favor of the strong differential susceptibility model as
a more optimal representation of the data.
Behavior problems. Contrary to results using the
typical exploratory approach to analyses, the fit of
the strong differential susceptibility model, Model
3a, to the behavioral problems data yielded a signif-
icant R
2
=.0167, p=.025 (see Table 2). The cross-
over point Cwas estimated fairly close to the sample
mean on child care, ^
C=2.64 (SE =0.17), and the CI
fell entirely within the range of child care, 95% CI of
^
C½2:30;2:98. Thus, Model 3a provides support for
Table 1 Results for alternate regression models for social competence
Standard parameterization
Re-parameterized regression equation
Parameter
Differential susceptibility Diathesis-Stress
Parameter
Gene (G) and
environment (E)
main effects: Model 1
Main effects and
GXE interaction:
Model 2
Strong:
Model 3a
Weak:
Model 3b
Strong:
Model 3c
Weak:
Model 3d
a
B
0
84.48 (7.26) 94.92 (8.11) B
0
104.5 (0.68) 104.3 (0.91) 105.1 (0.68) 109.1 (1.54)
B
1
7.12 (2.57) 3.41 (2.87) B
1
0.00 (–)
b
3.41 (2.87) 0.00 (–)
b
7.45 (2.59)
B
2
2.04 (1.48) 47.95 (17.9) C2.75 (0.08) 2.74 (0.09) 3.38 (–)
b
3.38 (–)
b
B
3
–17.51 (6.23) B
3
20.92 (5.54) 20.92 (5.53) 0.73 (2.58) 7.16 (3.40)
R
2
.0231 .0406 R
2
.0374 .0406 .0002 .0189
F5.15 6.12 F8.46 6.12 0.08 4.19
df 2, 435 3, 434 df 2, 435 3, 434 1, 436 2, 435
p.006 <.001 p<.0005 <.001 .77 .02
Fvs. 1 –7.90 Fvs. 3a –1.41 16.81 –
df –1, 434 df –1, 434 1, 435 –
p–.005 p–.23 <.0001 –
Fvs. 3b 1.41 –9.80 9.13
df 1, 434 –1, 434 2, 434
p.23 –.002 <.0001
AIC 2232.4 2226.6 AIC 2225.9 2226.6 2240.6 2234.3
BIC 2244.7 2242.9 BIC 2238.2 2242.9 2248.8 2246.6
AIC, Akaike information criterion; BIC, Bayesian information criterion.
Tabled values are parameter estimates, with their standard errors in parentheses. Fvs. 1 stands for an Ftest of the difference in R
2
for Model 2 versus Model 1. Fvs. 3a stands for an Ftest of the difference in R
2
for a given model versus Model 3a.
a
Although not reported in the text, results for this model are provided for completeness.
b
Parameter fixed at reported value; SE is not applicable, so is listed as ().
©2013 The Authors Journal of Child Psychology and Psychiatry ©2013 Association for Child and Adolescent Mental Health.
doi:10.1111/jcpp.12075 Confirmatory testing of GXE 1139

the strong differential susceptibility model for the
behavior problems data.
Once again, relaxing the constraint that B
1
=0
leads to Model 3b, the weak differential-susceptibil-
ity model. As seen in Table 2, Model 3b explained a
very small and non-significant amount of added
variance over that explained by Model 3a, DR
2
=
.0007, p=.59. In line with results for social compe-
tence, we find no statistical basis for rejecting the
parsimonious Model 3a in favor of the more highly
parameterized Model 3b, lending support in favor of
the strong differential susceptibility model as the
optimal representation of the behavior problems
data.
Differential susceptibility vs. diathesis-stress
Given the better fit of the strong differential suscep-
tibility model relative to the weak version of the
model, we proceeded to fit strong and weak versions
of the diathesis-stress model to allow comparative
evaluation of the fit of these models.
Social competence. The strong diathesis-stress
model is nested within the strong differential-sus-
ceptibility model, by fixing the cross-over point to be
at the maximum value of Xobserved in the study;
here, Xwas child care quality, and the maximal
value observed was 3.38. As shown in Table 1, this
model, Model 3c, had a very small level of explained
variance, R
2
=.0002, p=.77, and fit significantly
worse than Model 3a, p<.0001.
Relaxing the constraint that B
1
=0 leads to Model
3d, the weak diathesis-stress model. As seen in
Table 1, Model 3d had a modest increase in
explained variance over Model 3c, but still had a
relatively low level of explained variance, R
2
=.0189,
p=.02. As noted above, Models 3d and 3a cannot be
compared statistically because they have the same
number of parameter estimates. However, Model 3a,
the strong differential-susceptibility model,
explained about twice as much variance as Model
3d with the same number of estimates and had
substantially lower values of both AIC and BIC than
did Model 3d. Further, Model 3a had the lowest (i.e.,
best) levels of AIC and BIC of all six regression
models fit to the data, lending clear support to Model
3a as the preferred representation of data.
Problem behavior. The pattern of model compari-
sons for problem behavior was very similar to that for
social competence. Specifically, as shown in Table 2,
the strong diathesis-stress model, Model 3c, had a
very small level of explained variance, R
2
=.0009,
p=.52, and fit significantly worse than Model 3a,
p<.05.
Relaxing the constraint that B
1
=0 resulted in
Model 3d, the weak diathesis-stress model. As seen
in Table 2, Model 3d had a modest increase in
explained variance over Model 3c, but still had a
Table 2 Results for alternate regression models for behavior problems
Standard parameterization
Re-parameterized regression equation
Parameter
Differential susceptibility Diathesis-stress
Parameter
Gene (G) and
environment (E)
main effects: Model 1
Main effects and
GXE interaction:
Model 2
Strong:
Model 3a
Weak:
Model 3b
Strong:
Model 3c
Weak:
Model 3d
a
B
0
57.11 (4.78) 53.24 (5.36) B
0
50.36 (0.45) 50.57 (0.72) 50.10 (0.45) 48.59 (1.02)
B
1
2.40 (1.68) 1.02 (1.89) B
1
0.00 (–)
b
1.02 (1.89) 0.00 (–)
b
2.82 (1.70)
B
2
1.62 (0.98) 17.18 (11.9) C2.64 (0.17) 2.61 (0.21) 3.38 (–)
b
3.38 (–)
b
B
3
–6.59 (4.14) B
3
7.61 (3.68) 7.61 (3.69) 1.08 (1.70) 1.36 (2.24)
R
2
.0117 .0174 R
2
.0167 .0174 .0009 .0072
F2.59 2.57 F3.72 2.57 0.40 1.58
df 2, 438 3, 437 df 2, 438 3, 437 1, 439 2, 438
p.08 .054 p.025 .054 .52 .21
Fvs. 1 –2.53 Fvs. 3a –0.29 7.04 –
df –1, 437 df –1, 437 1, 438 –
p–.11 p–.59 .008 –
Fvs. 3b 0.29 –3.65 4.53
df 1, 437 –2, 437 1, 437
p.59 –.03 .03
AIC 1884.3 1883.7 AIC 1882.0 1883.7 1887.1 1886.3
BIC 1896.5 1900.1 BIC 1894.3 1900.1 1895.2 1898.6
AIC, akaike information criterion; BIC, Bayesian information criterion.
Tabled values are parameter estimates, with their standard errors in parentheses. Fvs. 1 stands for an Ftest of the difference in R
2
for Model 2 versus Model 1. Fvs. 3a and Fvs. 3b stand for Ftests of the difference in R
2
for a given model versus Model 3a and Model
3b, respectively.
a
Although not reported in the text, results for this model are provided for completeness.
b
Parameter fixed at reported value; SE is not applicable, so is listed as (–).
©2013 The Authors Journal of Child Psychology and Psychiatry ©2013 Association for Child and Adolescent Mental Health.
1140 Jay Belsky, Michael Pluess, and Keith F. Widaman J Child Psychol Psychiatry 2013; 54(10): 1135–43

relatively low level of explained variance, R
2
=.0072,
p=.21. As noted above, Models 3d and 3a cannot be
compared statistically because they have the same
number of parameter estimates. However, Model 3a,
the strong differential-susceptibility model,
explained over twice as much variance as Model 3d
with the same number of estimates. Once again, the
AIC and BIC values for Model 3a were noticeably
lower than comparable values for Model 3d as well as
for the remaining models fit to the data. This pattern
of results provides clear and consistent support for
Model 3a as the preferred representation of data.
Plotting predicted values under differential
susceptibility
Plots of predicted values provide a very useful way of
displaying and interpreting data with an interaction.
The plot of predicted social competence scores is
shown in Figure 2A, where the malleable group does
have systematically lower levels of competence than
the non-malleable group below the cross-over point.
However, above the cross-over point, the malleable
group shows consistently higher performance as a
function of higher levels of child care quality.
The plot of predicted values for behavior problems
is shown in Figure 2B. Below the cross-over point,
the malleable group exhibits worse (i.e., higher)
levels of behavior problems as a function of lower
levels of child care quality. But, above the cross-over
point, the malleable group shows improvements in
behavior problems with higher levels of quality care.
Discussion
Gene-environment interaction research has grown
dramatically over the past decade, as scholars have
discussed and debated whether and how the genetic
make-up of individuals moderates their susceptibil-
ity to environmental influences (Risch et al., 2009;
Uher & McGuffin, 2010).Most of this work has been
informed by the diathesis-stress view that some
individuals are genetically more vulnerable, suc-
cumbing to adverse environmental effects, than are
others, though the differential-susceptibility per-
spective offers an alternative, evolutionary-inspired
view: those most susceptible to negative influences
are simultaneously most likely to benefit from
positive ones. Either way, it remains the case that
all tests of GXE have been exploratory –and thereby
conservative –in nature, rather than optimally
sensitive to the theoretical propositions guiding the
research.
Here we illustrated an alternative approach in
which GXE data are evaluated in terms of competing
theoretical propositions. Rather than requiring a
significant GXE interaction derived from an explor-
atory analysis to serve as the gateway for determin-
ing the form of the interaction, we show that
interactions having different forms, inspired by
alternative theoretical frameworks, can be directly
tested –and compared. The fact that the findings
reported herein indicate, consistent with other work
on the effects of children’s caregiving environments
(Bakermans-Kranenburg & van IJzendoorn, 2011;
Bakermans-Kranenburg et al., 2008), that children
carrying the DRD4-7R allele prove sensitive to higher
and lower quality childcare in terms of their social
adjustment, whereas those lacking this allele prove
insensitive to childcare quality (see Figure 2A,B), is
no doubt interesting. The main contribution of this
analysis, however, is the demonstration that the
Widaman et al. (2012) confirmatory approach for
evaluating interactions can be used to address
alternative GXE hypotheses specifically and directly
contrast the fit of models that regard a particular
genotype as a ‘risk’ allele versus a ‘plasticity’ allele.
However, the Widaman et al. (2012) confirmatory
approach is not restricted to contrasting such ‘vul-
nerability’ and ‘susceptibility’ hypotheses. It is, in
fact, a flexible approach that can be fit to test GXE
hypotheses other than diathesis-stress and differen-
tial susceptibility. For example, Pluess and Belsky
(2012) recently introduced a new concept –Vantage
Sensitivity –which refers to individual differences in
response to exclusively positive experiences, as
reflected in the ‘bright side’ of differential suscepti-
bility. According to this framework, individuals who
benefit disproportionately from positive supportive
experiences (e.g., psychotherapy, positive life events)
manifest ‘vantage sensitivity’, whereas individuals
failing to respond positively to the same experience
are referred to as showing ‘vantage resistance’ –with
120
110
100
90
2.1 3.4
2.1 3.4
55
50
45
(A) GXE Interaction for Social Competence
(B) GXE Interaction for Behavioral Problems
Child Care Quality
Child Care Quality
Behavior Problems Social Competence
DRD4-7R absent
DRD4-7R absent
DRD4-7R present
DRD4-7R present
Figure 2 Plots of predicted values as a function of child care
quality under the strong differential susceptibility GXE model for
(A) social competence and (B) behavior problems [figures based
on Bakermans-Kranenburg and van IJzendoorn (2007)]
©2013 The Authors Journal of Child Psychology and Psychiatry ©2013 Association for Child and Adolescent Mental Health.
doi:10.1111/jcpp.12075 Confirmatory testing of GXE 1141

no differences between individuals expected in
response to negative experiences. This vantage-sen-
sitivity-interaction hypothesis can easily be tested
and contrasted with other GXE hypotheses –using
the Widaman et al. (2012) approach –by fixing the
cross-over point to the minimum end of the environ-
mental variable and, in case of strong vantage
sensitivity, constraining the slope of the vantage
resistant group to zero. Also important to note is that
Widaman et al. (2012) showed that their approach
works when genetic variables have more than just
two categories or are measured continuously.
Indeed, it is applicable not just to the study of
GXE, but to investigation of all sorts of interactional
effects.
One cannot but wonder whether some of the
debate surrounding the existence and detection of
GXE interactions in the extant literature may have
proven different if methodological ‘gloves’ had been
better fit to empirical ‘hands.’ Consider the possibil-
ity, for example, that even if some of the non-
replication of the 5HTTPLR-X-life-stress interaction
predicting depression resulted from limited mea-
surement (Uher & McGuffin, 2010), some of it may
also have been a product of limited statistical anal-
ysis. Perhaps some of what are considered null
findings would mirror what we found regarding
problem behavior: When tested in the traditional,
exploratory manner, no GXE interaction is dis-
cerned; yet when tested in a theoretically-informed
manner, evidence of GXE interaction emerges. Cer-
tainly some will contend that if GXE interactions are
so sensitive to subtleties of analysis, then they are
insufficiently robust to be of interest, much less
importance. Others will certainly disagree. This is a
debate worth having, but to have well informed
debate empirical tests themselves should fit the
hypotheses being tested.
Consider further the fact that so many GXE
designs measure neither a full range of environments
nor a full range of psychological functioning, from
positive to negative (Belsky et al., 2009). Instead,
some adverse condition (e.g., negative life events) is
contrasted with its absence and some pathological
outcome (e.g., depression) is evaluated versus its
absence. When coupled with the perhaps all-too-
conservative, exploratory approach to evaluating
GXE, there would seem to be grounds for question-
ing the conclusion of Risch et al. (2009), based on
the meta-analysis of a single GXE interaction and
outcome, dismissing the entire GXE paradigm. For
too long, perhaps, the debate about GXE interaction
has focused on sample size and measurements. We
contend that insufficient attention has been paid to
the theoretical foundations of GXE inquiry (e.g.,
diathesis-stress vs. differential susceptibility vs.
vantage sensitivity) (Belsky & Pluess, 2009; Ellis,
et al. 2011; Pluess & Belsky, 2012), the range of
environments and outcomes measured (Belsky, Bak-
ermans-Kranenburg, et al. (2007), and the statisti-
cal procedures adopted for evaluating the important
notion that individuals differ, for genetic reasons, in
their susceptibility to environmental effects.
Acknowledgements
Preparation of this paper was supported in part by the
Robert M. and Natalie Reid Dorn Professorship, UC
Davis (Jay Belsky), grant HD 064687 from the National
Institute of Child Health and Human Development
(Rand D. Conger, PI) and grant DA 017902 from the
National Institute of Drug Abuse and the National
Institute of Alcohol Abuse and Alcoholism (Rand D.
Conger, Richard W. Robins, and Keith F. Widaman,
Joint PIs).
Correspondence
Jay Belsky, Department of Human Ecology, Program in
Human Development and Family Studies, University
of California, Davis, Davis, CA 95616, USA; Email:
jbelsky@ucdavis.edu
Key points
•Extensive research highlights gene-X-environment interaction (GXE) when it comes to accounting for
variation in the extent to which individuals are affected by particular developmental experiences and/or
environmental exposures.
•Virtually all research on GXE relies on exploratory methods of statistical analysis, even though most such work
is based on explicit –and directional–predictions, typically consistent with diathesis-stress theorizing. Because
there is now a well-recognized alternative to this prevailing model of environmental action, one known as
differential susceptibility, there is a need for statistical methods that test competing models, which is what is
offered here.
•Discovering ‘what works for whom’ is a central goal of clinically relevant research. Methods such as those
presented can advance this cause by determining whether certain individuals are more susceptible to both
positive and negative developmental experiences and environmental exposures or simply just more vulnerable
to adversity, as long presumed.
©2013 The Authors Journal of Child Psychology and Psychiatry ©2013 Association for Child and Adolescent Mental Health.
1142 Jay Belsky, Michael Pluess, and Keith F. Widaman J Child Psychol Psychiatry 2013; 54(10): 1135–43

References
Achenbach, T. (1991). Manual for the child behavior checklist/
4–18 and 1991 profile. Burlington, VT: Author.
Aiken, L.S., & West, S.G. (1991). Multiple regression: Testing
and interpreting interactions. Newbury Park, CA: Sage.
Bakermans-Kranenburg, M.J., & van IJzendoorn, M.H. (2006).
Gene-environment interaction of the dopamine D4 receptor
(DRD4) and observed maternal insensitivity predicting
externalizing behavior in preschoolers. Developmental
Psychobiology,48, 406–409.
Bakermans-Kranenburg, M.J., & van IJzendoorn, M.H. (2007).
Research review: Genetic vulnerability or differential
susceptibility in child development: the case of
attachment. Journal of Child Psychology and Psychiatry,
48, 1160–1173.
Bakermans-Kranenburg, M.J., & van IJzendoorn, M.H. (2011).
Differential susceptibility to rearing environment depending
on dopamine-related genes: New evidence and a meta-
analysis. Development and Psychopathology,23,39–52.
Bakermans-Kranenburg, M.J., van IJzendoorn, M.H., Pijlman,
F.T., Mesman, J., & Juffer, F. (2008). Experimental evidence
for differential susceptibility: Dopamine D4 receptor
polymorphism (DRD4 VNTR) moderates intervention effects
on toddlers’ externalizing behavior in a randomized
controlled trial. Developmental Psychology,44, 293–300.
Belsky, J., Bakermans-Kranenburg, M.J., & van IJzendoorn,
M.H. (2007). For better and for worse: Differential
Susceptibility to environmental influences. Current
Directions in Psychological Science,16, 300–304.
Belsky, J., Jonassaint, C., Pluess, M., Stanton, M., Brummett,
B., & Williams, R. (2009). Vulnerability genes or plasticity
genes? Molecular Psychiatry,14, 746–754.
Belsky, J., & Pluess, M. (in press). Beyond risk, resilience and
dysregulation: Phenotypic plasticity and human
development. Development and Psychopathology.
Belsky, J., & Pluess, M. (2009). Beyond diathesis-stress:
Differential susceptibility to environmental influences.
Psychological Bulletin,135, 885–908.
Belsky, J., Vandell, D.L., Burchinal, M., Clarke-Stewart, K.A.,
McCartney, K., & Owen, M.T. (2007). Are there long-term
effects of early child care? Child Development,78, 681–701.
Brown, G.L., Mangelsdorf, S.C., & Neff, C. (2012). Father
involvement, paternal sensitivity, and father-child
attachment security in the first 3 years. Journal of Family
Psychology,26, 421–430.
Burchinal, M.R., & Clarke-Stewart, K.A. (2007). Maternal
employment and child cognitive outcomes: The importance
of analytic approach. Developmental Psychology,43, 1140–
1155.
Burmeister, M., McInnis, M.G., & Zollner, S. (2008).
Psychiatric genetics: Progress amid controversy. Nature
Reviews. Genetics,9, 527–540.
Ellis, B.J., Boyce, W.T., Belsky, J., Bakermans-Kranenburg,
M.J., & van IJzendoorn, M.H. (2011). Differential
susceptibility to the environment: An evolutionary –
Neurodevelopmental theory. Development and
Psychopathology,23,7–28.
Gresham, F., & Elliott, S. (1990). Social skills rating system.
Circle Pines, MN: American Guidance Service.
Hale, G.A. (1977). On use of ANOVA in developmental
research. Child Development,48, 1101–1106.
Kochanska, G., Kim, S., Barry, R.A., & Philibert, R.A. (2011).
Children’s genotypes interact with maternal responsive care
in predicting children’s competence: Diathesis-stress or
differential susceptibility? Development and Psychopathol-
ogy,23, 605–616.
McClelland, G.H., & Judd, C.M. (1993). Statistical difficulties
of detecting interactions and moderator effects.
Psychological Bulletin,114, 376–390.
NICHD Early Child Care Research Network. (2001).
Nonmaternal care and family factors in early development:
An overview of the NICHD Study of Early Child Care. Applied
Developmental Psychology,22, 457–492.
NICHD Early Child Care Research Network. (2005a). Child care
and child development: Results of the NICHD study of early
child care and youth development. New York: Guilford Press.
NICHD Early Child Care Research Network. (2005b). Early
child care and children’s development in the primary grades:
Follow-up results from the NICHD study of early child care.
American Educational Research Journal,42, 537–570.
Pluess, M., & Belsky, J. (2012). Vantage sensitivity: Individual
differences in response to positive experiences. Psychological
Bulletin, in press.
Preacher, K.J., Curran, P.J., & Bauer, D.J. (2006).
Computational tools for probing interactions in multiple
linear regressions, multilevel modeling, and latent curve
analysis. Journal of Educational and Behavioral Statistics,
31, 437–448.
Risch, N., Herrell, R., Lehner, T., Liang, K.Y., Eaves, L., Hoh,
J., …& Merikangas, K.R. (2009). Interaction between the
serotonin transporter gene (5-HTTLPR), stressful life events,
and risk of depression: A meta-analysis. JAMA,301, 2462–
2471.
Roisman, G.I., Newman, D.A., Fraley, R.C., Haltigan, J.D.,
Groh, A.M., & Haydon, K.C. (2012). Distinguishing
differential susceptibility from diathesis-stress: Recom-
mendations for evaluating interaction effects. Development
and Psychopathology,24, 389–409.
Rosnow, R.L., & Rosenthal, R. (1989). Statistical procedures
and the justification of knowledge in psychological science.
American Psychologist,44, 1276–1284.
Uher, R., & McGuffin, P. (2010). The moderation by the
serotonin transporter gene of environmental adversity in
the etiology of depression: 2009 update. Mol Psychiatry,15,
18–22.
Widaman, K.F., Helm, J.L., Castro-Schilo, L., Pluess, M.,
Stallings, M.C., & Belsky, J. (2012). Distinguishing ordinal
and disordinal interactions. Psychological Methods,17, 615–
622.
Zubin, J., & Spring, B. (1977). Vulnerability –A new view of
schizophrenia. Journal of Abnormal Psychology,86, 103–
126.
Accepted for publication: 4 February 2013
Published online: 25 April 2013
©2013 The Authors Journal of Child Psychology and Psychiatry ©2013 Association for Child and Adolescent Mental Health.
doi:10.1111/jcpp.12075 Confirmatory testing of GXE 1143