Path Analysis of IQ during Infancy and Early Childhood and an Index of the Home Environment in the Colorado Adoption Project

Path Analysis of IQ during Infancy and Early Childhood and an Index of the Home Environment in the Colorado Adoption Project

University of Colorado, Boulder

Pennsylvania State University

INTELLIGENCE 12, 27-45 (1988)

A parent-offspring adoption path model, which includes a measured index of the home environment, was formulated to assess the extent to which relationships between the environmental index and children’s behavior are mediated by genetic and environmental influences of the parents. In addition to the direct effect of the home environment on children’s behavior, three types of indirect effects mediated by parental phenotype are considered: a pure environmental effect, a pure genetic effect, and a combined environmental-genetic effect. To illustrate its application, the model was fitted to parental and offspring IQ data collected in the Colorado Adoption Project and an environmental index based on Caldwell and Bradley’s (1978) Home Observation for Measurement of the Environment (HOME). Four sets of data, including the HOME index and offspring IQ measured longitudinally at 1, 2, 3, and 4 years of age, were analyzed. The results suggest that in infancy (ages 1 and 2), the HOME reveals a direct environmental effect on children’s IQ as well as indirect effects mediated via parental IQ. Surprisingly, during early childhood (ages 3 and 4), the relationship between the HOME and children’s IQ is due only to indirect parental mediation. Moreover, other than at year 1, the mediation is purely genetic.

The first path model of parent-offspring resemblance for cognitive ability was reported by Barbara Burks in 1928. However, in this classic adoption study, only manifest variables of midparental intelligence and a measure of the home environment were used to predict offspring IQ. Subsequently, Sewall Wright (1931) reanalyzed Burks’ data using a path model that incorporated genetic and environmental influences as latent variables. Those latent variables included midparent and offspring additive genetic values, midparent environment, and residual effects due to midparent and offspring IQ, genotypes, and environments. Moreover, Wright’s model allowed for correlated genetic and environmental influences by acknowledging that parental IQ may be an important influence on offspring’s environment.

Subsequently, Jencks and coworkers (1972) elaborated Wright’s model by incorporating latent environmental influences for both parental and offspring generations. In addition, Jencks modeled single-parent/child resemblances and considered effects due to assortative marriage in the presence of correlated genetic and environmental influences.

During the mid- to late 1970s, various other path models were formulated which explored different aspects of genetic and cultural transmission and which incorporated statistical estimation procedures that more adequately evaluate the data (cf. Cloninger, Rice, & Reich, 1979; Eaves, Last, Young, & Martin, 1978; Loehlin, 1979; Rao, Morton, & Yee, 1974). For example, cultural transmission was modeled from parental phenotypes to offspring environment (Eaves et al., 1978; Jencks, 1972) and from parental environments to offspring environment (Cloninger et al., 1979; Rao et al., 1974). In addition, the effects of gene segregation and within-family transmission of socioculture values were considered (Cloninger et al., 1979), as were dominance deviations (Eaves et al., 1978).

The consequences of various models of assortative mating were also explored. Some assortment models assumed that the phenotypic correlations were primary, leading to secondary correlations between parental genetic and environmental variables (Eaves et al., 1978); others assumed that the genetic and environmental parental correlations were primary, leading to secondary correlations between parental phenotypes (Jencks, 1972). Both modes of assortment were considered by Rao, Morton, and Cloninger (1979).

In addition, an environmental index was reintroduced as a measure of latent environmental variables (Rao et al., 1974). The primary purpose of the observed index was to identify the model in order to separate the effects of genetic and environmental influences in nuclear families.

A more recent path analysis of genetic and environmental transmission for cognitive abilities was reported by Fulker and DeFries (1983) using data from the Colorado Adoption Project. In their path diagrams, which are based upon the Wright/Jencks model, the environmental index is a function of parental phenotypes (via causal paths) and has a causal influence on offspring’s environment. Moreover, parental phenotypes may have a direct effect on offspring’s environment independent of the index. Thus, the indexed measure of the environment may be correlated with offspring’s behavior because of direct transmission or because of indirect parental mediation.

The primary objectives of the present report are to formulate a modification of the Fulker and DeFries model that facilitates a more detailed analysis of the etiology of observed relationships between environmental indices and behavior and to apply this model to an analysis of IQ data from the Colorado Adoption Project. In the present study, parental mediation of ostensible environmental influences is partitioned into genetic and environmental components. In addition, changes in the etiology of these relationships as a function of child’s age will also be explored.


Path Model

The path model employed in this study is based on the adoption model reported by Fulker and DeFries (1983). The path diagrams for nonadoptive and adoptive families are shown in Figures 1 and 2, respectively. Two latent variables (shown in circles), additive genetic value (G) and environmental deviations (E), completely determine the observed phenotypic value (P – shown in square symbols) with paths h (the square root of heritability) and e (the square root of environmentality), respectively, in both the parental (subscripted M for mothers and F for fathers) and offspring (subscripted O) generations. G and E are correlated s. In the case of parents and nonadopted children, G, E, and P are standardized to zero mean and unit variance. Because passive genotype-environment correlation (Plomin, DeFries, & Loehlin, 1977) does not occur for adoptive children in the absence of selective placement, their variance may differ from that of nonadopted children. Additive genetic transmission is from parental G to offspring G with a path coefficient of ½. Environmental influences are transmitted from parental P to offspring E via paths m and f for mothers and fathers, respectively.

Phenotypic assortative mating is modeled using reverse path notation (see Fulker & DeFries, 1983), where the Greek symbols Γ and Φ represent the quantities (h + se) and (e + sh), respectively. The phenotypes of nonadoptive mothers and fathers (PM and PF, respectively), as well as those of the adoptive parents (PAM and PAF), are correlated p. However, the assortment correlation (q) for unwed biological parents (PBM and PBF) is allowed to differ. As shown in Figure 2, the possibility of selective placement correlations between the biological and adoptive parents’ phenotypes (x1 through x4) is also included in the model.

The major difference between the present model and that of Fulker and DeFries (1983) involves the relationship between parental variables and the index of the home environment (I). In the earlier model, the phenotype of the parents was causally related to the index via direct paths from parental phenotypes to I. In the present study, correlations are modeled between I and the underlying parental variables to partition the parent-index relationship into its underlying genetic and environmental components. Thus, in the present model, the index is correlated with parental G and E variables (rMG and rME for mothers, and rFG and rFE for fathers), thereby facilitating an analysis of the etiology of observed environment-behavior relationships.

There are four sources of covariation between offspring phenotype (PO and PAO for nonadopted and adopted children, respectively) and the index, one direct and three indirect. The direct environmental transmission is via paths [ec]. If we assume equal maternal and paternal correlations with the index, that is, rMG = rFG = rGI, and rME = rFE = rEI, the three indirect sources are as follows: environmental transmission of environmental mediation [e² rEI (m + f)]; genetic transmission of genetic mediation [hrGI]; and environmental transmission of genetic mediation [ehrGI (m + f)].

The novelty of these types of indirect effects warrants additional explanation. The first type of indirect effect, pure environmental mediation, occurs when the relationship between parental phenotypes and index is due to environmental effects on parental phenotypes, index, and offspring phenotype. For example, rearing factors in the parents’ childhood might affect parental general cognition and scores on the environmental index, as well as children’s IQ scores. The pure genetic effect occurs when genetic factors that affect the parental phenotypes and the environmental index also influence children’s phenotypes hereditarily. Genetic effects on IQ, for example, could plausibly affect parental scores on the environmental index, as well as parental IQ and offspring IQ. The critical point in the adoption design is that, in adoptive families, genetic mediation of this type cannot occur because adopted children are not related genetically to their adoptive parents.

The third type of indirect effect involves a combination of genetic and environmental mediation. Even when the relationship between parental phenotype and environmental index is mediated genetically, the effect on children’s phenotypes can be transmitted environmentally via the parental phenotype. This third type of combined genetic-environmental transmission occurs in adoptive families as well as in nonadoptive families.

The expected covariances for nonadoptive mothers, fathers, and their children are presented in partitioned form in the top portion of Table 1. As shown in this table, the full 4 x 4 expected matrix contains 6 unique covariances and 4 variances. The expected covariances for biological-adoptive families for which data are complete form a 6 x 6 matrix containing 15 covariances and 6 variances (see bottom portion of Table 1). Two expected correlations are fixed at zero because no relationships are expected between the biological parents’ phenotypes and the index. In fact, inspection of the empirical data shows an average correlation of .04. For those families in which data from biological fathers are not available, the expectations form a 5 × 5 matrix.

Except for those expectations involving adopted children, the expected covariances in Table 1 are expressed as correlations inside the square brackets and are scaled by phenotypic standard deviations outside the brackets. Expressions inside the brackets for expectations involving adopted children are standardized covariances because the expected phenotypic variances for adopted children are less than unity in the presence of positive genotype-environment correlations.


Biological and adoptive parents in the Colorado Adoption Project (CAP) were ascertained by referral from two private adoption agencies. Adopted children were separated from their biological mothers shortly after birth and were placed in adoptive homes a few weeks later. The average age at placement of adopted children in the CAP sample is 29 days.

Nonadoptive families (parents raising their own children) were matched to adoptive families on the basis of sex of the child; number of other children in the family; and age (±5 years), occupational status, and total years of education (±2 years) of the fathers.

The results in this report are based upon analyses of data from adopted and nonadopted children tested at 1, 2, 3, and 4 years of age and from their biological and adoptive parents. Although a concerted effort was made to test biological fathers of the adoptees, data from fewer biological fathers than from biological mothers were available for the present analysis. The numbers of subjects on which the analyses are based at each age are given in Tables 2 through 5. (For a more detailed description of the CAP sample, see DeFries, Plomin, Vandenberg, & Kuse, 1981, and Plomin and DeFries, 1985.)


Adults were administered a battery of 13 tests of specific cognitive abilities. Each of the resulting 13 scores was adjusted for age and sex using a multiple regression procedure. A first principal component score was computed from the 13 corrected test scores and used as a measure of general mental ability (see DeFries et al., 1981). These component scores have been found to correlate about .70 with Wechsler Adult Intelligence Scale scores of the same subjects tested over 7 years later (unpublished analyses). Thus, in the present path model, the symbols PM, PF, and PBM, PBF, PAM, and PAF represent general cognitive scores of the parents of nonadopted and adopted children, respectively.

Between 1 and 4 years of age, children in the CAP were tested yearly in their homes within 2 weeks of their birthday by trained examiners on a battery of tests assessing cognitive, motor, and personality traits. During each home visit, a standardized IQ test was administered: the Bayley Scales of Infant Development (Bayley, 1969) at ages 1 and 2, and the Stanford-Binet Intelligence Scale (Terman & Merrill, 1973) at ages 3 and 4. The home environment was rated during each visit using a modified version of Caldwell and Bradley’s (1978) HOME inventory. At each age, a general factor score representing the HOME was derived by principal component analysis of the quantitatively scored HOME items (see Plomin & DeFries, 1985). Thus, in the path diagrams, PO and PAO represent IQ scores of the nonadopted and adopted offspring, and I represents the Caldwell HOME principal component score.


The summary statistics to which the path model is fitted are variances and covariances calculated separately for adoptive and nonadoptive families. Tables 2 through 5 show the observed covariances and associated number of subjects for ages 1 through 4, respectively. The analyses were conducted separately for each age level.

Path models are fitted to these observed covariances using a maximum-likelihood estimation procedure. The minimized function is:


where Si is the ith observed covariance matrix with Ni degrees of freedom, ∑i is the ith expected covariance matrix, Ki is the rank of the ith matrix, and the function is summed over m pairs of observed and expected matrices. This function is minimized using MINUIT (CERN, 1977), a package of optimization and error analysis routines made available by CERN, the European Organization for Nuclear Research (see Fulker & DeFries, 1983).

After the full model is fitted to the observed covariances, a series of reduced models is fitted to test various hypotheses by setting specific parameters to some value or by equating parameters. If the change in chi square value between the full and a reduced model is nonsignificant, the reduced model is accepted as being more parsimonious. Alternatively, a significant change in chi square would suggest the parameters should be retained in the model.

Parameter estimates are obtained subject to the constraints listed at the bottom of Table 1. The constraint pertaining to genotype-environment correlations, s, is based on the assumption that maternal and paternal transmission parameters are responsible for the correlations and that equilibrium exists between generations. This constraint leads to an estimate of f (paternal environmental transmission) as a derived parameter. Additionally, the constraint that phenotypic variances are unity (h² + e² + 2hse = 1.0) leads to an estimate of e as a residual variable. Thus, s is estimated as a free parameter, and f and e are derived from the constraints.

The present model was formulated to facilitate analyses of the etiology of behavior-environment relationships. The model is plausible and includes alternative sources of covariation between measured environments and behavior. Although alternative full models could be fitted to the data, only differences among hierarchically related (i.e., nested) models may be tested for statistical significance.


The results of fitting the full model to the data are presented in Table 6. As shown, the fit of the model is acceptable at ages 1, 2, and 4, and is marginal at age 3, χ² (29) = 42.12, p = .052. These results suggest that the model provides an adequate representation of the underlying correlational structure among parental and offspring IQ measures and the HOME index.

We next fitted a series of reduced models by dropping or equating certain parameters so that interpretation of the results would be more parsimonious. As shown in Table 7, the test for dropping the four selective placement parameters (x1 through x4) between biological and adoptive parents’ general cognition was nonsignificant at all four ages, providing no evidence to retain those parameters (Model 2). Similarly, assortative mating can be equalized across the wed and unwed parents’ general cognitive ability (p = q) at all ages (Model 3).

The next set of parameters to be constrained were the parent cognitive-HOME index correlations. The four correlations, two between parental genotypes for general cognition (maternal and paternal) and the HOME index, and two between parental environments and the index, were tested. In Model 4, maternal and paternal correlations are equated. Because the changes in chi square are nonsignificant for this model, differences between the maternal and paternal correlations are not important. Thus, the correlations of maternal G with the HOME index (rMG) and paternal G with the index (rFG) may be equalized and will be denoted rGI. Similarly, the environment-index correlations (rME and rFE) may be equalized (rEI).

Next, Models 5, 6, and 7 test whether the two types of parent cognitive-HOME index correlations may be dropped. At age 1, the test for the gene-index correlation (Model 5) is nonsignificant, suggesting that it may be dropped from the model. Although dropping the environment-index correlation (Model 6) results in only a marginally significant change in chi square, χ² (1) = 3.56, p > .05, the change when both the gene-index and environment-index correlations are dropped (Model 7) is significant, χ² (2) = 12.34, p < .005. Therefore, the environment-index correlation was retained, but the gene-index correlation was dropped at age 1. At year 2, the change in chi square is substantial when the gene-index correlation is constrained to be zero, χ² (1) = 5.15, p < .025, but the environment-index correlation may be dropped without loss of fit. At age 3, dropping the gene-index correlation results in only a marginal chi square change, χ² (1) = 3.54, p > .05, and the change when the environment-index correlation is dropped is not significant. However, dropping both correlations at age 3 produces a worse fit, χ² (2) = 17.81, p < .0005. Therefore, only the gene-index correlation was retained at ages 2 and 3. For the data at 4 years of age, no evidence was found for retaining either the gene-index or the environment-index correlation. However, both parent-index correlations may not be dropped concurrently, χ² (2) = 18.28, p < .0005. Because loss of fit associated with dropping the gene-index correlation is higher than that when the environment-index correlation is dropped, the former was retained in the model.

These results suggest that the model will adequately distinguish between gene-index and environment-index correlations. Although not reported in Table 7, setting rGI to zero increases the parameter estimate involving direct transmission from index to offspring (c). However, setting rEI to zero has little effect on the other parameters.

In the last test of the model, the direct transmission parameter (c) from the HOME index to offspring environment for IQ (E) was constrained to be zero (Models 8a and 8b). As may be seen in Table 7, the test for the direct path between the HOME index and offspring IQ was significant at year 1, χ² (1) = 3.31, p > .05 (Model 8a) and year 2, χ² (1) = 23.31, p < .0005 (Model 8b), but was nonsignificant at years 3 and 4. Combined with the results of testing Models 5, 6, and 7, these data suggest significant direct and indirect transmission between the HOME index and offspring’s IQ at ages 1 and 2. Therefore, Model 5 provides the most parsimonious representation of the data at year 1, and Model 6 best characterizes the data at year 2. However, at ages 3 and 4, only the indirect genetic relationships are significant, and Model 8b best summarizes the data.

Table 8 shows the resulting parameter estimates for the most parsimonious models for each data set, that is, Model 5 at 1 year of age, Model 6 at age 2, and Model 8b for ages 3 and 4. Although not shown in Table 8, the parameter estimates for heritable (h) and maternal environmental (m) influences were fairly stable across the various models within each set of data. Assuming isomorphism of measures across generations, heritability of IQ (h²) appears to be increasing as the child gets older (.08, .13, .12, and .21, at years 1, 2, 3, and 4, respectively). Maternal environmental influence is somewhat lower than heritability but also appears to be increasing as a function of the child’s age (.01, .05, .12, and .11, at ages 1, 2, 3, and 4, respectively).

Parameter estimates involving the HOME index also show developmental trends. For the most parsimonious model at each year (Table 8), the correlation between the index and parental G generally decreases as a function of child’s age (.54, .52, and .40, for ages 2, 3, and 4, respectively), rEI and the direct transmission parameter (c) are significant only during infancy and may be dropped from the model in early childhood.

Although these results suggest moderately high parental gene-index correlations, their contribution to the correlation between the HOME index and child’s IQ is not substantial. As outlined previously, this correlation can be decomposed into four sources – direct environmental transmission [ec], indirect environmental transmission [e²rEI (m + f)], indirect genetic transmission [hrGI], and indirect combined genetic-environmental transmission [ehrGI (m + f)]. The covariances due to these four sources may be derived using the parameter estimates from the most parsimonious models and are given in Table 9.

Path Analysis of IQ during Infancy and Early Childhood and an Index of the Home Environment in the Colorado Adoption Project - Table 9

As can be seen in Table 9, the indirect genetic source [hrGI] of the correlation between the index and offspring IQ is only about .20 at ages 2 through 4. However, this source of covariance is substantially larger than that due to indirect combined genetic-environmental transmission at those ages. At 2 years of age, the covariance attributable to the direct environmental source (.24) is about the same as that contributed by the indirect genetic source (.19), but it is nonsignificant at the other ages. Thus, the indirect genetic source of covariance between the HOME index and offspring IQ accounts for about one half or more of the observed covariance at 2 to 4 years of age.


The primary purpose of this study was to assess the etiology of relationships between environmental indices and behavior, and to determine if ostensible environmental influences are mediated at least in part by heritable factors. In order to accomplish this, we formulated an adoption model in which a measure of the home environment is related to an individual’s behavior directly as well as indirectly via correlations with parental environmental and/or genetic variables. Four sets of data spanning infancy and early childhood were analyzed to illustrate various relationships between the environmental (HOME) index and children’s IQ scores.

At age 1, evidence was found for both direct and indirect relationships between the index and offspring’s IQ. To illustrate the year-1 results shown in Tables 8 and 9, the relevant parameter estimates are presented in the form of a path diagram in Figure 3. The direct environmental effect can be derived [ec = (.95)(.09) = .08], as can the indirect environmental [e²rEI (m + f) = (.95²)(.13)(.07) ≈ .01] and the indirect genetic [hrGI = (.29)(0) = 0] effects. Therefore, the index-behavior relationship at age 1 appears to be solely a function of environmental transmission, both direct and indirect.

Path Analysis of IQ during Infancy and Early Childhood and an Index of the Home Environment in the Colorado Adoption Project - Figure 3

At age 2, direct environmental effects and indirect parental mediation of the index-behavior relationship were again found. However, the parental mediation at age 2 is genetic in origin, leading to a mixture of both direct environmental and indirect genetically mediated influences. In contrast, at ages 3 and 4, no evidence for direct environmental influences was found, although indirect parental mediation through latent genetic variables was significant. In contrast to the model formulated by Fulker and DeFries (1983), parental mediation was partitioned into genetic and environmental components in the present study. Results of the present study suggest that parental mediation is often genetic in origin (ages 2 through 4), and that the HOME may be a better environmental measure during infancy than in early childhood.

The developmental trends apparent in the data are dependent upon the assumption of isomorphism of measures – for parental general cognition and offspring IQ, as well as for longitudinal measures of child’s IQ and the home environment across the four ages of the offspring. Given these assumptions, a trend of increasing heritability and environmental transmission for IQ is seen. However, if the parent-offspring IQ measures are not isomorphic, then heritability is a function of h in adulthood (ha), h in childhood (hc), and the genetic correlation across the two ages – [hcrGcaha]. If we assume equal heritabilities of about .5 for IQ in the two generations (ha = hc; cf. Plomin & DeFries, 1980), then the genetic correlation between childhood and adulthood measures may be derived. Those indices of genetic stability are. 17, .26, .23, and .42 for ages 1 through 4, respectively. However, if heritability in childhood is about half that in adulthood (Plomin & DeFries, 1980; Wilson, 1983), then the genetic correlations are increased by the square root of 2 (.24, .37, .33, and .60 for ages 1 through 4, respectively). Thus, genetic continuity may be substantially greater at age 4 than at earlier ages. The increasing magnitude of these correlations as a function of age suggests that individual differences in mental ability during early childhood and adulthood are due to many of the same genetic influences.

Results of the present study and others point to the need for fully examining the etiology of ostensible environment-behavior relationships, rather than assuming that such relationships are mediated environmentally. Plomin, Loehlin, and DeFries (1985) pointed out that a simple comparison of adopted-offspring/index correlations with nonadopted-offspring/index correlations provides a test of parental mediation. If the latter correlation is larger than the former, then parental mediation of some type is suggested. The advantage of using a model-fitting approach is that the nature of this mediation can be explored in more detail. As the present results suggest, parental mediation may be either genetic or environmental in origin.

From a developmental perspective, results of the present study suggest that the heritability of IQ increases as a function of child’s age. Moreover, the relationship between ostensible environmental measures (e.g., the Caldwell HOME) and child’s IQ also increases. However, this change is not due to greater environmental influences – it is due to parental genetic mediation. That is, during early childhood, hereditary effects on IQ seem to be the mediating factor between parental cognition, parental scores on the HOME index, and offspring’s IQ, although during infancy (year 1) there is some direct environmental effect of the HOME on offspring’s IQ. This suggests that the HOME is an environmental measure only during infancy. In summary, the extent to which environmental measures are truely environmental in etiology and the extent to which parental mediation is either genetic or environmental in origin can be assessed from data on adoptive and nonadoptive families such as those tested in the Colorado Adoption Project.

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