Beyond Nature Versus Nurture: DF Analysis of Nonshared Influences on Problem Behaviors

Transcription

1 Developmental Psychology 1994, Vol. 30, No. 3, Copyright 1994 by the American Psychological Association, Inc. O0I2-1649/94/S3.0O Beyond Nature Versus Nurture: DF Analysis of Nonshared Influences on Problem Behaviors Joseph Lee Rodgers, David C. Rowe, and Chengchang Li J. C. DeFries and D. W. Fulker's (1985) regression model (since named DF analysis) used kinship pair data to separate heredity and shared environmental influences. This article extends DF analysis to include measured indicators of the nonshared environment. These indicators represent specific sources of environmental influence that cause related children to be different from one another. We present two empirical studies using twin, full-sibling, half-sibling, and cousin pairs from over 7, to 11 -year-old children in the National Longitudinal Survey of Youth. Study 1 is a validity analysis of kinship height and weight data. Study 2 is a DF analysis of problem behavior scores. Spanking, reading, and quality of the home environment are shown to account for nonshared variance. A third of a century ago, Anastasi (1958, p. 197) summarized the previous third of a century or so of work on heredity and environment: The traditional questions about heredity and environment may be intrinsically unanswerable. Psychologists began by asking which type of factor, hereditary or environmental, is responsible for individual differences in a given trait. Later, they tried to discover how much of the variance was attributable to heredity and how much to environment. It is the primary contention of this paper that a more fruitful approach is to be found in the question "How?" In that same spirit, in this article, we address a new methodology that can help answer the "how" question as applied to the nonshared environment. The methodology accounts for genetic, shared environmental, and nonshared environmental sources of variance, all within the same model. A simple but ingenious multiple regression model for analyzing kinship data was introduced in the behavioral genetic literature by DeFries and Fulker (1985) and has since been termed DF analysis by Plomin and Rende (1991), who highlighted this type of modeling approach in their general review of human behavioral genetics. Given models like the one underlying DF analysis, the name behavioral genetics is quickly becoming a misnomer; these methods are as powerful for studying environmental influences as they are for studying genetic influences. Or, more properly, the models simultaneously account for both Joseph Lee Rodgers, Department of Psychology, University of Oklahoma; David C. Rowe, Division of Family Studies, University of Arizona; Chengchang Li, Institute of Statistics and Decision Sciences, Duke University. Part of the work for this research was completed while Joseph Lee Rodgers was a visiting faculty member at Duke University in the Institute of Statistics and Decision Sciences. This research was supported by National Institute of Child Health and Human Development Grant RO1-HD We thank Henry Harpending, Lyle Jones, David Thissen, and three anonymous reviewers for comments on the manuscript. Correspondence concerning this article should be addressed to Joseph Lee Rodgers, Department of Psychology, University of Oklahoma, Norman, Oklahoma genetic and environmental influences. Alternatively, each type of influence can be controlled in the study of the other. Such control is necessary to solve the type of problem referred to by Scarr and Grajek (1982, p. 374): "Passive genotype-environment correlations arise in biologically related families and render all of the research literature on 'socialization' uninterpretable." The purpose of this article is twofold: First, we review DF analysis models and describe their breadth of application. As most previous development of the DF analysis approach has occurred in specialized journals, our focus here is on making this analytic method understandable and usable by the general developmental research community. Second, we describe and illustrate several extensions to the model. The new theoretical contribution of this article is one that introduces measured nonshared environmental influences into a model already accounting for genetic and shared environmental influences. We present two empirical analyses of child kinship pairs from the National Longitudinal Survey of Youth (NLSY) Child-Mother data, analysis of height and weight, and a larger analysis of problem behaviors in childhood. DF Analysis: Background Biometrical genetic concepts (Jinks & Fulker, 1970) offer a conceptual structure that apportions influences on developing children into genetic, shared (common) environmental, and nonshared (unique) environmental influences (see McCall, 1983; Rowe & Plomin, 1981). Shared influences are those that, by definition, make kin pairs (e.g., cousins, siblings, or twins) similar to one another. Nonshared environmental influences, by definition, make kin pairs different from one another. Recent work has shown that nonshared influences are considerably more potent than previously believed (e.g., Daniels, 1986; Dunn & Plomin, 1990; Plomin & Daniels, 1987; Plomin & Rende, 1991). DF analysis permits simultaneous testing and estimation of both genetic and shared environmental influences. Furthermore, as we demonstrate, nonshared influences can be accounted for as well. DF analysis was developed for and first applied to twin re- 374

2 BEYOND NATURE VS. NURTURE 375 search designs in which at least one member of a twin pair (the proband) is selected for some extreme trait (e.g., high IQ, reading disability). Such samples have been referred to in the literature as selected samples or trait-selected samples, because at least one proband per pair of relatives is identified on the basis of trait extremity. DF analysis of this type of sample uses the following regression equation: r = b 0 + b x K 2 + b 2 R + e, (1) where K t is the score for thefirstmember of the kinship pair, K 2 is the score for the second member of the kinship pair, R is the coefficient of genetic relatedness (R= 1.0 for identical twins, R =.5 for fraternal twins and siblings, R =.25 for half siblings, R =.125 for cousins, etc.), the bs are least squares regression coefficients, and e is the error or residual. The logic of this basic DF model is that nonselected siblings should "regress" to the population mean. That is, the cotwins of extreme twins should look more like the population average than their twin siblings who are the selected probands. If this return toward the population mean is greater for relatives who are less genetically related to each other, then the regression coefficient b 2 is mathematically related to a special kind of trait heritability, namely, the heritability of variation for extreme trait scores (h g 2 ), which may be different from the trait heritability in the general population (/z 2 ). The "augmented" DF model provides separate parameters estimating shared environmental (c 2 ) and genetic variation (h 2 ). This model is expressed in the following equation: (K 2 *R) + e. (2) In this equation, the b 6 coefficient estimates population h 2, the bn, coefficient estimates c 2, and other notation follows Equation 1. The coefficient with the interaction term, b 6, may be conceptually understood as follows: When it is statistically significant, kin resemblance is conditioned on the degree of genetic relatedness, hence the trait is heritable. The 64 coefficient, because it represents kin resemblance independent of genetic resemblance, must estimate shared environmental variation. The DF model in Equation 2 can be applied either to selected samples or to nonselected samples. The original authors, their colleagues, and a few independent research teams have published illustrations and extensions of the technique (Cherny, Cardon, Fulker, & DeFries, 1992; Cyphers, Phillips, Fulker, & Mrazek, 1990; DeFries & Fulker, 1985; Fulker et al., 1991; LaBuda & DeFries, 1990; LaBuda, DeFries, & Fulker, 1986; Ramakrishnan et al., 1992; Rodgers & Rowe, 1987; Zieleniewski, Fulker, DeFries, & LaBuda, 1987) and analytic work showing its validity (Cherny, DeFries, & Fulker, 1992; LaBuda et al., 1986). The assumptions that underlie the model are those of traditional behavioral genetic analysis, including additivity, trivial assortative mating, and equal shared environmental influences for the different levels of kinship pairs. In trait-selected samples, this latter assumption can be directly tested within the model by testing b 5. If nonsignificant, the assumption is plausible; if significant, the assumption is not strictly met, although the inclusion of the R coefficient and the estimated b s term adjusts the model for its violation. If nonselected samples, the b 5 term has a different interpretation that we discuss later. The residuals within Equation 2 (the e's) contain a combination of measurement error and the influences on the trait that are systematic but that do not operate to make kin pairs similar to one another. These latter influences are exactly what are referred to in the behavior genetics literature as nonshared or unique influences. Thus the DF model provides two powerful mechanisms for empirical analysis of kinship pair data. First, the model itself explicitly estimates genetic and shared environmental variation. Second, residuals from the model contain structure that is related to nonshared influences. We briefly review several early DF analysis articles. In the original article, DeFries and Fulker (1985) examined reading performance data from reading-disabled probands and their nonaffected cotwins (29 monozygotic [MZ] and 20 dizygotic [DZ] pairs). When they fit Equation 2, they estimated h 2 =.92 and c 2 = -.09; neither coefficient was significant in the context of small sample sizes, although a strong genetic influence and no shared environmental influence were suggested. Zieleniewski et al. (1987) added full siblings to the MZ and DZ reading data and estimated a number of subscale values of h 2 and c 2. LaBuda and DeFries (1990) extended these analyses to 117 reading-disabled twins (62 MZ and 55 DZ pairs). They fit Equation 2 and found h 2 =.52 and c 2 =.39. LaBuda et al. (1986) used 42 MZ and 37 DZ pairs, one of whom was reading disabled, and 45 MZ and 33 DZ control pairs who were not reading disabled (matched to the first group on age, sex, and zygosity). Using Equation 2, they obtained estimates of Z> 4 = c 2 =.36, b s =.21, and b 6 = h 2 =.68 for the reading-disabled sample, and 64 = c 2 = -.04, b 5 = -.85, and b 6 = h 2 =.86 for the control sample. They suggested that DF analysis "may be applied to either selected or nonselected datasets" (LaBuda et al., 1986, p. 432) and also "may be applied to other genetic relationships (e.g., adoptive and nonadoptive siblings) and to the analysis of more than two relationships simultaneously" (p. 432). Several DF analyses other than those on reading-disabled twins have been published. Plomin (1991)fit DF models to personality data from a sample of selected twins. Cyphers et al. (1990) used DF analysis to study infant and toddler temperament in nonselected twin pairs. Cognitive and intellectual ability measures in nonselected samples of twins were fit with DF analysis models by Cherny, Cardon, et al. (1992), Cherny, DeFries, and Fulker (1992), and Detterman, Thompson, and Plomin (1990). Virtually all previous DF analyses have used two levels of genetic relatedness, with two exceptions. Zieleniewski et al. (1987) used three levels of familial relatedness MZ and DZ twins and full siblings but only two levels of R, R = 1.0 and R =.50. Rodgers and Rowe (1987) used Fels Research Institute IQ data from a nonselected sample with five levels of genetic relatedness (MZ twins, siblings, half siblings, cousins, and random pairs) and estimated h 2 =.39 and c 2 =.39. They also fit DF models separately by age. (LaBuda and DeFries, 1990, p. 56, demonstrated a more elegant age adjustment by including age as an independent variable in the model.) The article by Rodgers and Rowe is, apparently, the only DF analysis using nonselected data and more than two levels of genetic relatedness. DF Analysis: Extensions We discuss four extensions of DF analysis in this section. The first two using multiple levels of kinship relatedness and non-

3 376 J. RODGERS, D. ROWE, AND C. LI selected samples have been introduced earlier. The second two applications to national data and adaptation of the model to include nonshared environmental influences are new. DF Analysis With Multiple Levels of Kinship and Nonselected Samples With the exception noted earlier, twin pairs have been used almost exclusively in work by DeFries, Fulker, and their colleagues. In twin research designs, DF analysis is equivalent to traditional behavioral genetic modeling in which correlations computed separately for levels of genetic relatedness are used to estimate h 2 and c 2 (e.g., Plomin, 1990, p. 43). However, correlational analyses are limited compared to the breadth of application of DF analysis. Whereas these simple approaches rely on categorization of levels of genetic relatedness, DF analysis treats the level of genetic relatedness as a measured characteristic of the kinship pair. Ultimately (when molecular genetic methods to do so are practically available), this approach would permit measuring the exact proportion of shared genes (which for siblings only averages.5, for half siblings,.25, and so on) and using that value in the regression model, rather than assuming an R of.5 for DZ twins and siblings,.25 for half siblings, and so on. In this case, computing separate correlations by level of R would be impractical, whereas DF analysis would handle such information easily and properly. Of course other sophisticated modeling approaches also permit comparison of multiple kinships (e.g., biometrical modeling approaches and pedigree likelihood methods). DF analysis permits many of the same kinds of analytic possibilities as these sophisticated methods, but with a statistical procedure that is simpler, straightforward, and in which developmental scientists have been widely trained. Cherny, DeFries, and Fulker (1992) presented a direct comparison betweenfindingsof DF analysis and biometrical LISREL analyses. One of the disadvantages of using multiple levels of genetic relatedness is the decreased likelihood that the equal environments assumption of the model will be met. Especially if kin pairs raised in different households are included in the analysis (e.g., cousin pairs, some half-sibling pairs), we expect the shared environmental influences to operate differentially by level of genetic relatedness. DeFries and Fulker (1985) suggested entering dummy variables into the model to distinguish particular categories in which the equal environment assumption is not met. Zieleniewski et al. (1987) illustrated the use of such dummy variables by adding regular siblings to their MZ and DZ twin data. Although DF analysis was developed for and wasfirstdemonstrated with selected samples, it works as well in general nonselected settings. In nonselected samples the estimated h 2 and c 2 apply to the trait in the general population (whereas in selected samples these values apply to heritability and shared environmental variance of extreme behavior; see LaBuda & DeFries, 1990, pp , for algebraic presentation). There are two theoretical issues that arise with nonselected samples of the type we treat in this article: the question of whether the parameter estimates of h 2 and c 2 are unbiased (given the model) and the problem of how to distinguish the proband (K 2 ) from the cotwin (AT,). The first problem is a technical theoretical issue. LaBuda et al. (1986) and Cherny, DeFries, and Fulker (1992) have given the expected partial regression coefficients of b 4, b$, and b 6 (showing unbiasedness) from Equation 2 for selected samples. In the Appendix, we present algebra showing expectations for these parameters for nonselected samples as well. The second issue is more practical and is easily handled with a simple data entry trick. In nonselected samples it is unclear which member of the pair should be identified as a proband and which as a cotwin. This problem is typically handled by using the standard doubleentry methodology (e.g., Haggard, 1958; LaBuda & DeFries, 1990). In the double-entry approach, every pair is entered twice, once with one member's score as the dependent variable and the other's score as the independent variable, and the second time with the independent variable and dependent variable scores reversed. In a sense this is not double entry at all (although this standard name will be used); rather, we are simply predicting each individual's score from that of their related kin (and other independent variables). In other words, the analysis of trait-selected samples uses a model of pairs, and the analysis of nonselected samples uses a model of individuals. The statistical problem that occurs because the two pairs are separate observations whose scores are not independent is easily handled by simply adjusting the sample size used for significance tests back to the number of pairs. Thus, stated test statistics and p values on computer printouts from double-entry analyses will be liberal, but the appropriate standard errors and critical values can be easily recomputed and the tests reinterpreted. DF Analysis Using National Samples DF analysis provides a natural analytic procedure for analyzing data from probability samples of large populations. The demographic orientation of national data collection efforts seldom accounts for genetic relatedness, even when within-family data are collected. But data management procedures can sometimes be used to link kinship pairs from such data sets, even when explicit genetic relatedness is unavailable. Hence, DF analysis of national data sources can provide a methodological bridge between these two traditionally separate endeavors. Information to link kinship pairs exists within the NLSY data set, for example, whose virtues for general psychological research have been promoted on many other grounds as well (e.g., Chase-Lansdale, Mott, Brooks-Gunn, & Phillips, 1991). Furthermore, in such data sources the plethora of variable domains support behavioral genetic modeling broadly within and across conceptual arenas. Plomin and Rende (1991) listed a number of areas within behavioral genetic research that have been neglected in past work. A surprising number of these can be treated by using DF analysis (or with other multivariate procedures; see Neale & Cardon, 1992) with the NLSY data. DF Analysis With Measured Indicators of the Nonshared Environment Since the introduction of DF analysis, its authors and their colleagues have illustrated several useful extensions of the DF analysis model. A test for differential c 2 s across genetic categories was illustrated in Zieleniewski et al. (1987). Other work

4 BEYOND NATURE VS. NURTURE 377 showed how to test for age and gender effects by including them as independent variables in the model (Fulker et al., 1991; La- Buda & DeFries, 1990). LaBuda et al. (1986) discussed using a dummy variable to compare selected twin pairs with nonselected twin pairs. Finally, Detterman et al. (1990) and Cherny, Cardon, et al. (1992) added quadratic and interaction terms to the augmented model to account for differential heritability across subgroups. Our adjustment is in the spirit of these previous DF model modifications, except that it uses measured variables and difference scores in place of dummy variables. The goal of our modification is to test for specific measured sources of nonshared environmental influences on the trait of interest. The model already accounts for shared environmental and genetic components through estimation of c 2 and h 2. The residuals of the augmented model thus contain extra information beyond genetic and shared environmental influences. The semipartial regression coefficients obtained by fitting additional variables will account for variance in these residuals. To measure nonshared sources of influence, we define difference scores from variables that might reasonably act to make related children different from one another. For example, we can think of many such variables that might influence problem behaviors in children. The amount that a mother spanks a child is one. Others include measures of maternal nurturing (e.g., amount the mother reads or speaks to a child), measures of paternal attention (e.g., amount of time the father plays with the child), or measures of punitive parental behavior. When we define a score measuring differences between treatment of two children, this difference score may have a systematic relationship to the residuals of the DF augmented model (or, equivalently, will cause the R 2 to go up significantly when added to the model). In this case, the result would suggest that this variable (or, of course, some other variable correlated with it) is an explicit source of nonshared influence on the child. Furthermore, if the difference score interacts with the genetic coefficient reflecting the level of relatedness of the pairs, this would suggest that the type of nonshared influence has a genetic component. The genetic component acting to make related children different from one another is obviously a source of nonshared genetic influence, an additional source of variance that this formulation can account for. This adjustment can be defined explicitly within the following two extensions of the DF analysis models: K t = b n + b» K 2 + b 9 R + b l0 (K 2 *R) + &,, ENVDIF+e, and (3) b l3 K 2 b l5 (K 2 *R) + b l6 ENVDIF + b u (ENVD\F*R) + e, (4) where the Ks are the scores for Kin 1 and Kin 2 on the trait of interest (as before), R is the coefficient of genetic relatedness, ENVDIF is a difference score from the two kin on a specific measured environmental source that might account for differences between them on the trait, the bs are least squares regression coefficients, and the es are error terms or residuals. Within these models, the ENVDIF variable provides tests for a nonshared environmental influence. The interaction of this term with R provides a test for a nonshared genetic influence, given that the nonshared environmental influence has been detected.' A comparison of the R 2 from the most complete model with that from the regular augmented model (Equation 2) provides a test of whether the particular nonshared influence reflected in ENVDIF is related to the differences between the kin pairs. Testing the specific coefficient associated with ENVDIF (Z>, r) is a test for a particular nonshared environmental influence. Testing the interaction coefficient of ENVDIF and R (bn) is a test for whether this nonshared environmental influence differs by genetic category; if so, this suggests a nonshared genetic influence as well. A reasonable general logic (others exist as well) would be to first fit the augmented model from Equation 2 to the data as a preliminary analysis to detect genetic and shared environmental influences on the trait. If this model can be refined by deleting terms (e.g., Cherny, DeFries, & Fulker, 1992), then Equations 3 and 4 could be so adjusted as well. Next, the full model reflected in Equation 4 could be fit, and the interaction component corresponding to b n evaluated. If it is significant, then the ENVDIF variable can be evaluated by testing b i6 in the full model. If the interaction term is not significant, it can be dropped and ENVDIF can be evaluated by itself, a test of b n from Equation 3. All of these tests are printed out in the Type I and Type III tests routinely reported in a statistical package like SAS's (Statistical Analysis System's) PROC GLM. If the model in Equation 4 is fit, tests ofbn and b\(, are included in the Type III tests, and a test of b\ \ is contained in the Type I test (assuming variables are ordered as listed in Equation 4). This model comparison strategy can be applied individually to any number of measured nonshared influences. Or, two or more difference variables could be added simultaneously (along with their interactions with R). Furthermore, any of the model modifications already suggested in the literature can be combined with those in Equations 3 and 4. Thus, for example, gender differences in the nonshared environmental influence of maternal spanking on problem behaviors in twins and siblings could be evaluated. 1 There are other formulations to account for nonshared environmental influences as well. As one anonymous reviewer noted, we could use, "for example, residual environmental scores for one twin with the contribution of the other partialed out." Such formulations are excellent ways to investigate nonshared environmental influences. Our extension of DF analysis has the attraction of accounting for the nonshared environment within the same model that is used to account for genetic and shared environmental influences. We note that derivations of unbiasedness for /r 2 and c 2 (e.g., LaBuda, DeFries, & Fulker, 1986) assume that the correct model is specified in Equation 2 (e.g., Draper & Smith, 1981, p. 117). But adding extra variables to a model even if they should not be there does not bias estimates of parameters associated with other variables (it can, however, decrease the precision of those estimates). On the other hand, leaving out variables that should be there (e.g., the nonshared environmental influences that we are modeling) can bias the other estimates. Thus, testing for nonshared environmental influences within our formulation leaves the coefficients estimating h 2 and c 2 unbiased. Furthermore, including these terms can potentially reduce bias in h 2 and c 2, to the extent that these specific nonshared environmental influences account for real variance in the original scores.

5 378 J. RODGERS, D. ROWE, AND C. LI Several caveats apply to such modeling exercises. First, because such models quickly become very complex, the tests should be driven by a theoretical rationale. Second, the assumptions an additive model, trivial assortative mating, and equal environments carry through to these more complex analyses. Third, in most DF analyses there will be different numbers of members of the genetic categories. This can impose an artificial correlational structure on the analysis. In highly unbalanced designs, the estimated coefficients can depend on the numbers of pairs of each level as well as the correlational structure that is being modeled; caution should be exercised in conclusions drawn from such settings. Finally, tests for nonshared influences are for specific sources of influence, those reflected by (or correlated with) EN VDIF variables. Unlike the tests for genetic and shared environmental influences, these should not be considered general tests of these nonshared influences. NLSY Data Set Method The NLSY survey began in 1979 as a household probability sample of 11,406 civilian respondents age years in the United States. Because the survey interviewed all available youth in a sampled household (household N = 2,400), many siblings are represented within the sample: 3,336 original respondents lived with one sibling, 1,705 with two, 591 with three, 126 with four, and 18 withfive.in 1986, when the original sample ranged in age from 21 to 28 years, all children ever born to NLSY women were interviewed. Of the 5,828 original women, 3,053 (52%) had children by An extensive battery of assessments was completed for 4,971 children (95% of the 5,236 contacted). By 1988, when the second child assessment was completed, a total of 7,346 children had been born. Thus, within the NLSY-children data set are a large number of siblings and half siblings, and a few twins of unknown zygocity. In addition, because the children of sisters from the original sample were cousins, a large number of cousins are identifiable in the data set as well. The NLSY contains no explicit information about genetic relatedness. Zygocity of twins was not established, and full and half siblings were not distinguished. However, we were able to take advantage of certain variables suggestive of genetic relatedness to classify a large percentage of the NLSY children kinship pairs. Using our classification algorithms, we constructed 165 cousin pairs, 182 half-sibling pairs, 451 full-sibling pairs, and 24 same-sex twin pairs. 2 These were assigned R values of.125,.25,.50, and.75, respectively. (Opposite-sex twin pairs were automatically assigned to R =.50; same-sex twin pairs of unknown zygocity were assigned an R =.75, because in the population, half of same-sex twin pairs should be MZ and half DZ.) We limited our analyses to children between the ages of 5 and 12 years (which accounted for most of the sample) to support our focus on preadolescent children (and also because the age-adjustment procedure we describe later would become nonlinear beyond age 12). The 822 NLSY kinship pairs were double-entered, resulting in 1,644 total observations (which were reduced slightly for each analysis by the restriction to ages of 12 years and under not a very limiting restriction, because few of the NLSY children were over 12 and missing data patterns). Variables We report two different studies of the NLSY data. Thefirstis a small validity study of height and weight scores from the NLSYfiles.For this analysis we used measures obtained at the 1986 interview. Height was measured in inches, weight in pounds. In our larger study demonstrating the several extensions discussed earlier, we used measures of problem behaviors. Our primary dependent variable was the Behavior Problem Index (BPI). The BPI was developed by Peterson and Zill (1986); many of its items came from the earlier Behavior Problems Checklist developed by Achenbach and Edelbrock (1981). The BPI is scaled and normed to have a national mean of 100, and high scores indicate higher levels of behavior problems. Because the NLSY children in our study are children born to unusually young mothers, selection bias exists for variables related to maternal age. The mean BPI score among the NLSY children is and increases systematically with the age of the child; the mean for children 10 years old and over is 111.4, for those 8 to 9 years old it is 109.8, for those 6 to 7 years old it is 108.6, and for those 4 to 5 years old it is (Center for Human Resource Research, 1991, Table ). In addition to an overall BPI score, there were six subscales: BPI- Antisocial, BPI-Anxious/Depressed, BPI-Dependent, BPI-Hyperactive, BPI-Peer Conflict, and BPI-Headstrong. Correlations between the subscales ranged from.26 (for Dependent with Antisocial) to.53 (for Headstrong with Anxious/Depressed and for Headstrong with Hyperactive). Part-whole correlations between subscales and the BPI-Total ranged from.53 for Peer Conflict to.81 for Headstrong. Note that the BPI subscales can be divided into two groups: one a set of measures of how the child interacts with the social environment (Antisocial, Headstrong, Peer Conflict, and, to some extent, Dependent), and the other a set of measures of more traitlike features of the child (Anxiety, Hyperactivity, and Dependent). The independent variables we used to evaluate nonshared environ- 2 In the NLSY data, sibling and half siblings are simply listed as being in the sibling category. We used two other variables from the NLSY and the following logic to separate them. All siblings and half siblings were living with their common mother (because the design of the child survey involved interviewing all biological offspring of the mothers from the original NLSY survey). Mothers indicated whether the father of each child lived in the home. If the father of both members of a "sibling" pair lived in the home with the mother, we classified the two as full siblings (which further assumes that few mothers live simultaneously with different fathers of her two children). If the father of one member of a sibling pair lived in the home and the other's father did not, we classified the two as half siblings. If neither father lived in the home, we looked at a second variable for each child, in which the mother indicated how far away the child's father lived (with four orfivecategories: within 1 mile, 1-10 miles more than 200 miles). If these did not match, we classified the two children as half siblings. If they did match, we considered the sibling status indeterminate. Of the total of 962 pairs of siblings, 451 (47%) were classified as definitely full siblings, 182 (19%) were classified as definitely half siblings, 212 (22%) were classified as probably full siblings, and 117 (12%) were indeterminate. Although we performed analyses with various combinations of these categories, we report those using the classifications for which we are sure, based on 633 (66%) of the sibling pairs. The slightly smaller sample sizes listed in the text were caused by missing data patterns in the height, weight, and age variables. We classified cousins by linking the children of mothers who we knew to be sisters from the original NLSY data set. Because some of those NLSY mothers may have been half sisters (and their children therefore half cousins), some of these cousin pairs may be slightly misclassified, although the effect of misclassification around genetic coefficients ofr =. 125 (for cousins) is probably not enough to damage the DF analysis. We are currently working on algorithms to define genetic relatedness of the original NLSY respondents (the mothers in the present study), which will support better classification in both data sets. Of course, ultimately, this type of genetic information should be collected in national surveys directly from the respondents as a part of routine data collection.

6 BEYOND NATURE VS. NURTURE 379 mental and genetic influences (from which ENVDIF scores were constructed) were chosen on theoretical grounds from dozens available in the NLSY data file because we believed that they might explain differences between related children in their problem behaviors. The measures we used came from the overall scale and two specific items from the Home Observation for Measurement of the Environment (HOME) measure. The specific items indicated how often the mother spanked the child in the last week (ranging from 0 to 16 times or more) a measure of punitive behavior and how often she read to the child (coded into one of six categories ranging from 1 = never to 6 =. every day) a measure of maternal nurturing. The HOME scores in the NLSY files were obtained by using the HOME-SF (short form), a modification of the overall HOME Inventory (Caldwell & Bradley, 1984). This instrument combines the mother's responses about her child and the child's responses into an overall measure of how rich and supportive the child's environment is. Different forms of the HOME were administered to children 3 to 5 years of age, those 6 to 9, and those 10 and older, and HOME scores were age standardized. Specific items were not age standardized, however, and we used a regression adjustment that is described shortly. The Center for Human Resource Research (1989) reported reliabilities for the BPl-Total of.87 and subscale reliabilities between.54 and.69. For children age 6 and above, HOME reliability was.70 for the total test, with subscale reliabilities in the lower.60s. Validity properties of these measures have been carefully studied, and a large literature documents their theoretical and practical utility. Because we averaged ageadjusted BPI and HOME scores from two ages, actual reliabilities were higher than these. Wefitthe models to the combined four-category (cousins, half siblings, full siblings, and twins) data set. The large sample sizes in the NLSY data set result in reduced standard errors compared with smaller data sets, which naturally increases the power available to test hypotheses. Furthermore, the fact that these children were born to a probability sample of women increases the generalizability of the sample. Nevertheless, we hasten to note that the select nature of the mothers (and therefore also of the children) weakens the external validity of these data. However, although the national appearance of our data set is valuable, our methods focused more strongly on internal validity than on external validity. Before we could run the DF analysis, the different ages of the matched kin (except, obviously, for twins) were accounted for. Some variables were already age adjusted in the norming process (e.g., the BPI and HOME-Total score). For the others, we ran a preliminary regression analysis of each variable on age for the whole data set (and these regression were, as expected, highly significant). Then we constructed residuals for each variable from the regressions. For children in this age range, it was not necessary to conduct separate regressions by sex. We also investigated nonlinear regressions (e.g., height on age 2 ) as well. Because the most complete and comprehensive height and weight scores were collected during the 1986 interview, we used that wave of data for our first study. For the problem behavior analysis, we used an average of nonmissing scores from the 1986 and 1988 surveys as the variables to enter into the models. Because there are missing data for some children for one or the other year, this allowed us to maximize sample size (since all that was required was a particular score from 1986 or 1988; for most respondents we had both). We note that, because a mother gives information about all of her children, our HOME and BPI measures for twins and siblings can have artificially inflated correlations. If mothers tend to rate their children identically, then correlations would approach 1.0. However, inspection of the scores indicates that mothers were quite willing to rate their children as different. For example, 1986 BPI and HOME sibling correlations were.50 and.83, respectively. Many of the items on the HOME scale are automatically equal for different children in the family (e.g., "How many magazines does your family take?" and "Is the home interior clean?"). Sibling correlations for the particular spanking and reading items from the HOME (with scores averaged across the 2 years), which are explicit measures of the unique environmental or genetic influences, were.46 and.60, respectively. Previous researchers (e.g., Plomin, DeFries, & Fulker, 1988) have considered the HOME a more objective measure of features of the child's family environment than other studies that rely on direct responses of the children. Results Study 1: DF Analysis ofheight and Weight When DF analysis using Equation 2 (the augmented model) wasfit to the age-adjusted weight scores, we obtained estimates of &, = c 2 =.01, b 5 = -2.5, and b 6 = h 2 =.69. Standard errors were.06 for b 4, 1.50 for b 5, and. 15 for b 6 ; b 6 was significant (p <.0001), b$ and b A were nonsignificant (note that sample sizes have been adjusted to the number of pairs for double-entry significance tests, as previously discussed). Grilo and Pogue-Geile (1991) presented a general review of behavior genetic studies of weight and obesity. By combining results from many studies, they reported estimates of A 2 =.70, c 2 =.00, and significant levels of nonshared environmental influence that account for around.20 of the variance (also see Stunkard, Harris, Pedersen, & McClearn, 1990). Plomin, De- Fries, and McClearn (1990, p. 322) suggested a "broad-sense heritability" of weight of r 2 =.66. These are virtually identical to those obtained from our analysis of the NLSY data. Our estimates of A 2 and c 2 are within.01 of those obtained by Grilo and Pogue-Geile and within.02 of the Plomin et al. estimate. Furthermore, the existence of 30% of unaccounted variance suggests the possibility of nonshared sources of environmental influence on the weight scores in the NLSY data. When DF analysis was run on the age-adjusted height scores, we obtained estimates of b t = c 2 =.01, b 5 =.31, and b 6 = h 2 =.87. Standard errors were.08 for b A,.44 for b$, and. 17 for b(,. Only b(, was significant (p <.0001). Plomin (1990) noted that three types of behavior genetic designs studies using identical twins raised apart, those comparing identical and fraternal twins, and those comparing parents and offspring all converge on a height heritability estimate of h 2 =.90 (also see Mittler, 1971). The estimate from the NLSY data is only.03 away from his estimate. These results strongly support the validity of DF analysis in our nonselected national sample with multiple levels of kinship. Estimates of h 2 were remarkably similar to those in the literature, and estimates of c 2 matched statements in the literature concerning the virtually nonexistent shared environmental influences on these two variables. Obviously, this validity analysis applies to particular traits, and ones that are highly heritable. However, estimates of heritability are known much more precisely than are those of c 2, so this is a reasonable starting point to demonstrate that DF analysis can work effectively in nonselected populations, with multiple levels of kinship, and in large national data sets. We now turn to a demonstration of our extension of DF analysis to account for nonshared environmental influences.

7 380 J. RODGERS, D. ROWE, AND C. LI Table 1 Mean Absolute Difference and Correlations Between Cousins, Half Siblings (HS), Full Siblings (FS), and Twins in the NLSY Children Data, by Level of Genetic Relatedness Mean absolute differences r Variable Cousins HS FS Twins Cousins HS FS Twins BPI-Antisocial BPI-Anxiety BPI-Headstrong BPI-Hyperactivity BPI-Dependent BPI-Peer Conflict BPI-Total Note. The average sample size (number of pairs) is 144 for cousins, 170 for half siblings, 428 for full siblings, and 23 for twins. NLSY = National Longitudinal Survey of Youth; BPI = Behavior Problem Index. Study 2: DF Analysis ofproblem Behaviors In Table 1 we present mean differences and correlations between kinship BPI scores by genetic category. Across different levels of R, the order of similarity is consistent with a genetic influence for the BPI and its subscales. Of course the genetic model makes stronger predictions than just the order of correlations, and these quantitative predictions are used by DF analysis; similarity beyond genetic predictions are modeled as shared environmental influences. After similarities are accounted for, our extension models the patterns in the remaining measured differences between children. Some of the twin correlations are surprisingly high, in particular for Peer Conflict (r =.96) and Hyperactivity (r =.90). We account for these in part by noting the "autocorrelation" caused by a mother rating both twins. But the inflation is substantively interpretable as well, because twin children act as the primary peer for one another. These high correlations suggest substantially higher similarity among DZ twins than among full siblings, which is predictable in variables like peer conflict; almost certainly some of the size is due to measurement artifact as well. Because of these high correlations, and because we lack zygocity information, we ran our analyses both including and excluding twins. In Table 2 (on the left), we present results from fitting the augmented DeFries and Fulker (1985) model to data from twins, full and half siblings, and cousins, which gave estimates of h 2 and c 2. The b 5 coefficient has an expected value of -h 2 % as previously discussed. Comparison of the h 2 estimates from b$ and bf, suggests consistency across these two different coefficients. After dividing the b$ coefficients by the opposite of the mean of the trait (to obtain h 2 ), fa and bf, h 2 estimates are.65 and.60 for BPI-Antisocial,.96 and.92 for BPI-Anxiety,.21 and.21 for BPI-Headstrong,.82 and.77 for BPI-Hyperactivity,.75 and.70 for BPI-Dependent,.41 and.37 for BPI-Peer Conflict, and.78 and.74 for BPI-Total. The b$ h 2 estimates were consistently slightly higher than those from b 6. Analyses of variance testing whether the seven dependent variable means were different across levels of R were consistently significant, casting doubt on the validity of the equal environments assumption. Inspection of means showed that BPI means for half siblings were systematically larger than for the other categories. When the DF analysis was re-run with only three levels of relatedness (i.e., excluding half-sibling pairs), h 2 and c 2 estimates were similar to those in Table 2, and differences between h 2 estimates from b 5 and b$ were smaller. We also reran the analyses excluding the 23 twin pairs. The right side of Table 2 shows coefficients from this analysis. Patterns of results are virtually identical, with the exception that BPI-Peer Conflict heritability dropped to zero. We have already noted suspicious correlations among twins for BPI-Peer Conflict, so that it is not surprising that this subscale was influenced by dropping twins from the analysis. In summary, in the four-level analysis, six of the seven dependent variables (all except Headstrong) had a significant h 2, and three of the seven had a significant c 2 (see Table 2). The difference between the sum of these two values and 1.0 is a measure of how much nonshared variance and measurement error is left in the system. The amount of variance left to be explained by a combination of nonshared influences and measurement error ranged from 10% to 49%. Table 2 shows a clean and interpretable pattern of substantive results. The variables that show significant shared environmental components are exactly those that are environmentally based measures. To engage in peer conflict, to be headstrong, or to be antisocial (which had a marginally significant c 2 ) requires another actor from the social environment to express those behaviors. The other measures, anxiety and hyperactivity in particular, are more trait-based measures that we do not expect to be as sensitive to environmental influences. Headstrong had the strongest environmental component, and it was the only dependent variable for which there was no evidence of genetic influence. In the next step we added into the model difference scores from the HOME reflecting nonshared environmental influences (which we call HOMEDIF scores). The reestimated h 2 and c 2 measures are on the left-hand side of Table 3; these are very similar in all cases to those estimated from the augmented DF model but are less biased if the nonshared sources should be included in the model. Coefficients and significance tests for each nonshared influence are shown on the right side of Table 3. If the interaction terms are significant, then the coefficient testing the HOMEDIF variable is 6 i6 from Equation 4; if the

8 BEYOND NATURE VS. NURTURE 381 Table 2 Results offitting the Basic DF Multiple Regression Models to BPI Scores From Kinship Pairs From the NLSY Children Data Shared influences, twins included Shared influences, twins excluded Variable c 2 b~ t 6 5 h 2 h c 2 b* 6 5 h 2 h BPI-Antisocial BPI-Anxiety BPI-Headstrong BPI-Hyperactivity BPI-Dependent BPI-Peer Conflict BPI-Total * *.17* -71.2* * * -79.2* -43.7* -84.9*.60*.92*.21.77*.70*.37*.74* * *.20* -66.5* -94.7* * -65.8* *.55*.86*.13.54*.56* * Note. DF = DeFries and Fulker (1985) analysis; BPI = Behavior Problem Index; NLSY = National Longitudinal Survey of Youth; c 1 = shared environmental variation; /i 2 = genetic variation; b& = least squares regression coefficients. *p<.05. interaction is not significant, the coefficient is b n from Equation 3. Two of the subscales (BPI-Anxiety and BPI-Headstrong) had significant interactions. Differences in the overall HOME scores (the HOMEDIFs) were significantly related to the differences between the kin pairs after the genetic and environmental similarity had been accounted for, for all dependent variables except for BPI-Peer Conflict. All coefficients with the HOMEDIF scores were negative, suggesting that the higher scoring member of the kin pair on the HOME had lower behavioral problems. (Note that because of the double-entry format, these were entered as signed difference variables; thus, a particular ENVDIF value for one member of the pair was always opposite that for the other member of the pair.) Next, we turned to the specific spanking and reading variables and evaluated whether differences in (age-adjusted) spanking (SPANKDIF) and reading (READDIF) scores were related to differences in problem behaviors. For spanking, none of the SPANKDIF variables interacted with the genetic categories, suggesting absence of nonshared genetic influences. Three of the SPANKDIF variables were significant, however, for BPI-Antisocial, BPI-Headstrong, and BPI-Total. The coefficient for each was positive, suggesting that the member of the kin pair spanked the most had higher levels of behavioral problems. This analysis suggests that, net of shared genetic and environmental influences, spanking (or some variable closely correlated with it) is related to higher levels of behavioral problems in general, and to antisocial and headstrong behavior in particular. Of course the causal direction is ambiguous; whether spanking causes higher behavioral problems or whether children with behavioral problems get spanked more (or both) is not distinguishable. In either case, there is question raised from these results as to whether spanking has the desired result of "adjust- Table 3 Results offitting the Adapted DF Multiple Regression Models to BPI Scores From Kinship Pairs From the NLSY Children Data Nonshared influences Variable c Shared influences h fr or 6.6 HOME 6,7 6.i or 6.6 Spanking 6,7 6..or6i6 Reading 6,, BPI-Antisocial BPI-Anxiety BPI-Headstrong BPI-Hyperactivity BPI-Dependent BPI-Peer Conflict BPI-Total.15*.01.35* *.20* -64.4* -95.7* * -79.9* -36.5* -78.0*.54*.87*.13.75*.70*.30.68* -.018* -.013* -.019* -.010* -.005* * *.041* * * * Note. A 6n coefficient is estimated if the 6.7 coefficient is nonsignificant. A 6.6 coefficient is estimated if the 6 J7 coefficient is significant. See the text for an explanation of the model-fitting logic and statements of the models. DF = DeFries and Fulker (1985) analysis; BPI = Behavior Problem Index; NLSY = National Longitudinal Survey of \buth; c 2 = shared environmental variation, ft 2 = genetic variation; 6s = least squares regression coefficients. *p<.05.

9 382 J. RODGERS, D. ROWE, AND C. LI ing" children's behavior in a positive direction. These are provocative questions and interesting results for child psychologists and health-care experts. When the difference between the amount that the mother read to the child (READDIF) was entered into the model, none of the interactions or the READDIF variables were significant. The coefficients were consistently negative, suggesting that any effect is in the direction of lower behavioral problems for the member of the kin pair who was read to more. Of particular note is that the highest coefficients for the READDIF variables were the same as the highest coefficients for the HOMEDIF and SPANKDIF variables for BPI-Total, BPI-Antisocial, and BPI- Headstrong (all of which were marginally significant in statistical tests). In summary, two of the BPI subscales and the BPI-Total were consistent in suggesting nonshared environmental influences associated with specific behaviors. Nonshared genetic influences were found for only two of the subscales for the overall HOME measure. BPI-Antisocial and BPI-Headstrong had the highest coefficients for all three nonshared measures, spanking, reading, and the overall measure of the home environment. This consistent pattern of results across the three different measures of the nonshared environment perfectly matches the findings for the shared environmental coefficients in Table 2 as well. Thisfindingis the first of the two empirical findings we would like to highlight from this DF analysis. It appears that the behaviors measured by the BPI-Antisocial and BPI-Headstrong subscales are those that are particularly susceptible to environmental influence, both shared and nonshared. Our analyses show consistent environmental influence on antisocial and headstrong behavior. Finally, the second result we would like to highlight is that five of the six BPI subscales and the overall BPI-Total had nonshared environmental influences identified in relation to the overall HOME measure. This is a notable success in illustrating the utility of this analytic technique. The HOME is a general and reliable measure of the quality of the home environment; if nonshared environmental influences are as potent as the literature is suggesting they are, we would fully expect that differences in the HOME should be related to differences in BPI scores. To provide context for these differences, we note that the increase in overall R 2 obtained by adding the unique environmental and genetic measures to the model is small. The R 2 s for the augmented DeFries and Fulker model ranged from 9% to 23%. The addition of the unique environmental variables typically added 1% or even less to the R 2. This was often a highly reliable addition, given the large sample sizes; however, there is still a great deal more unexplained variance in the BPI scores than there is explained variance. We note, however, that reliably explaining even 1 % of the variance in national data using a specific measure of sibling differences and with proper controls to account for both genetic and shared environmental influence (which themselves account for a great deal of the variance between families) may be a considerably more valuable modeling exercise than many others that have explained more variance in problem behaviors. Furthermore, this 1% of the total may be as high as 5%-10% of the remaining family variance after shared environment and heritability are accounted for. Also, we were testing for specific nonshared influences, so that identifying several of these might combine to account for much more variance than any single source would. Discussion DF analysis has hidden dimensions. Originally, it was proposed as a method for estimating h 2 and c 2 in selected settings with MZ and DZ twin data. Then, a number of adaptations were proposed by the original developers and their colleagues, including model adjustments to account for age, gender differences, ability differences, and differences in selected versus nonselected settings. All of these approaches focused on the results of DF analysis. The adjustment proposed here to the DF analysis model extending it to nonshared genetic and environmental sources of influence used the original DF analysis model to control for the shared influences. Then, we studied the nonshared influences by entering potential causes of differences between the related kin into the model (along with its interaction with genetic relatedness). We illustrated earlier that the model can account for features of the family environment that relate to the differences between related children in their problem behavior, after the similarities have been accounted for. The overall HOME environment scale was a source of nonshared environmental influence for almost all of the behavioral problems scales and subscales investigated. How much the mother spanked the child and how much she read to the child were more specific potential sources of both nonshared environmental and nonshared genetic influence. Furthermore, we added both theoretical and empirical support for using DF analysis in nonselected populations and with more than two levels of relatedness. We showed that the interpretation of one parameter of the augmented model shifts in nonselected settings, and we demonstrated the validity of DF analysis in such settings by matching results of a DF analysis of NLSY height and weight scores to those from the literature. The matches were close. The DF analysis approach has, in less than a decade, been adapted in a number of ways to increase its breadth and utility. Other adjustments would push its value even further. Ideally, a model like the original DF model providing quantitative estimates for nonshared environmental and genetic influences in a general sense would be valuable. Alternatively, it would be valuable to have tests for the specific mechanisms underlying the general estimates of shared environmental influences that come from the original augmented model. We are currently working on methods to evaluate these similar to the one proposed here for specific nonshared influences (e.g., Rowe & Waldman, 1993). DF analysis is rapidly becoming not just a model but a very flexible approach to the analysis of kinship data. The numerous extensions that have been proposed since its publication only 9 years ago provide early hints as to its ultimate utility. Those who criticize behavioral genetics for past preoccupation with estimating heritabilities and for focusing on the nature-nurture competition will appreciate how DF analysis can simultaneously account for each in the presence of the other. Ultimately, the DF approach may provide a powerful and systematic way to search for specific mechanisms Anastasi's (1958)

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Multiple regression analysis of twin and sibling data. Personality and Individual Differences, 8, (Appendix follows on next page)

11 384 J. RODGERS, D. ROWE, AND C. LI Appendix Expectations for & 4, b 5, and b 6 From Equation 2 in Nonselected Samples LaBuda, DeFries, and Fulker (1986) developed expectations of the regression coefficients estimated from the augmented model in selected samples; Cherny, DeFries, and Fulker (1992) provided expectations for certain submodels. La Buda et al. showed E(b*) = c 2, E(bt) = h 2, and E(b 5 ) = 2{(C MZ - C DZ ) -J/WA 2 + c 2 ) - P DZ (h 2 /2 + c 2 )]}, where Pis the mean for probands, C is the mean for their cotwins, and MZ and DZ index monozygotic and dizygotic twins, respectively. Thus, b 4 and bf, axe unbiased estimates of A 2 and c 2. Their algebra for b* and b 6 applies whether the sample is selected or nonselected. We show here that the expectation for b$ simplifies if the sample is nonselected, however. In this case, because the data are double^ntered (so that every subject is both a proband and a cotwin), C M z = PMZ and C DZ = P DZ. CalHhese MZ and DZ, respectively. Then, E(b s ) = 2{MZ (i - A 2 - c 2 ) - Z>Z( 1 - h 2 /2 -c 2 )}. But assuming that the MZ and DZ twin means are the same in the population (a reasonable assumption in nonselected samples), which we call T (an estimate of the mean of the trait), this reduces to E(b,) = -/r*f (Henry Harpending originally suggested this result to us). Thus, theft 5 term does not give a test for equal environments in nonselected samples, but rather provides a second estimate of h 2 (once bs is divided by the opposite of the trait mean). The h 2 estimates that derive from b 5 and b 6 can be compared to judge the internal consistency of these two different estimates from nonselected samples. These two different h 2 estimates will be equal only if the means from the separate levels of relatedness are equal in the sample. In other words, while their expectations are the same across samples, b 5 depends on equality of the MZ and DZ means to provide an estimate of A 2 that is the same as that in b 6. To the extent that these means are different, the two h 2 estimates will be different. If these differ by more than sampling variability, the question is raised as to whether the different samples truly came from unselected populations (in which these means are expected to be equal). The definition of expected partial regression coefficients (the bs from Equations 1 and 2) were presented in LaBuda et al. (1986) and adapted for nonselected samples above assuming only two levels of genetic relatedness, MZ and DZ twin pairs. The equivalent derivations for more than two levels of relatedness including nontwins as well as twins (e.g., cousins or half siblings) could be derived similarly, although the number of terms in the variable expectations used to define the expected variance and covariance matrices gets unwieldy quickly. We are developing simpler algebra for the expected values of A 2 and c 2 for nonselected samples that will be presented in future work. Received August 19, 1992 Revision received August 4, 1993 Accepted August 4,1993