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Understanding How Family Socioeconomic Status Mediates the Maternal Intelligence–Child Cognitive Outcomes Relationship: A Moderated Mediation Analysis D. Diego Torres
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Houston Education Research Consortium , Kinder Institute for Urban Research, Rice University , Houston , Texas , USA Published online: 12 Nov 2013.
To cite this article: D. Diego Torres (2013) Understanding How Family Socioeconomic Status Mediates the Maternal Intelligence–Child Cognitive Outcomes Relationship: A Moderated Mediation Analysis, Biodemography and Social Biology, 59:2, 157-177, DOI: 10.1080/19485565.2013.833804 To link to this article: http://dx.doi.org/10.1080/19485565.2013.833804
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Biodemography and Social Biology, 59:157–177, 2013 Copyright © Society for Biodemography and Social Biology ISSN: 1948-5565 print / 1948-5573 online DOI: 10.1080/19485565.2013.833804
Understanding How Family Socioeconomic Status Mediates the Maternal Intelligence–Child Cognitive Outcomes Relationship: A Moderated Mediation Analysis
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D. DIEGO TORRES Houston Education Research Consortium, Kinder Institute for Urban Research, Rice University, Houston, Texas, USA In a model of moderated mediation using matched data from the 1979 National Longitudinal Survey of Youth and the 1979 National Longitudinal Survey of Youth, Children and Young Adults, I test (1) whether family socioeconomic status (SES) mediates the maternal intelligence-child cognitive outcomes relationship and (2) the extent to which this mediating impact is dependent on the level of maternal intelligence. Results reveal that the mediating impact of SES on the maternal intelligence–child cognitive outcomes relationship varies as a function of the level of maternal intelligence. The positive effect of higher SES on children’s academic ability decreases as the cognitive ability of mothers increases, such that children in low IQ households benefit most from higher SES, while children in high IQ households benefit somewhat less.
The covariance between socioeconomic status (SES) and phenotypic IQ is well known in the field of behavioral genetics (Gottfredson 2011). About 30 percent of the variance in the primary factors that comprise SES indices is explained by cognitive ability (Neisser et al. 1996:82). Gottfredson (1997), Jensen (1998), and Rowe (1997) have highlighted that tests of intelligence, in both the civilian and military spheres, reveal individuals’ ability to appropriate difficult material and expose the rate at which individuals can learn new material. Taken together, these two factors are strongly predictive of the type of employment individuals can perform well and therefore the amount of income they are likely to earn. Research also shows that higher levels of cognitive ability are required in more prestigious occupations (Gottfredson 1997:87), and the more prestigious the job, the greater the level of remuneration. Moreover, the predictive validity of general cognitive ability for both job performance and training rises with the overall complexity of the work being done (Gottfredson 1997:82). Since one of the most studied relationships in social science research is that of parental SES with children’s cognitive and academic development (Astone and McLanahan 1991; Bankston and Caldas 1998; Smith, Brooks-Gunn, and Klebanov 1997; Taylor, Dearing, and McCartney 2004), properly understanding the relationship between parental SES and The author would like to extend thanks to those who provided their insights and feedback during the preparation of this manuscript: David J. Harding, of the University of California at Berkeley, and Barbara A. Anderson, Brian A. Jacob, and Yu Xie, all of the University of Michigan–Ann Arbor. Address correspondence to D. Diego Torres, Houston Education Research Consortium, Kinder Institute for Urban Research, Rice University, 6100 Main Street, MS-28, Houston, TX 77005. E-mail: [email protected]
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phenotypic parental IQ, as well as the ways in which high levels of one might alter or augment the downward pressure of the low levels of the other on children’s academic performance, is important to the formation of effective policies aimed at closing the class gap in educational outcomes. If, however, much of the existing social science literature, particularly in the field of sociology, has viewed the variation in the measures of SES or social class—for example, years of education, income, and career prestige—as well as their associations with child cognitive outcomes, as completely environmental in origin (Rowe, Vesterdal, and Rodgers 1998), researchers will need to appreciate the fact that part of the variation is genetic. To the degree that parental SES is associated with children’s cognitive and academic development (e.g., school grades, psychometric test scores), the relationship is likely genetically moderated, given that an underlying heritable characteristic relates to the correlated factors. For those who have at least recognized the implications that the covariance between SES and phenotypic IQ poses to stratification research, their analyses in the past couple of decades have tended to pit the one against the other rather than investigate the opportunity that this covariance offers to test interesting hypotheses with respect to their combined effects on children’s life chances (Rowe, Vesterdal, and Rodgers 1998). The origin of this contention dates back to the publication of Herrnstein and Murray’s (1994) The Bell Curve: Intelligence and Class Structure in American Life and the rejoinders to it. The main argument proffered in that text is that social background is of decreasing importance and that measured intelligence matters more to individuals’ likelihood of committing crime; being unemployed, in poverty, or on welfare; or providing substandard care for their children, factors that are associated with fewer years of completed education and, hence, the range of career opportunities available. Fischer et al. (1996), arguing that Herrnstein and Murray’s analysis overstates the importance of IQ as a predictor of outcomes, carried out phenotypic regression analyses on the same data used by Herrnstein and Murray, entering a host of additional “environmental” characteristics that the authors did not, and showed the effect of IQ to be nearly equal to, not greater than, that of social context. A general criticism of both sets of analyses, though, is that they are incapable of explaining the underlying sources of variation between SES and phenotypic IQ (Jensen 1998; Rowe 1994). Whether researchers are studying the relationship of phenotypic parental IQ to child cognitive outcomes or parental SES to child cognitive outcomes, controlling for parental SES in the case of the former relationship or for phenotypic parental IQ in the case of the latter relationship leads to the removal of, respectively, shared genetic and shared environmental variance. Except in comparisons of monozygotic and dizygotic twins or other clever natural experiments, partialing out the true effect of measured parental intelligence on children’s cognitive outcomes is perhaps impossible to do well, given the broad array of environmental and genetic factors that can be controlled for. Inasmuch as the goal of research with regard to these relationships is to separate the sources of variance, then, phenotypic regression analyses are not the optimal choice of method. Assuming a causal path from phenotypic parental IQ to child cognitive outcomes that is perhaps mediated by parental SES, however, it may still be possible to test, using phenotypic regression methods, whether and how said mediation varies across levels of phenotypic parental IQ, a question that has yet to be adequately addressed in the literature. For instance, research in the field of behavioral genetics—which typically makes use of the twin design and other sibling analyses instead of phenotypic regression analyses, methods that can actually separate the sources of variance just discussed—contends that children raised in more advantaged homes have more opportunities to engage in the environmental experiences that assist them in reaching their genetic potential for cognitive growth, while
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children from disadvantaged homes do not (Bronfenbrenner and Ceci 1994; Dickens and Flynn 2001). McGue (1997) has published research supporting this genotype by environment interaction, finding that parental SES positively moderates children’s cognitive ability. Turkheimer et al. (2003) has found the heritability of cognitive ability to be greater by a factor of seven in high SES families compared to low SES families. More recently, work by Harden, Turkheimer, and Loehlin (2007) and Tucker-Drob et al. (2011) has shown, respectively, the presence of a genotype by environment interaction effect on cognitive ability among adolescents and among infants. This research indicates that the influence of high parental SES is likely associated with a stronger correlation between the measured cognitive abilities of parents and those of their children. Given the positive effect of parental SES on children’s cognitive ability, it at least seems apparent that the cognitive ability of disadvantaged children from low cognitive ability homes is likely to rise along with the level of parental SES, something social scientists have long argued. What remains unclear is whether the effects of higher parental SES on the phenotypic parental IQ–child cognitive ability relationship are the same at all values of the phenotypic parental IQ.
The Present Study The social environments that parents provide for their children is not independent of parents’ cognitive ability, and, to the degree that environmental variables such as parental SES predict children’s academic performance, part of that effect is explained by the phenotypic expression of heritable genetic traits. The important question is whether the indirect effect of phenotypic parental IQ on child cognitive outcomes through parental SES is conditional on phenotypic parental IQ. This article aims to test a model of moderated mediation, a conceptual model that is shown in Figure 1 (Preacher, Rucker, and Hayes 2007). Whereas models of simple mediation and simple moderation have been employed in the past to examine the phenotypic parental IQ–child cognitive outcomes relationship, this is the first research that integrates the assumptions of both models into one model of moderated mediation. I hypothesized an indirect effect of phenotypic parental IQ on children’s academic performance through parental SES that is conditional on the level of phenotypic parental IQ. Given the findings of the genotype by environment interaction in the field of behavioral genetics in particular, I also posited that the indirect impact of phenotypic parental IQ
Parental IQ × Parental SES (X × M) b2
Parental IQ (X)
a1
Parental SES (M)
b1
Child Outcome (Y)
c’
Figure 1. Conceptual moderated mediation model in which the independent variable moderates the mediated path.
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on children’s academic performance via parental SES should be larger at lower levels of phenotypic parental IQ and smaller at higher levels of phenotypic parental IQ. That is, I anticipated larger returns to children’s psychometric test scores as a result of higher parental SES when phenotypic parental IQ was low and smaller returns as a result of higher parental SES when phenotypic parental IQ was high.
Methods
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Sample In order to test the strength of the indirect effect of phenotypic parental IQ on children’s academic outcomes via parental SES, I use matched mother-child data from the 1979 National Longitudinal Survey of Youth (NLSY79) and the 1979 National Longitudinal Survey of Youth, Children and Young Adults (NLSY79-CYA). The original NLSY79 sample included 12,686 individuals who were between the ages of 14 and 21 as of January 1, 1979; 6,283 of these individuals were female. Of these 6,283 women, 451 were in the military and were subsequently dropped from future surveys in 1984. Because of financial constraints, another 901 women from the economically disadvantaged white oversample were dropped from future surveys in 1990. With the passage of time and the attendant growth in NLSY79 women’s family size, the weighted mother-child data begins to be representative of a cross-section of women in the United States. Child cognitive assessments, my primary outcomes of interest, were administered biennially to the children of the NLSY79 women beginning in 1986. Taking eight rounds of data from 1986 to 2000, I retained from separate datasets (one for each of the relevant outcomes) the most recent round for which a valid score was recorded for a respondent as of the completion of the 2000 survey, excepting those individuals whose most recent valid score was recorded in 1986. This restrictive measure was employed so that each individual contributed at least two scores across the eight rounds of data for any given outcome, one score to serve as the dependent variable in my models, the other the prior year’s score to serve as a control. Half of the scores for each outcome observed came from the 1998 and 2000 survey years, while the other half were distributed across the five rounds prior to 1998, going back to 1988. Preliminary analyses comparing regression models between earlier and later years and by year separately showed consistent, if slightly different, estimates. Therefore, for each outcome of interest, all the data were combined into a single model of moderated mediation. Many of the NLSY79 mothers represented multiple children in 2000. It is important to note here that although childbearing is estimated to be 90 percent complete for the NLSY79 cohort as of the completion of the 2000 survey round, concerns may arise in some quarters about two related facts. First, whereas previously it was the case that many of the NLSY79-CYA children were born to teen mothers, by 2000, the trend has changed to one in which more children are being born to women in their 20s and 30s (see Center for Human Resource Research 2002a). Second, it is reasonable to expect to see differences in socioeconomic status between families of children born earlier to predominantly younger mothers and families of children born later to older mothers. Stated more clearly, the youngest children in the sample are more likely than their older peers to hail from middle class rather than poor households, a fact that necessitates treating withinsample age comparisons with caution. NLSY79-CYA documentation suggests, however, that it is increasingly reasonable by 2000 to generalize to the broader child population, despite these concerns.
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Dependent Measures Measures of children’s performance, returned as a raw score, are provided for three of the five subtests of the Peabody Individual Achievement Test, Revised (PIAT-R)— the reading recognition, reading comprehension, and mathematics subtests—and for the Peabody Picture and Vocabulary Test-Revised (PPVT-R); these scores constitute the child cognitive outcomes of interest. The complete battery of Peabody assessments, outlined in greater detail later, is both well normed and standardized, and both the PIAT-R and the PPVT-R have high test-retest reliability, are strong in predictive validity, and have been shown to correlate well with other measures of cognitive ability. The total number of child scores available for each of the four outcomes is as follows. The reading recognition subtest of the PIAT-R consisted of 6,756 child scores, the reading comprehension subtest consisted of 5,987 child scores, the mathematics subtest consisted of 6,767 child scores, and the PPVT-R consisted of 5,427 child scores. The total number of NLSY79 mothers represented in each of the four subtests was, respectively, 3,335, 3,073, 3,334, and 2,850. Children’s mean age ranged from a low of 11.61 years on the PPVT-R to a high of 12.69 years on the reading comprehension subtest of the PIAT-R. PIAT-R Reading Recognition. The reading recognition subtest of the PIAT-R, which consists of 84 items of increasing difficulty from the preschool to the high school level, measures, among children age five and up, how well children recognize words and how well they pronounce the words recognized. Children are assessed on their ability to match letters, name names, and read single words. The completion rate for the PIAT-R reading recognition subtest is a little less than 90 percent, with little difference between racial/ethnic groups. A disparity in completion rates does, however, exist between children of different ages; the oldest and youngest children have below average completion rates compared to children in the middle ages of childhood. Regarding achieved scores, the weighted distribution for the 2000 survey reveals that white children had a mean percentile score of 67.3, with Hispanics following at 57.7 and blacks still lower at 50.2, a trend that is similar across all rounds of the NLSY79-CYA data. The corresponding mean standard scores were 109.1 for whites, 104.4 for Hispanics, and 100.2 for blacks (Center for Human Resource Research 2002b). NLSY79 documentation highlights the point that scores on this subtest are increasingly confounded with acculturation factors once children leave the early grades of formal schooling. PIAT-R Reading Comprehension. The reading comprehension subtest of the PIAT-R, which consists of 66 items of increasing difficulty, measures children’s ability to derive meaning from sentences read silently. Children are assessed on their ability to choose from among four possible picture answers the best portrayal of a sentence’s meaning. The PIAT-R reading comprehension subtest is only administered to children who score 15 or higher on the PIAT-R reading recognition subtest. Completion rates for this measure are lowest relative to the other PIAT-R subtests considered in this study, though, like them, it reveals little evidence of racial/ethnic disparities. The racial/ethnic disparities in mean percentile and raw scores on the 2000 PIAT-R reading comprehension subtest were not dissimilar to those found with respect to the 2000 PIAT-R reading recognition subtest. White children had higher mean percentile and standard scores (61.5 and 105.4, respectively) than Hispanic children (48.3 and 98.9), who, in turn, had higher mean scores than blacks (41.3 and 95.4; Center for Human Resource Research 2002b).
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PIAT-R Mathematics. Consisting of 84 multiple-choice questions of increasing difficulty that range from basic numeral recognition and addition to more complex trigonometry, the mathematics subtest of the PIAT-R measures children’s knowledge of concepts and skills taught in mainstream mathematics education. While the test has an overall completion rate of 91 percent, the rate is lower among children older than 11 years of age. Completion rates do not vary by race/ethnicity. Racial/ethnic differences did, however, arise with respect to the mean percentile and standard scores in 2000. Again, whites outperformed Hispanics, who outperformed blacks. PPVT-R. Dunn and Dunn (1981) describe the PPVT-R as measuring “an individual’s receptive (hearing) vocabulary for standard American English [that] provides, at the same time, a quick estimate of verbal or scholastic aptitude.” Consisting of 175 vocabulary items of increasing difficulty, the PPVT-R assesses children’s ability to choose from among four picture answers the best portrayal of a word’s meaning. Of all the Peabody measures, the PPVT-R revealed the greatest racial/ethnic disparities in mean percentile and standard score outcomes for 2000. The mean percentile score for whites was more than 20 points higher than the mean percentile score for Hispanics and more than 30 points higher than the mean percentile score for blacks. The mean standard score on the PPVT-R was 103.3 for white children, which was almost 15 points higher than the 88.4 mean standard score achieved by Hispanic children and nearly 20 points higher than the 82.5 mean standard score achieved by black children. Interestingly, these differences remain strong even after controlling for demographic and socioeconomic controls. Independent Measure Maternal AFQT. Maternal percentile score on the Armed Forces Qualification Test (AFQT), which consists of word knowledge, paragraph comprehension, arithmetic reasoning, and mathematics knowledge assessments of the Armed Services Vocational Aptitude Battery (ASVAB), serves as an indicator of phenotypic parental IQ. The AFQT, administered to most of the original members of the NLSY79 cohort, is used by the U.S. Department of Defense to predict maximal performance and to match military recruits to job tasks they can do well (Armor and Sackett 2004; Hoewing 2004). As such, it is a very good proxy for the score an individual might receive on a formal test of intelligence, which also has high predictive validity for job trainability, job performance, and the ability to quickly appropriate and manipulate knowledge in dynamic environments (Gottfredson 1997; Jensen 1998). Indeed, both the AFQT and formal tests of intelligence are highly correlated with one another, with r averaging about .8 (Herrnstein and Murray 1994). AFQT scores’ ability to explain nearly 65 percent of the variation in IQ, and vice versa, suggests that both tests are measuring the same underlying trait. The measured intelligence of parents is expected to correlate well with their children’s psychometric test scores, consistent with the behavioral genetics literature that shows cognitive ability to have a substantial heritable component (Jensen 1998; Rowe 1994). While heritability tends to be highest at older ages, research by Rodgers, Rowe, and May (1994) that uses the same dataset used here suggests that it is a sizable 50 percent in childhood and adolescence. Maternal intelligence should also correlate well with parental SES, which has an independent effect on children’s academic performance. I treat intelligence as preceding in time both parental SES and children’s ability, though, as I will address in the discussion, it is also reasonable to reverse this relationship. Intelligence is hypothesized to have both a direct impact on child cognitive outcomes and an indirect effect on child cognitive outcomes via parental SES.
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Mediator Parental Socioeconomic Status (SES). An SES index was created by standardizing, for all rounds, the sum of the z-transformed values of (1) the natural log of net family income plus one; (2) the highest grade of the NLSY79 woman and her spouse; and (3) the maximum Duncan SEI value, first transformed to deciles, of either the NLSY79 woman or her spouse. Cronbach’s alpha, a gauge of the reliability of multi-item scales, returned a value in the excellent range of about 0.92, indicating that a shared underlying trait is being measured by these composite indices.
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Control Measures In addition to the typical demographic covariates of race/ethnicity, sex, and age included in each of the four models measuring the conditional indirect effect of maternal AFQT on children’s test scores through parental SES, I also included as a control respondents’ previous grand mean centered raw scores. Data Analysis Plan Missing values of the four independent measures constituting the basis for the creation of the parental SES indices were handled via multivariate imputation by fully conditional specification (FCS) (Raghunathan et al. 2001) using SPSS Statistics 19.0. Also referred to as multiple imputation by chained equations (MICE), FCS imputes missing values on a variable-by-variable basis given, or conditional on, information on all the variables observed. The imputations are generated through a sequence of regression models, differentiated by the type of variable being imputed (e.g., continuous, binary, categorical), in which the covariates include both observed and imputed values for a given individual. Subsequent to the imputation procedure, indirect (or simple mediation) and conditional indirect effects (or moderated mediation) were assessed in each of the four outcomes. Descriptions of the procedures used follow. Simple Mediation. While Preacher, Rucker, and Hayes (2007:211) note that a “significant unconditional indirect effect [or simple mediation] does not constitute a prerequisite for examining conditional indirect effects [or moderated mediation],” I nonetheless carried out preliminary analyses for each of the four outcome measures outlined previously by confirming that maternal AFQT has a strong and significant independent effect on children’s psychometric test scores and then testing whether the direct effect was mediated by parental SES (Figure 2). To assess the strength of the mediating impact of parental SES on the maternal AFQT–child cognitive outcomes relationship and to avoid issues arising from nonnormally distributed data, I used the product-of-coefficients strategy with bootstrapping (Preacher and Hayes 2004; Preacher, Rucker, and Hayes 2007).1 The indirect effect, then, 1
While the product-of-coefficients strategy assumes that the point estimate of the indirect effect is normally distributed, this is usually not the case, even in large samples in which the expectation of the point estimate is that it tends toward normality. The standard error used to determine the statistical significance of aˆ 1 bˆ 1 is therefore problematic. Bootstrapping overcomes the problems associated with the product-of-coefficients strategy by quantifying the indirect effect as the product of the mean bootstrapped sample estimates of the regression coefficients, with the optimum lower limit of bootstrap resamples being 5,000. Confidence intervals are produced using the estimated standard error of the mean indirect effect, and ranges excluding zero signify that mediation exists.
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a1
Parental IQ (X)
c’
Child Outcome (Y)
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Figure 2. A model of simple mediation.
was estimated by first regressing parental SES on maternal AFQT (M) and then regressing children’s scores on parental SES, controlling for maternal AFQT (Y): M = a0 + a1 X + r
(1)
Y = b0 + c X + b1 M + r
(2)
Sample indirect effects were then quantified as products of the mean bootstrapped sample estimates of the regression coefficients aˆ 1 and bˆ 1 , where aˆ 1 refers to the slope coefficient of M regressed on X and bˆ 1 refers to the conditional coefficient of Y regressed on M. Given that the unconditional indirect effect is generally given as c – c’, where c denotes the effect of X on Y in the absence of M and c’ denotes the effect of X on Y in the presence of M, c – c’ and aˆ 1 bˆ 1 are equivalent (MacKinnon, Lockwood, and Williams 2004). Moderated Mediation. Preacher, Rucker, and Hayers (2007) note several cases in which the magnitude of an indirect effect may depend on a moderator. Regarding the graphical representation of simple mediation in Figure 2, one can imagine cases in which some fourth variable (W) impacts (1) the a1 path, (2) the b1 path, or (3) both the a1 and b1 paths. Additionally, W may also impact only (4) the a1 path, while a fifth variable (Z) affects the b1 path. For the purposes of this study, I focused on how the indirect effect of maternal AFQT on children’s academic performance via parental SES might depend on maternal AFQT. This is a case of the independent variable itself functioning as the moderator of the b1 path (see Figure 1 in this article and Model 1 in Preacher, Rucker, and Hayes 2007:194). As in the preliminary examination of simple mediation addressed previously, I tested the hypothesis of moderated mediation in two regression analyses using bootstrapping. First, I regressed parental SES (M) on maternal AFQT (X) (see Equation 1). I then regressed children’s test scores (Y) on maternal AFQT (X), parental SES (M), and the interaction between maternal AFQT (X) and parental SES (M), Y = b0 + c X + (b1 + b2 X) M + r
(3)
The dependent variable model represented in Equation 3 differs from that represented in Equation 2, in that it now elucidates how the regression of Y on M can be seen as conditional on X. The hypothesis of moderation, or causal interaction, in the terminology of Wu and Zumbo (2008), goes beyond what is assumed in a simple interaction between two main effects in stressing that the mediating effect of M is expected to vary at the values of the
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moderator, X (Morgan-Lopez and MacKinnon 2006). The aim of moderated mediation is not to highlight the combined effect of X and M on Y—which is what statistical interaction achieves—but to elucidate how the moderator, also the main predictor in the case of the present analyses, alters the established causal relationship of M and Y. Given a direct effect of maternal AFQT on parental SES in the mediator model, a significant interaction effect between maternal AFQT and parental SES in the dependent variable model suggests, then, that mediation was indeed moderated. In cases in which a significant interaction was found to exist, I probed the indirect effect by completing regression analyses at the mean and ±1 SD of maternal AFQT to ascertain the extent to which the indirect effect varied AFQT. Since the of maternal as a function ˆ ˆ ˆ conditional indirect effect is quantified as f θ |X = aˆ 1 b1 + b2 X , the values of X at the mean and ±1 SD were simply inserted into this equation. I used 95 percent bias-corrected bootstrapping to achieve more precise confidence intervals on which to judge statistical significance from zero. Preacher, Rucker, and Hayes (2007) also suggest an extension of the Johnson-Neyman approach to moderated mediation analysis, because it allows for easy identification of the value of the moderator for which the indirect effect is just statistically significant (α = 0.05). Additional values of the moderator that are below α = .05 constitute the region of significance for the indirect effect, while values greater than α = .05 indicate statistical nonsignificance.
Results Descriptives Table 1 shows the means and standard deviations for maternal AFQT, parental SES, and the four Peabody measures. While the full range of the AFQT is represented among mothers in the dataset, it is interesting that the mean percentile score of the present sample is only about 35. This squares, though, with the fact addressed previously that many of the women represented were early childbearers, who tend, on average, to have lower cognitive ability than their delaying peers. It is true that by 2000, more of the women bearing children were older, but this trend is not yet fully reflected in the child data; hence, the obviously low mean maternal AFQT percentile score. A cursory look at the pairwise correlations shown in Table 2 reveals statistically significant pairwise correlations among the dependent, main independent, and mediator variables. Maternal AFQT explains just less than 30 percent of the variance in parental SES, about Table 1 Means and standard deviations for main predictor, mediator, and children’s raw scores on the Peabody instruments Variables Maternal AFQT (n = 3,363) Parental SES (n = 3,363) PIAT-R Reading Recognition (n = 6,756) PIAT-R Reading Comprehension (n = 5,987) PIAT-R Mathematics (n = 6,767) PPVT-R (n = 5,427)
Mean
SD
34.723 −0.038 53.118 49.199 48.537 108.633
26.573 2.563 15.954 12.308 12.911 20.633
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Table 2 Pairwise correlations for maternal AFQT, parental SES, and children’s raw scores (all measures) Variables Maternal AFQT (1) Parental SES (2) PIAT-R Reading Recognition (3) PIAT-R Reading Comprehension (4) PIAT-R Mathematics (5) PPVT-R (6)
(1)
(2)
(3)
(4)
(5)
(6)
1 0.529 0.259 0.352 0.295 0.395
1 0.188 0.248 0.190 0.270
1 0.741 0.717 0.586
1 0.643 0.629
1 0.574
1
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Note: All pairwise correlations are significant at the p < .001 level.
7 percent of the variance in reading recognition performance, 12 percent of the variance in reading comprehension performance, about 9 percent of the variance in mathematics performance, and about 16 percent of the variance in children’s performance on the PPVT-R. The percentage of variance in child cognitive ability explained by maternal AFQT comports with findings in the literature (Plomin et al. 2001). It should be apparent from the correlations shown that although a huge portion of parental SES is explained by maternal AFQT, the relationship between parental SES and children’s test scores is indicative of a possible mediating effect of parental SES on the maternal AFQT–child cognitive outcomes association. If maternal AFQT explains about 30 percent of the variance in parental SES, and if parental SES explains about 5 percent of the variance in children’s ability (about the average r2 value across the four pairwise correlations of parental SES and the Peabody measures), it is likely that, in addition to the direct effect of maternal AFQT on child scores, there is an indirect effect of maternal AFQT through parental SES. The pairwise correlations among the PIAT-R measures reveal that about 41 percent to more than half of the variance is explained between any two measures, with these values being significant at the p
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Understanding How Family Socioeconomic Status Mediates the Maternal Intelligence–Child Cognitive Outcomes Relationship: A Moderated Mediation Analysis D. Diego Torres
a
a
Houston Education Research Consortium , Kinder Institute for Urban Research, Rice University , Houston , Texas , USA Published online: 12 Nov 2013.
To cite this article: D. Diego Torres (2013) Understanding How Family Socioeconomic Status Mediates the Maternal Intelligence–Child Cognitive Outcomes Relationship: A Moderated Mediation Analysis, Biodemography and Social Biology, 59:2, 157-177, DOI: 10.1080/19485565.2013.833804 To link to this article: http://dx.doi.org/10.1080/19485565.2013.833804
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Biodemography and Social Biology, 59:157–177, 2013 Copyright © Society for Biodemography and Social Biology ISSN: 1948-5565 print / 1948-5573 online DOI: 10.1080/19485565.2013.833804
Understanding How Family Socioeconomic Status Mediates the Maternal Intelligence–Child Cognitive Outcomes Relationship: A Moderated Mediation Analysis
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D. DIEGO TORRES Houston Education Research Consortium, Kinder Institute for Urban Research, Rice University, Houston, Texas, USA In a model of moderated mediation using matched data from the 1979 National Longitudinal Survey of Youth and the 1979 National Longitudinal Survey of Youth, Children and Young Adults, I test (1) whether family socioeconomic status (SES) mediates the maternal intelligence-child cognitive outcomes relationship and (2) the extent to which this mediating impact is dependent on the level of maternal intelligence. Results reveal that the mediating impact of SES on the maternal intelligence–child cognitive outcomes relationship varies as a function of the level of maternal intelligence. The positive effect of higher SES on children’s academic ability decreases as the cognitive ability of mothers increases, such that children in low IQ households benefit most from higher SES, while children in high IQ households benefit somewhat less.
The covariance between socioeconomic status (SES) and phenotypic IQ is well known in the field of behavioral genetics (Gottfredson 2011). About 30 percent of the variance in the primary factors that comprise SES indices is explained by cognitive ability (Neisser et al. 1996:82). Gottfredson (1997), Jensen (1998), and Rowe (1997) have highlighted that tests of intelligence, in both the civilian and military spheres, reveal individuals’ ability to appropriate difficult material and expose the rate at which individuals can learn new material. Taken together, these two factors are strongly predictive of the type of employment individuals can perform well and therefore the amount of income they are likely to earn. Research also shows that higher levels of cognitive ability are required in more prestigious occupations (Gottfredson 1997:87), and the more prestigious the job, the greater the level of remuneration. Moreover, the predictive validity of general cognitive ability for both job performance and training rises with the overall complexity of the work being done (Gottfredson 1997:82). Since one of the most studied relationships in social science research is that of parental SES with children’s cognitive and academic development (Astone and McLanahan 1991; Bankston and Caldas 1998; Smith, Brooks-Gunn, and Klebanov 1997; Taylor, Dearing, and McCartney 2004), properly understanding the relationship between parental SES and The author would like to extend thanks to those who provided their insights and feedback during the preparation of this manuscript: David J. Harding, of the University of California at Berkeley, and Barbara A. Anderson, Brian A. Jacob, and Yu Xie, all of the University of Michigan–Ann Arbor. Address correspondence to D. Diego Torres, Houston Education Research Consortium, Kinder Institute for Urban Research, Rice University, 6100 Main Street, MS-28, Houston, TX 77005. E-mail: [email protected]
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phenotypic parental IQ, as well as the ways in which high levels of one might alter or augment the downward pressure of the low levels of the other on children’s academic performance, is important to the formation of effective policies aimed at closing the class gap in educational outcomes. If, however, much of the existing social science literature, particularly in the field of sociology, has viewed the variation in the measures of SES or social class—for example, years of education, income, and career prestige—as well as their associations with child cognitive outcomes, as completely environmental in origin (Rowe, Vesterdal, and Rodgers 1998), researchers will need to appreciate the fact that part of the variation is genetic. To the degree that parental SES is associated with children’s cognitive and academic development (e.g., school grades, psychometric test scores), the relationship is likely genetically moderated, given that an underlying heritable characteristic relates to the correlated factors. For those who have at least recognized the implications that the covariance between SES and phenotypic IQ poses to stratification research, their analyses in the past couple of decades have tended to pit the one against the other rather than investigate the opportunity that this covariance offers to test interesting hypotheses with respect to their combined effects on children’s life chances (Rowe, Vesterdal, and Rodgers 1998). The origin of this contention dates back to the publication of Herrnstein and Murray’s (1994) The Bell Curve: Intelligence and Class Structure in American Life and the rejoinders to it. The main argument proffered in that text is that social background is of decreasing importance and that measured intelligence matters more to individuals’ likelihood of committing crime; being unemployed, in poverty, or on welfare; or providing substandard care for their children, factors that are associated with fewer years of completed education and, hence, the range of career opportunities available. Fischer et al. (1996), arguing that Herrnstein and Murray’s analysis overstates the importance of IQ as a predictor of outcomes, carried out phenotypic regression analyses on the same data used by Herrnstein and Murray, entering a host of additional “environmental” characteristics that the authors did not, and showed the effect of IQ to be nearly equal to, not greater than, that of social context. A general criticism of both sets of analyses, though, is that they are incapable of explaining the underlying sources of variation between SES and phenotypic IQ (Jensen 1998; Rowe 1994). Whether researchers are studying the relationship of phenotypic parental IQ to child cognitive outcomes or parental SES to child cognitive outcomes, controlling for parental SES in the case of the former relationship or for phenotypic parental IQ in the case of the latter relationship leads to the removal of, respectively, shared genetic and shared environmental variance. Except in comparisons of monozygotic and dizygotic twins or other clever natural experiments, partialing out the true effect of measured parental intelligence on children’s cognitive outcomes is perhaps impossible to do well, given the broad array of environmental and genetic factors that can be controlled for. Inasmuch as the goal of research with regard to these relationships is to separate the sources of variance, then, phenotypic regression analyses are not the optimal choice of method. Assuming a causal path from phenotypic parental IQ to child cognitive outcomes that is perhaps mediated by parental SES, however, it may still be possible to test, using phenotypic regression methods, whether and how said mediation varies across levels of phenotypic parental IQ, a question that has yet to be adequately addressed in the literature. For instance, research in the field of behavioral genetics—which typically makes use of the twin design and other sibling analyses instead of phenotypic regression analyses, methods that can actually separate the sources of variance just discussed—contends that children raised in more advantaged homes have more opportunities to engage in the environmental experiences that assist them in reaching their genetic potential for cognitive growth, while
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children from disadvantaged homes do not (Bronfenbrenner and Ceci 1994; Dickens and Flynn 2001). McGue (1997) has published research supporting this genotype by environment interaction, finding that parental SES positively moderates children’s cognitive ability. Turkheimer et al. (2003) has found the heritability of cognitive ability to be greater by a factor of seven in high SES families compared to low SES families. More recently, work by Harden, Turkheimer, and Loehlin (2007) and Tucker-Drob et al. (2011) has shown, respectively, the presence of a genotype by environment interaction effect on cognitive ability among adolescents and among infants. This research indicates that the influence of high parental SES is likely associated with a stronger correlation between the measured cognitive abilities of parents and those of their children. Given the positive effect of parental SES on children’s cognitive ability, it at least seems apparent that the cognitive ability of disadvantaged children from low cognitive ability homes is likely to rise along with the level of parental SES, something social scientists have long argued. What remains unclear is whether the effects of higher parental SES on the phenotypic parental IQ–child cognitive ability relationship are the same at all values of the phenotypic parental IQ.
The Present Study The social environments that parents provide for their children is not independent of parents’ cognitive ability, and, to the degree that environmental variables such as parental SES predict children’s academic performance, part of that effect is explained by the phenotypic expression of heritable genetic traits. The important question is whether the indirect effect of phenotypic parental IQ on child cognitive outcomes through parental SES is conditional on phenotypic parental IQ. This article aims to test a model of moderated mediation, a conceptual model that is shown in Figure 1 (Preacher, Rucker, and Hayes 2007). Whereas models of simple mediation and simple moderation have been employed in the past to examine the phenotypic parental IQ–child cognitive outcomes relationship, this is the first research that integrates the assumptions of both models into one model of moderated mediation. I hypothesized an indirect effect of phenotypic parental IQ on children’s academic performance through parental SES that is conditional on the level of phenotypic parental IQ. Given the findings of the genotype by environment interaction in the field of behavioral genetics in particular, I also posited that the indirect impact of phenotypic parental IQ
Parental IQ × Parental SES (X × M) b2
Parental IQ (X)
a1
Parental SES (M)
b1
Child Outcome (Y)
c’
Figure 1. Conceptual moderated mediation model in which the independent variable moderates the mediated path.
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on children’s academic performance via parental SES should be larger at lower levels of phenotypic parental IQ and smaller at higher levels of phenotypic parental IQ. That is, I anticipated larger returns to children’s psychometric test scores as a result of higher parental SES when phenotypic parental IQ was low and smaller returns as a result of higher parental SES when phenotypic parental IQ was high.
Methods
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Sample In order to test the strength of the indirect effect of phenotypic parental IQ on children’s academic outcomes via parental SES, I use matched mother-child data from the 1979 National Longitudinal Survey of Youth (NLSY79) and the 1979 National Longitudinal Survey of Youth, Children and Young Adults (NLSY79-CYA). The original NLSY79 sample included 12,686 individuals who were between the ages of 14 and 21 as of January 1, 1979; 6,283 of these individuals were female. Of these 6,283 women, 451 were in the military and were subsequently dropped from future surveys in 1984. Because of financial constraints, another 901 women from the economically disadvantaged white oversample were dropped from future surveys in 1990. With the passage of time and the attendant growth in NLSY79 women’s family size, the weighted mother-child data begins to be representative of a cross-section of women in the United States. Child cognitive assessments, my primary outcomes of interest, were administered biennially to the children of the NLSY79 women beginning in 1986. Taking eight rounds of data from 1986 to 2000, I retained from separate datasets (one for each of the relevant outcomes) the most recent round for which a valid score was recorded for a respondent as of the completion of the 2000 survey, excepting those individuals whose most recent valid score was recorded in 1986. This restrictive measure was employed so that each individual contributed at least two scores across the eight rounds of data for any given outcome, one score to serve as the dependent variable in my models, the other the prior year’s score to serve as a control. Half of the scores for each outcome observed came from the 1998 and 2000 survey years, while the other half were distributed across the five rounds prior to 1998, going back to 1988. Preliminary analyses comparing regression models between earlier and later years and by year separately showed consistent, if slightly different, estimates. Therefore, for each outcome of interest, all the data were combined into a single model of moderated mediation. Many of the NLSY79 mothers represented multiple children in 2000. It is important to note here that although childbearing is estimated to be 90 percent complete for the NLSY79 cohort as of the completion of the 2000 survey round, concerns may arise in some quarters about two related facts. First, whereas previously it was the case that many of the NLSY79-CYA children were born to teen mothers, by 2000, the trend has changed to one in which more children are being born to women in their 20s and 30s (see Center for Human Resource Research 2002a). Second, it is reasonable to expect to see differences in socioeconomic status between families of children born earlier to predominantly younger mothers and families of children born later to older mothers. Stated more clearly, the youngest children in the sample are more likely than their older peers to hail from middle class rather than poor households, a fact that necessitates treating withinsample age comparisons with caution. NLSY79-CYA documentation suggests, however, that it is increasingly reasonable by 2000 to generalize to the broader child population, despite these concerns.
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Dependent Measures Measures of children’s performance, returned as a raw score, are provided for three of the five subtests of the Peabody Individual Achievement Test, Revised (PIAT-R)— the reading recognition, reading comprehension, and mathematics subtests—and for the Peabody Picture and Vocabulary Test-Revised (PPVT-R); these scores constitute the child cognitive outcomes of interest. The complete battery of Peabody assessments, outlined in greater detail later, is both well normed and standardized, and both the PIAT-R and the PPVT-R have high test-retest reliability, are strong in predictive validity, and have been shown to correlate well with other measures of cognitive ability. The total number of child scores available for each of the four outcomes is as follows. The reading recognition subtest of the PIAT-R consisted of 6,756 child scores, the reading comprehension subtest consisted of 5,987 child scores, the mathematics subtest consisted of 6,767 child scores, and the PPVT-R consisted of 5,427 child scores. The total number of NLSY79 mothers represented in each of the four subtests was, respectively, 3,335, 3,073, 3,334, and 2,850. Children’s mean age ranged from a low of 11.61 years on the PPVT-R to a high of 12.69 years on the reading comprehension subtest of the PIAT-R. PIAT-R Reading Recognition. The reading recognition subtest of the PIAT-R, which consists of 84 items of increasing difficulty from the preschool to the high school level, measures, among children age five and up, how well children recognize words and how well they pronounce the words recognized. Children are assessed on their ability to match letters, name names, and read single words. The completion rate for the PIAT-R reading recognition subtest is a little less than 90 percent, with little difference between racial/ethnic groups. A disparity in completion rates does, however, exist between children of different ages; the oldest and youngest children have below average completion rates compared to children in the middle ages of childhood. Regarding achieved scores, the weighted distribution for the 2000 survey reveals that white children had a mean percentile score of 67.3, with Hispanics following at 57.7 and blacks still lower at 50.2, a trend that is similar across all rounds of the NLSY79-CYA data. The corresponding mean standard scores were 109.1 for whites, 104.4 for Hispanics, and 100.2 for blacks (Center for Human Resource Research 2002b). NLSY79 documentation highlights the point that scores on this subtest are increasingly confounded with acculturation factors once children leave the early grades of formal schooling. PIAT-R Reading Comprehension. The reading comprehension subtest of the PIAT-R, which consists of 66 items of increasing difficulty, measures children’s ability to derive meaning from sentences read silently. Children are assessed on their ability to choose from among four possible picture answers the best portrayal of a sentence’s meaning. The PIAT-R reading comprehension subtest is only administered to children who score 15 or higher on the PIAT-R reading recognition subtest. Completion rates for this measure are lowest relative to the other PIAT-R subtests considered in this study, though, like them, it reveals little evidence of racial/ethnic disparities. The racial/ethnic disparities in mean percentile and raw scores on the 2000 PIAT-R reading comprehension subtest were not dissimilar to those found with respect to the 2000 PIAT-R reading recognition subtest. White children had higher mean percentile and standard scores (61.5 and 105.4, respectively) than Hispanic children (48.3 and 98.9), who, in turn, had higher mean scores than blacks (41.3 and 95.4; Center for Human Resource Research 2002b).
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PIAT-R Mathematics. Consisting of 84 multiple-choice questions of increasing difficulty that range from basic numeral recognition and addition to more complex trigonometry, the mathematics subtest of the PIAT-R measures children’s knowledge of concepts and skills taught in mainstream mathematics education. While the test has an overall completion rate of 91 percent, the rate is lower among children older than 11 years of age. Completion rates do not vary by race/ethnicity. Racial/ethnic differences did, however, arise with respect to the mean percentile and standard scores in 2000. Again, whites outperformed Hispanics, who outperformed blacks. PPVT-R. Dunn and Dunn (1981) describe the PPVT-R as measuring “an individual’s receptive (hearing) vocabulary for standard American English [that] provides, at the same time, a quick estimate of verbal or scholastic aptitude.” Consisting of 175 vocabulary items of increasing difficulty, the PPVT-R assesses children’s ability to choose from among four picture answers the best portrayal of a word’s meaning. Of all the Peabody measures, the PPVT-R revealed the greatest racial/ethnic disparities in mean percentile and standard score outcomes for 2000. The mean percentile score for whites was more than 20 points higher than the mean percentile score for Hispanics and more than 30 points higher than the mean percentile score for blacks. The mean standard score on the PPVT-R was 103.3 for white children, which was almost 15 points higher than the 88.4 mean standard score achieved by Hispanic children and nearly 20 points higher than the 82.5 mean standard score achieved by black children. Interestingly, these differences remain strong even after controlling for demographic and socioeconomic controls. Independent Measure Maternal AFQT. Maternal percentile score on the Armed Forces Qualification Test (AFQT), which consists of word knowledge, paragraph comprehension, arithmetic reasoning, and mathematics knowledge assessments of the Armed Services Vocational Aptitude Battery (ASVAB), serves as an indicator of phenotypic parental IQ. The AFQT, administered to most of the original members of the NLSY79 cohort, is used by the U.S. Department of Defense to predict maximal performance and to match military recruits to job tasks they can do well (Armor and Sackett 2004; Hoewing 2004). As such, it is a very good proxy for the score an individual might receive on a formal test of intelligence, which also has high predictive validity for job trainability, job performance, and the ability to quickly appropriate and manipulate knowledge in dynamic environments (Gottfredson 1997; Jensen 1998). Indeed, both the AFQT and formal tests of intelligence are highly correlated with one another, with r averaging about .8 (Herrnstein and Murray 1994). AFQT scores’ ability to explain nearly 65 percent of the variation in IQ, and vice versa, suggests that both tests are measuring the same underlying trait. The measured intelligence of parents is expected to correlate well with their children’s psychometric test scores, consistent with the behavioral genetics literature that shows cognitive ability to have a substantial heritable component (Jensen 1998; Rowe 1994). While heritability tends to be highest at older ages, research by Rodgers, Rowe, and May (1994) that uses the same dataset used here suggests that it is a sizable 50 percent in childhood and adolescence. Maternal intelligence should also correlate well with parental SES, which has an independent effect on children’s academic performance. I treat intelligence as preceding in time both parental SES and children’s ability, though, as I will address in the discussion, it is also reasonable to reverse this relationship. Intelligence is hypothesized to have both a direct impact on child cognitive outcomes and an indirect effect on child cognitive outcomes via parental SES.
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Mediator Parental Socioeconomic Status (SES). An SES index was created by standardizing, for all rounds, the sum of the z-transformed values of (1) the natural log of net family income plus one; (2) the highest grade of the NLSY79 woman and her spouse; and (3) the maximum Duncan SEI value, first transformed to deciles, of either the NLSY79 woman or her spouse. Cronbach’s alpha, a gauge of the reliability of multi-item scales, returned a value in the excellent range of about 0.92, indicating that a shared underlying trait is being measured by these composite indices.
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Control Measures In addition to the typical demographic covariates of race/ethnicity, sex, and age included in each of the four models measuring the conditional indirect effect of maternal AFQT on children’s test scores through parental SES, I also included as a control respondents’ previous grand mean centered raw scores. Data Analysis Plan Missing values of the four independent measures constituting the basis for the creation of the parental SES indices were handled via multivariate imputation by fully conditional specification (FCS) (Raghunathan et al. 2001) using SPSS Statistics 19.0. Also referred to as multiple imputation by chained equations (MICE), FCS imputes missing values on a variable-by-variable basis given, or conditional on, information on all the variables observed. The imputations are generated through a sequence of regression models, differentiated by the type of variable being imputed (e.g., continuous, binary, categorical), in which the covariates include both observed and imputed values for a given individual. Subsequent to the imputation procedure, indirect (or simple mediation) and conditional indirect effects (or moderated mediation) were assessed in each of the four outcomes. Descriptions of the procedures used follow. Simple Mediation. While Preacher, Rucker, and Hayes (2007:211) note that a “significant unconditional indirect effect [or simple mediation] does not constitute a prerequisite for examining conditional indirect effects [or moderated mediation],” I nonetheless carried out preliminary analyses for each of the four outcome measures outlined previously by confirming that maternal AFQT has a strong and significant independent effect on children’s psychometric test scores and then testing whether the direct effect was mediated by parental SES (Figure 2). To assess the strength of the mediating impact of parental SES on the maternal AFQT–child cognitive outcomes relationship and to avoid issues arising from nonnormally distributed data, I used the product-of-coefficients strategy with bootstrapping (Preacher and Hayes 2004; Preacher, Rucker, and Hayes 2007).1 The indirect effect, then, 1
While the product-of-coefficients strategy assumes that the point estimate of the indirect effect is normally distributed, this is usually not the case, even in large samples in which the expectation of the point estimate is that it tends toward normality. The standard error used to determine the statistical significance of aˆ 1 bˆ 1 is therefore problematic. Bootstrapping overcomes the problems associated with the product-of-coefficients strategy by quantifying the indirect effect as the product of the mean bootstrapped sample estimates of the regression coefficients, with the optimum lower limit of bootstrap resamples being 5,000. Confidence intervals are produced using the estimated standard error of the mean indirect effect, and ranges excluding zero signify that mediation exists.
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a1
Parental IQ (X)
c’
Child Outcome (Y)
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Figure 2. A model of simple mediation.
was estimated by first regressing parental SES on maternal AFQT (M) and then regressing children’s scores on parental SES, controlling for maternal AFQT (Y): M = a0 + a1 X + r
(1)
Y = b0 + c X + b1 M + r
(2)
Sample indirect effects were then quantified as products of the mean bootstrapped sample estimates of the regression coefficients aˆ 1 and bˆ 1 , where aˆ 1 refers to the slope coefficient of M regressed on X and bˆ 1 refers to the conditional coefficient of Y regressed on M. Given that the unconditional indirect effect is generally given as c – c’, where c denotes the effect of X on Y in the absence of M and c’ denotes the effect of X on Y in the presence of M, c – c’ and aˆ 1 bˆ 1 are equivalent (MacKinnon, Lockwood, and Williams 2004). Moderated Mediation. Preacher, Rucker, and Hayers (2007) note several cases in which the magnitude of an indirect effect may depend on a moderator. Regarding the graphical representation of simple mediation in Figure 2, one can imagine cases in which some fourth variable (W) impacts (1) the a1 path, (2) the b1 path, or (3) both the a1 and b1 paths. Additionally, W may also impact only (4) the a1 path, while a fifth variable (Z) affects the b1 path. For the purposes of this study, I focused on how the indirect effect of maternal AFQT on children’s academic performance via parental SES might depend on maternal AFQT. This is a case of the independent variable itself functioning as the moderator of the b1 path (see Figure 1 in this article and Model 1 in Preacher, Rucker, and Hayes 2007:194). As in the preliminary examination of simple mediation addressed previously, I tested the hypothesis of moderated mediation in two regression analyses using bootstrapping. First, I regressed parental SES (M) on maternal AFQT (X) (see Equation 1). I then regressed children’s test scores (Y) on maternal AFQT (X), parental SES (M), and the interaction between maternal AFQT (X) and parental SES (M), Y = b0 + c X + (b1 + b2 X) M + r
(3)
The dependent variable model represented in Equation 3 differs from that represented in Equation 2, in that it now elucidates how the regression of Y on M can be seen as conditional on X. The hypothesis of moderation, or causal interaction, in the terminology of Wu and Zumbo (2008), goes beyond what is assumed in a simple interaction between two main effects in stressing that the mediating effect of M is expected to vary at the values of the
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moderator, X (Morgan-Lopez and MacKinnon 2006). The aim of moderated mediation is not to highlight the combined effect of X and M on Y—which is what statistical interaction achieves—but to elucidate how the moderator, also the main predictor in the case of the present analyses, alters the established causal relationship of M and Y. Given a direct effect of maternal AFQT on parental SES in the mediator model, a significant interaction effect between maternal AFQT and parental SES in the dependent variable model suggests, then, that mediation was indeed moderated. In cases in which a significant interaction was found to exist, I probed the indirect effect by completing regression analyses at the mean and ±1 SD of maternal AFQT to ascertain the extent to which the indirect effect varied AFQT. Since the of maternal as a function ˆ ˆ ˆ conditional indirect effect is quantified as f θ |X = aˆ 1 b1 + b2 X , the values of X at the mean and ±1 SD were simply inserted into this equation. I used 95 percent bias-corrected bootstrapping to achieve more precise confidence intervals on which to judge statistical significance from zero. Preacher, Rucker, and Hayes (2007) also suggest an extension of the Johnson-Neyman approach to moderated mediation analysis, because it allows for easy identification of the value of the moderator for which the indirect effect is just statistically significant (α = 0.05). Additional values of the moderator that are below α = .05 constitute the region of significance for the indirect effect, while values greater than α = .05 indicate statistical nonsignificance.
Results Descriptives Table 1 shows the means and standard deviations for maternal AFQT, parental SES, and the four Peabody measures. While the full range of the AFQT is represented among mothers in the dataset, it is interesting that the mean percentile score of the present sample is only about 35. This squares, though, with the fact addressed previously that many of the women represented were early childbearers, who tend, on average, to have lower cognitive ability than their delaying peers. It is true that by 2000, more of the women bearing children were older, but this trend is not yet fully reflected in the child data; hence, the obviously low mean maternal AFQT percentile score. A cursory look at the pairwise correlations shown in Table 2 reveals statistically significant pairwise correlations among the dependent, main independent, and mediator variables. Maternal AFQT explains just less than 30 percent of the variance in parental SES, about Table 1 Means and standard deviations for main predictor, mediator, and children’s raw scores on the Peabody instruments Variables Maternal AFQT (n = 3,363) Parental SES (n = 3,363) PIAT-R Reading Recognition (n = 6,756) PIAT-R Reading Comprehension (n = 5,987) PIAT-R Mathematics (n = 6,767) PPVT-R (n = 5,427)
Mean
SD
34.723 −0.038 53.118 49.199 48.537 108.633
26.573 2.563 15.954 12.308 12.911 20.633
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Table 2 Pairwise correlations for maternal AFQT, parental SES, and children’s raw scores (all measures) Variables Maternal AFQT (1) Parental SES (2) PIAT-R Reading Recognition (3) PIAT-R Reading Comprehension (4) PIAT-R Mathematics (5) PPVT-R (6)
(1)
(2)
(3)
(4)
(5)
(6)
1 0.529 0.259 0.352 0.295 0.395
1 0.188 0.248 0.190 0.270
1 0.741 0.717 0.586
1 0.643 0.629
1 0.574
1
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Note: All pairwise correlations are significant at the p < .001 level.
7 percent of the variance in reading recognition performance, 12 percent of the variance in reading comprehension performance, about 9 percent of the variance in mathematics performance, and about 16 percent of the variance in children’s performance on the PPVT-R. The percentage of variance in child cognitive ability explained by maternal AFQT comports with findings in the literature (Plomin et al. 2001). It should be apparent from the correlations shown that although a huge portion of parental SES is explained by maternal AFQT, the relationship between parental SES and children’s test scores is indicative of a possible mediating effect of parental SES on the maternal AFQT–child cognitive outcomes association. If maternal AFQT explains about 30 percent of the variance in parental SES, and if parental SES explains about 5 percent of the variance in children’s ability (about the average r2 value across the four pairwise correlations of parental SES and the Peabody measures), it is likely that, in addition to the direct effect of maternal AFQT on child scores, there is an indirect effect of maternal AFQT through parental SES. The pairwise correlations among the PIAT-R measures reveal that about 41 percent to more than half of the variance is explained between any two measures, with these values being significant at the p
