Description of externalizing problems

We first computed descriptive statistics for children’s externalizing and aggression scores at each assessment. There was little age-related change in the sample means on these measures (TRF means, child age 5 = 5.75, age 6 = 6.61, age 7 = 7.02, age 8 = 6.63, age 9 = 6.59; CBCL means for child age 5 = 11.51, age 6 = 10.34, age 7 = 9.60, age 8 = 9.33, age 9 = 9.27). Variability was similarly stable, for both TRF scores (standard deviations from 8.67 to 10.42) and CBCL scores (standard deviations from 6.80 to 7.47). Age-related changes in peer reports of aggression were not explored, as these scores were standardized within each annual assessment. Stability of individual rank within the sample was estimated using correlations between each assessment. For all three outcome measures, individual differences were stable (*p* < .001): teacher ratings *r* = .51 to .63 (*n* = 444 to 532), mother ratings *r* = .55 to .74 (*n* = 385 to 484), peer reports *r* = .40 to .60 (*n* = 466^{1}). For subsequent analyses, we computed average externalizing and aggression scores across all 5 years, teacher ratings average score (TRF), (*M* = 6.49, *SD* = 7.89); mother ratings average score (CBCL; *M* = 10.13, *SD* = 6.12); peer reports of aggression average score (PEER; *M* = −0.09, *SD* = 0.72).

We used analysis of variance (ANOVA) to test gender and ethnic group mean differences in these averaged externalizing and aggression scores.^{2} Teacher-rated externalizing raw scores were higher for boys (*M* = 8.12, *SD* = 8.55) than girls (*M* = 4.72, *SD* = 6.58), *F*(1, 516) = 15.96, *p* < .001, as were peer reports of aggression; boys *M* = 0.24, *SD* = .79; girls *M* = −0.45, *SD* = .37), *F*(1, 465) = 86.62, *p* < .001. In contrast, there were no gender differences in mother-rated externalizing raw scores (boys *M* = 10.62, *SD* = 6.03; girls *M* = 9.62, *SD* = 6.18). Teacher-rated externalizing raw scores were higher for African American children (*M* = 9.04, *SD* = 9.25) compared to European American children (*M* = 5.94, *SD* = 7.41), *F*(1, 516) = 13.72, *p* < .001, as were peer reports of aggression (African American *M* = .08, *SD* = .72; European American *M* = −0.13, *SD* = .70), *F*(1, 465) = 10.32, *p* < .001. The two ethnic groups were not significantly different in mother-rated externalizing raw scores (African American *M* = 10.70, *SD* = 6.56; European American *M* = 10.04, *SD* = 6.08). It is noteworthy that the ethnic group differences in teachers’ and peers’ ratings were no longer significant (*p* > .50) when socioeconomic status (SES) was included as a covariate in the analyses. For all three outcome measures, the interaction between gender and ethnic group was not significant.

Individual risk variables and externalizing behavior problems

The first question we asked was whether these 20 selected risk variables from four domains of risk were associated with externalizing behavior problems. We computed bivariate Pearson correlations between the 20 risk variables, and between these risk variables and the averaged externalizing raw scores and aggression scores (see ). First, risk variable intercorrelations were explored within each of the four risk domains using pairwise deletion of missing data (*n* = 566 to 427). The three child risk variables were uncorrelated (gender, temperament, and medical problems at birth; *r*s from .04 to .08, *ns*). The correlations between the seven sociocultural risk variables were modest to moderate (SES, marital status, child:adult ratio, teenage pregnancy, unplanned pregnancy, stressful life events, and social isolation; *r*s from ± .01, *ns*, to .35, *p* < .001). There was also covariation between the eight parenting/caregiving risk variables (extensiveness of daycare, father’s involvement, parent conflict, exposure to violence outside of home, harsh discipline, likelihood of physical harm, no positive parenting, and attitudes about aggression; *r*s from ± .00, *ns*, to .55, *p* < .001). The two peer experience risk variables were uncorrelated (peer rejection in kindergarten, and unstable peer group; *r* = −.05, *ns*).

| **Table 1**Correlations: Between risk variables and with externalizing problems |

Next, the risk variables were correlated with externalizing outcomes using pairwise deletion of missing data (*n* = 520 to 375). Eighteen of the 20 risk variables were significantly correlated with at least one of the three externalizing problems measures. In general, higher externalizing and aggression scores were associated with variables from all four sets of risk variables: child risk variables (being a boy, more adverse temperament, more medical problems at birth), sociocultural risk variables (lower SES, living with a single mother, higher child-to-adult ratio, teenage pregnancy, unplanned pregnancy, more stressful life events), parenting/caregiving risk variables (more extensive nonmaternal child care, lower father involvement, higher parental conflict, more exposure to violence, harsher discipline, a greater likelihood of physical abuse, and maternal positive attitudes toward aggression), and peer experience risk variables (peer rejection in kindergarten). Two risk variables—maternal isolation and the stability of the peer group—were not correlated with any of the outcome measures.

Multiple risk factors and externalizing behavior problems

The second question was whether there was evidence for multiple risk factors for externalizing behavior problems. To test the statistical prediction of externalizing problems and aggression from each of the four sets of risk variables (child, sociocultural, parenting/caregiving, and peer experience), we used two regression models. In the first model, we estimated the maximized or initial statistical prediction of each set of risk factors and interactions with ethnicity and gender, using the following hierarchical regression: ethnic group, the set of risk factors of interest. This model provided an estimate of the variance accounted for by each set of risk factors without regard to covariation with the other three sets of risk variables.

In the second model, we estimated the unique contribution of each of the four sets of risk variables using the following hierarchical regression: ethnicity; the three other cumulative-risk variables; the cumulative-risk variable of interest.

Separate models were tested for TRF scores, CBCL scores, and peer-reported aggression scores. In every model, ethnic group status was entered first into the model. The results are shown in . Overall, the 20 risk variables accounted for 36% of the variance in TRF externalizing raw scores, 37% of the variance in CBCL externalizing raw scores, and 45% of the variance in peer-reported aggression scores, each *p* < .001.

| **Table 2**Prediction of externalizing problems from ethnic group and individual risk variables: Initial and unique regression weights and explained variance |

All four sets of risk variables (child, sociocultural, parenting/caregiving, and peer experiences) accounted for variance in externalizing and aggressive behaviors. Child risk variables explained 7–24% of the variance in externalizing outcomes (“initial” regression model). Half or more of this variance was unique to these child risk variables—this set of factors accounted for 4% to 19% of the unique variance in these outcomes when all other risks had been statistically controlled (“unique” regression model). Sociocultural risks accounted for 4% to 11% (*p* < .05 to *p* < .001) of the variance in externalizing problems (initial regression model). Up to slightly more than half of this was variance unique to the sociocultural risk variables, 1% (*ns*) to 4% (*p* < .05) of the variance in the unique regression model. Parenting and caregiving risk variables accounted for 10% to 20%, all *p* < .001, of the variance in externalizing outcomes (initial regression model)—up to slightly more than one-quarter of this variance was unique variance, 2% (*ns*) to 6% (*p* < .001) in the unique regression model. Peer experience risks accounted for 6% to 16%, all *p* < .001, of the variance in externalizing outcomes in the initial regression model. Half to nearly all of this variance was unique to these peer risks, 5% to 13% of the variance, all *p* < .001, in the unique regression model.

Cumulative-risk status: Individual and group differences

The third question was whether there was evidence for cumulative-risk in the prediction of externalizing problems, and the fourth related question was whether this cumulative-risk effect varied across gender and ethnic groups. First, we estimated the prevalence of each dichotomous risk variable (see Method, where we have described how these were derived) for the entire sample as well as within ethnic and gender groups. These prevalence rates are shown in .

| **Table 3**Prevalences of risk variables: Ethnic and gender group comparisons |

The prevalences of the child and peer-related risk variables were similar for African American and European American children. However, African American children had higher, *p* < .05 or less, prevalences for six of the seven sociocultural risk variables (low-SES, single-mother, high child:adult ratio, teenage pregnancy, unplanned pregnancy, and maternal social isolation) and five of the eight parenting/caregiving risk variables (father not helpful, exposure to violence, harsh discipline, physical harm, and positive attitudes about aggression).

By comparison, there were few gender differences in the prevalences of these risk variables. There were no statistically significant, *p* < .05, gender differences in the prevalences of child or sociocultural risk variables. However, there were a few gender differences in the prevalences for the parenting/caregiving and peer experiences risk variables. Boys were more likely to have received harsh discipline (55 vs. 45% of girls), to have mothers who valued aggression (8 vs. 4% of girls), and to have been rejected by their peers in kindergarten (14 vs. 8% of girls). More girls had fathers who were uninvolved in childcare (13 vs. 5% of boys).

Next, we computed bivariate Pearson correlations between the cumulative-risk variables, and between these and the outcomes. These, along with the descriptive statistics for the cumulative-risk variables, are shown in . Children had just less than four risk factors (*M* = 3.81, *SD* = 2.5), on average. These included 1.45 parenting/caregiving risks, 1.25 sociocultural risks, 0.83 child risks, and 0.27 peer experience risks. African American children had significantly (*t* test, *p* < .001) more risk factors, on average (*M* = 5.67), compared to European American children (*M* = 3.44), including over twice as many sociocultural risks (*p* < .001), and nearly twice as many parenting/caregiving risks (*p* < .001). In contrast, boys and girls had nearly identical numbers of risk factors; the only difference, as shown in Table 4, is an artifact of the inclusion of child gender in the child cumulative-risk variable (so that boys have, on average, one more risk factor than girls, given that being male was included as one of the child risk variables).

| **Table 4**Cumulative-risk factors: Descriptive statistics and correlations with externalizing and aggression |

The number of child risks was independent of the number of sociocultural, parenting/caregiving, and peer experience risks. In contrast, sociocultural risk was moderately correlated with the number of parenting/caregiving risk variables, *r* = .42, *p* < .001, and both of these were correlated with the number of peer-related risk variables, *r* = .19 for sociocultural, and .17 for parenting/caregiving, *p* < .001. All four cumulative-risk variables, as well as the total cumulative-risk variable, were correlated with externalizing and aggression scores, *r*s ranged from .15 to .40, *p* < .001, so that externalizing and aggression scores were higher for children with more risk factors.

To test the statistical prediction of externalizing problems and aggression from each of the four cumulative-risk variables (child, sociocultural, parenting/caregiving, and peer experience), we used two regression models (see ). In the first model, we estimated the maximized or initial statistical prediction (*I*Δ*R*^{2} in ) of each cumulative-risk factor and its interactions with ethnicity and gender, using the following hierarchical regression: ethnic group and gender; the cumulative-risk variable of interest; two-way interactions between the cumulative-risk variable with ethnicity, and with gender; and the three-way interaction between the cumulative-risk variable, ethnicity, and gender. This model provided an estimate of the main effect of each cumulative-risk variable without regard to overlapping covariation with the other three cumulative-risk variables.

| **Table 5**Prediction of externalizing problems from cumulative-risk factors: Initial explained variance for ethnic and gender group, initial and unique explained variance for each cumulative-risk variable, and significance of interaction terms |

In the second model, we estimated the *unique* contribution of each of the four cumulative-risk variables (*U*Δ*R*^{2} in ), using the following hierarchical regression: ethnicity and gender; the three other cumulative-risk variables; the cumulative-risk variable of interest; the two-way interactions between the cumulative-risk variable of interest, with ethnicity, and with gender; and the three-way interaction between the cumulative-risk factor of interest, ethnicity, and gender. We have also reported the total explained variance for each of these two regression models (Final *R*^{2}) once all of the variables and interaction terms had been entered into the equation. Note that the variance estimates for each of the four cumulative-risk variables from either the maximized variance model or from the unique variance model do not necessarily sum to equal the Final *R*^{2}, because these models do not account for prediction from overlapping or shared variance among these four cumulative-risk variables, and the contribution of interaction terms to the final explained variance in a model also varied depending on the cumulative-risk variable being tested. Overall, the total number of risk factors accounted for about 20% of the variance in TRF externalizing raw scores, about 20% of the variance in CBCL externalizing raw scores, and about 30% of the variance in peer-reported aggression scores. This Final *R*^{2} varied slightly, depending on the contribution of interaction terms to explained variance in the final equation.

The number of child risk variables accounted for 2% of the variance (1% of the unique variance) in TRF scores, and 8% of the variance (7% of the unique variance) in CBCL scores. This cumulative-risk variable also accounted for just less than 1% of the variance in peer-reported aggression (although this effect was not significant for the unique variance model). The interaction terms were not significant.

Sociocultural risk explained 6% of the variance (2% unique) in TRF scores, 6% of the variance (1% unique) in CBCL scores, and 3% of the variance (1% unique) in peer-reported aggression scores. Both two-way interactions, as well as the three-way interaction, were significant in the prediction of peer-reported aggression. Having more sociocultural risks was related to higher aggression scores among European American children and especially boys, *r* = .33, *n* = 202, *p* < .001; European American girls, *r* = .20, *n* = 176, *p* < .001, but not among African American children, boys *r* = .01, *n* = 45, *ns;* girls *r* = −.08, *n* = 46, *ns*.

Parenting/caregiving risk accounted for 5% of the variance (1% unique) in TRF scores, 8% of the variance (4% unique) in CBCL scores, and 1% of the variance (none unique) in peer-reported aggression scores. There was a marginally significant interaction between parenting/caregiving risk and ethnicity in the prediction of TRF scores, whereby higher risk was associated with higher externalizing scores, but only for European American children, *r* = .30, *n* = 426, *p* < .001 versus African American children, *r* = .04, *n* = 94, *ns*. The same interaction term was significant for peer-reported aggression, so that higher risk was related to higher aggression scores, but again only for European American children, *r* = .21, *n* = 378, *p* < .001 versus African American children, *r* = −.09, *n* = 91, *ns*.

Peer experience risk accounted for 5% of the variance (3% unique) in TRF scores, 4% of the variance (1% unique) in CBCL scores, and 3% of the variance (2% unique) in peer-reported aggression scores. The interaction with ethnicity was significant in the prediction of CBCL scores, so that higher risk was associated with higher externalizing scores, but only for European American children, *r* = .26, *n* = 402, *p* < .001 versus African American children, *r* = −.09, *n* = 85, *ns*.

We also analyzed the total number of risk variables (summing the number of child, sociocultural, parenting/caregiving, and peer experience risks) as a predictor. This total cumulative-risk variable accounted for 10% of the variance in TRF scores, 16% of the variance in CBCL scores, and 4% of the variance in peer-reported aggression scores. The interaction with ethnic group status was significant for TRF and peer-reported aggression scores, and was marginally significant for CBCL scores. Higher risk was more strongly related to higher externalizing for European American children, TRF: *r* = .44, *n* = 426, *p* < .001 versus African American children, *r* = .15, *n* = 94, *ns;* CBCL: *r* = .44, *n* = 402, *p* < .001 versus African American children, *r* = .25, *n* = 85, *p* < .05; peer-reported aggression: *r* = .41, *n* = 378, *p* < .001 versus African American children, *r* = −.02, *n* = 91, *ns*.

The statistical prediction of these outcome measures from the total cumulative-risk variable was very similar at each assessment. The results of the hierarchical regression analyses (described in the previous paragraph) for the total multiple-risk variable, predicting TRF, CBCL, and peer-reported aggression at each assessment (child age 5, 6, 7, 8, and 9 years), are shown in . Having more risk factors was consistently associated with higher externalizing raw scores and peer-reported aggression scores, regardless of child age. There was also consistency in the contribution of the risk-status by ethnic group status interaction term.

| **Table 6**Prediction of externalizing problems from total cumulative-risk variable, at each assessment |

One general issue regarding the interaction between ethnic group status and cumulative-risk status is whether this effect is in fact due to social-class differences. Although we statistically controlled SES in these analyses, we estimated the correlations between total cumulative-risk and TRF and peer-reported aggression scores (the two significant interaction effects in the total cumulative-risk model just described) separately for low-SES and middle/high SES European American and African American children. For European American children, the correlations were similar for low-SES, TRF: *n* = 65, *r* = .32, *p* < .001; peer-reported aggression: *n* = 62, *r* = .32, *p* < .001 and middle-SES children, TRF: *n* = 361, *r* = .39, *p* < .001; peer-reported aggression: *n* = 316, *r* = .37, *p* < .001. Among African American children, the correlations were similar for low-SES, TRF: *n* = 51, *r* = .08, *ns;* peer-reported aggression: *n* = 50, *r* = .03, *ns* and middle-SES children, TRF: *n* = 43, *r* = .10, *ns;* peer-reported aggression: *n* = 41, *r* = .06, *ns*. The observed ethnic group difference in the covariation of cumulative-risk status and externalizing outcomes was not due to any SES differences between European American and African American children.

Another related issue was whether risk status was related to children’s subsequent aggression and externalizing behavior problems, once earlier measures of aggression and externalizing had been taken into account. In other words, given the high stability of these behaviors over middle childhood, does risk status at age 5 years statistically predict later aggression and externalizing problems, once individual differences in our initial measures of these behaviors (also assessed when the children were 5 years old) had been statistically controlled? In order to answer this question, we estimated the first-order partial correlations between total cumulative-risk status and children’s subsequent teacher, mother, and peer reports of externalizing and aggression scores, controlling for our initial measure (age 5 years) of teacher, mother, or peer reports of externalizing and aggression. Even after controlling for initial levels of aggression or externalizing behaviors, having more risk factors was correlated with higher subsequent (5th year) aggression or externalizing scores, TRF: *n* = 460, *r* = .34, *p* < .001; CBCL: *n* = 410, *r* = .23, *p* < .001; peer-reported aggression (4th year due to incomplete peer report data in 5th year; see Footnote 1): *n* = 430, *r* = .16, *p* < .01.

Lastly, we tested whether each of the four domains of individual risk variables accounted for any variance above and beyond the effect of the total cumulative-risk variable. That is, we wanted to estimate the degree to which the variance attributable to each domain of individual risk factors was due to the number of risk factors present. We used hierarchical regression analysis with the following steps: ethnicity; total number of risks; set of risk variables of interest (child, sociocultural, parenting/caregiving, or peer experiences). Four separate models were estimated, one for each set of risk variables. For all four domains, individual risk factors accounted for variance beyond that due to the total number of risk factors present: (a) child risks: TRF *R*^{2} = .03 (*p* < .01), CBCL *R*^{2} = .09 (*p* < .001), peer-reported *R*^{2} = .17 (*p* < .001); (b) sociocultural risks: TRF *R*^{2} = .02 (*ns*), CBCL *R*^{2} = .04 (*p* < .01), peer-reported *R*^{2} = .01 (*ns*); (c) parenting/caregiving risks: TRF *R*^{2} = .05 (*p* < .01), CBCL *R*^{2} = .04 (*p* < .01), peer-reported *R*^{2} = .07 (*p* < .001); (d) peer risks: TRF *R*^{2} = .10 (*p* < .001), CBCL *R*^{2} = .02 (*p* < .01), peer-reported *R*^{2} = .13 (*p* < .001). Thus, the prediction of externalizing outcomes from these risk factors was not only a function of cumulative risk; individual risk variables accounted for variance in externalizing behavior problems, even after the total number of risk factors had been statistically controlled.

Patterns of cumulative risk: Equifinality

The fifth and final question we asked was whether there was evidence for equifinality in the prediction of externalizing behavior problems from these multiple risk factors. Hierarchical cluster analysis (between-group linkage method) of the four multiple-risk variables (child, sociocultural, parenting/caregiving, and peer) was used to identify groups with different sets of multiple-risk factors, and to test whether these different groups had similar or different outcomes (based on an approach used by

Sameroff et al., 1993). We selected those children who had 4 or more of the 20 risks (above the sample mean of 3.88 risks). This resulted in a subsample of 272 children (60% male, 27% African American).

Five clusters with samples large enough for statistical analyses were identified (see ). The first group (*n* = 100) was undifferentiated, with risk factors present from all four domains (child, sociocultural, parenting/caregiving, and peer). The second group (*n* = 41) was high in child and sociocultural risks. The third group (*n* = 32) was high in child and parenting/caregiving risks. The fourth group (*n* = 51) was high in sociocultural and parenting risks, with moderate levels of peer-related risks. The final group (*n* = 32) was similar to the fourth (high sociocultural and parenting risk), but had low levels of peer-related risks. Sixteen children did not cluster into these five groups and were excluded from analyses.

| **Table 7**Five clusters of cumulative-risk factors: M and SD, and mean comparisons, on total number of risk factors, and externalizing problems |

Group membership was related to gender (χ^{2}[4] = 41.47, *p* < .001) and ethnic status (χ^{2}[4] = 22.36, *p* < .001). Boys were overrepresented (compared to the selected subsample proportion of 60%) in the second and third groups. However, this gender difference is an artifact, because these two groups were high in child risks, and child gender was included as a child risk in this multiple-risk variable. African American children were overrepresented (compared to the selected subsample proportion of 27%) in the second, fourth, and fifth groups. Interestingly, all three of these groups were similarly high in sociocultural risks.

There was a significant association between group membership and total number of risks, Tukey honestly significant difference, *F*(4, 251) = 91.78, *p* < .001, as is evident from the means shown in . The fourth group (high sociocultural, parenting, moderate peer risks) was particularly high in total number of risks compared to the other groups, whereas the first three groups had similar total risk means.

We tested whether group membership was related to mean differences in externalizing and aggression (analysis of covariance—ANCOVA), once the effect of total number of risks had been statistically controlled. Group differences would indicate that particular patterns of risk factors were more or less important in the prediction of externalizing problems. Group similarity would indicate that the different patterns of risks led to similar outcomes. The adjusted means (adjusted for total number of risks present) and observed standard deviations for TRF, CBCL, and peer-reported aggression are also shown in . All five groups of children had similar levels on the outcomes; the group membership factor in the ANCOVA models was not significant, TRF: *F*(4, 225) = 0.42, *p* > .7; CBCL: *F*(4, 209) = 0.93, *p* > .4; peer-reported aggression: *F*(4, 205) = 1.55, *p* > .18. Once overall level of risk had been statistically controlled, the particular pattern of risks was unrelated to externalizing and aggression.