Running head: Early externalizing growth curves




Predicting Growth Curves of Externalizing Behavior Across the Preschool Years

Elizabeth B. Owens a    and Daniel S. Shaw b




a Institute of Human Development, University of California, Berkeley, CA

b Department of Psychology, University of Pittsburgh, Pittsburgh, PA



Acknowledgements: We would like to thank the mothers and sons who generously donated their time participating in our research project. This research was sponsored by a National Research Service Award from NIH to the first author (#MH 12792) and both R01 (#MH 50907) and K awards (#MH 01666) from NIH to the second author.


Correspondence to: Elizabeth Owens, Institute of Human Development, mc 1690, University of California, Berkeley, CA, 94720. Email: Phone: (510) 642-1985. Fax: (510) 643-5336.


Journal of Abnormal Child Psychology (in press)


            Hierarchical linear modeling was used to examine the rate of change from age 2 to 6 and the age-6 level of externalizing behavior among 299 boys from low-income families. Maternal depressive symptoms, maternal acceptance of child behavior, parental conflict and the interaction between maternal acceptance and depressive symptoms were each uniquely associated with age-6 externalizing behavior. Regarding the interaction, primarily when depressive symptoms were low was maternal acceptance associated with externalizing behavior. Interactions between infant negative emotionality and maternal depressive symptoms and between parental conflict and maternal acceptance were associated with rate of change. Plots suggested a protective effect of low infant negative emotionality when depressive symptoms were high and a larger effect of maternal acceptance when parental conflict was low compared to when it was high. Results add to a small but growing literature regarding predictors of change over time in early child externalizing behavior, a topic with potential to inform developmental psychopathology.


Key words:  growth curves, externalizing, preschool









Predicting Growth Curves of Externalizing Behavior Across the Preschool Years

The study of early childhood externalizing problems has implications for the science of developmental and clinical child psychology. During the preschool period rapid behavioral changes are apparent and therefore may be particularly informative regarding processes of human development. Early externalizing behaviors are highly predictive of externalizing behavior over a 1- to 2-year period (Campbell, Breaux, Ewing, & Szumoski, 1984; Cummings, Ianotti, & Zahn-Waxler, 1989; Rose, Rose, & Feldman, 1989), with at least moderate predictability over much longer periods (Campbell & Ewing, 1990; Egeland, Kalkoske, Gottesman, & Erickson, 1990; Richman, Stevenson, & Graham, 1982). Yet early externalizing behavior is not stable. On average, absolute levels decrease over time (Campbell, 1995) despite individual rank order remaining relatively unchanged. Furthermore, about 50% of preschoolers with notable externalizing-type problems display such problems during middle childhood (Campbell & Ewing, 1990), but the other half do not. The study of early childhood externalizing problems is also relevant to clinical practice. Externalizing behaviors are a common concern for parents of young children (Campbell, 1995), show stability coefficients from childhood to adulthood that are comparable to those of IQ scores (Olweus, 1979), and when they begin at a young age, are associated with increased risk for seriously antisocial outcomes (Moffitt, 1993). Examining the development of such problems before they are entrenched could help us to fashion effective interventions targeted toward those most likely to benefit.

The study of behavior trajectories, including the present focus on over-time trends in early externalizing behavior, begins with the measurement of behavior change. Scores at different time points should reflect change in the behavioral construct of interest rather than change in how the construct was measured (Eddy, Dishion, & Stoolmiller, 1998; Stoolmiller, 1995).  One implication of this idea might be that constructs should be defined and measured in the same way at each age, an approach that assumes the construct is expressed in exactly the same way across age. This assumption cannot be made about externalizing behavior during the preschool period because of the strong likelihood of heterotypic continuity of such behavior. Heterotypic continuity means that the same underlying construct or process manifests differently across age because development has occurred in the interim. Accordingly, behaviors considered problematic vary as a function of age because those considered normal vary as a function of age. We therefore adopt the stance that rather than necessarily measuring identical behaviors at each time point, behaviors assessed should be developmentally-relevant and possibly different. In support of this approach, Boyle and Willms (2001) state that repeated measures in developmental studies should have identical meaning across the period of study but need not be invariant. Furthermore, the use of dynamic constructs has been recommended (Eddy et al., 1998), and at least one other study of externalizing growth curves used different but developmentally-relevant items at each age (Patterson & Yoerger, 2001).

Potential predictors of early externalizing behavior are often grouped into child, parenting, and family domains (Greenberg, Speltz, DeKlyen, & Jones, 2001; Keller, Gilchrist, & Lewis, 2001). (Regarding the peer domain, peer influence on externalizing problems gains increasing importance with formal school entry. Therefore, given the age of our participants, the peer domain will not be considered here). Within the child domain, temperamental features including negative emotionality or difficulty are often investigated (e.g., Bates, Maslin, & Frankel, 1985; Chess & Thomas, 1984; Earls & Jung, 1987; Rothbart & Bates, 1998; Sanson, Smart, Prior, & Oberklaid, 1993; Shaw, Vondra, Hommerding, Keenan, & Dunn, 1994). Several conceptual possibilities exist:  Individual differences in negative emotionality may directly predispose one to the development of externalizing behavior, children with high levels of negative emotionality may elicit caregiver responses (e.g., harsh discipline) that then lead to later externalizing problems, or underlying biological processes may contribute to both negative emotionality and the subsequent behavior problems (Rothbart & Bates, 1998). High negative emotionality has been posited to be a central facet of psychopathology (Cicchetti, Ackerman, & Izard, 1995), with some data indicating that fussy infants who have difficulty regulating anger may later become aggressive in social relationships (Rubin, Coplan, Fox, & Calkins, 1995). Empirical evidence supports linkages between infant negative emotionality and the future level of externalizing problems, at least when both constructs are assessed via maternal-report (Bates et al., 1985; Chess & Thomas, 1984; Earls & Jung, 1987; Sanson et al., 1993; Shaw, Vondra, et al., 1994). However, it is not clear whether infant negative emotionality, or any temperament feature, is related to the growth (i.e., rate of change) of externalizing behavior. Colder, Mott, and Berman (2002) is the only study we know of providing evidence for a link between temperament features (in this case, high activity level and low fear) and growth of externalizing problems.

Within the parenting domain, maternal acceptance of child behavior is one of many behaviors purportedly associated with early externalizing behavior. Theoretically, acceptance may increase the effectiveness of socialization attempts by enhancing the parent-child relationship and/or may positively influence child self-esteem, both of which may decrease the likelihood of future behavior problems. Rohner (1986) argues for a biologically-based need for positive and accepting interactions with caretakers, with behavioral adjustment being a response to caregiver acceptance. Empirical evidence supports relations between maternal acceptance and low levels of child behavior problems (Chen, Rubin, & Li, 1997; Rothbaum, Rosen, Pott, & Beatty, 1995; Wolchik, Wilcox, Tein, & Sandler, 2000). Furthermore, constructs related to acceptance (e.g., warmth, responsiveness, supportiveness, reciprocity) are clearly predictive of low levels of externalizing problems in young children (Erickson, Sroufe, & Egeland, 1985; Gardner, 1994; Harnish, Dodge, & Valente, 1995; Pettit & Bates, 1989; Shaw, Keenan, & Vondra, 1994; Shaw et al., 1998). As was true for infant negative emotionality, empirical evidence thus far supports prediction of future level of externalizing behavior. We know of no studies documenting relations between maternal acceptance and changes in early externalizing behavior, although maternal coercion and nonaffection (McFayden-Ketchum, Bates, Dodge, & Pettit, 1996) and maternal negative control (Spieker, Larson, Lewis, Keller, & Gilchrist, 1999) have shown relations with rate of externalizing behavior change across the preschool and school-aged periods.

In the family domain we tested maternal depressive symptoms and parental conflict as predictors of early externalizing problems. Both are variables whose well-documented relations with externalizing problems may be environmentally-mediated (Cummings & Davies, 2002; Goodman & Gotlib, 1999). The environmental mediation hypothesis involves the impact of these variables on parenting behaviors, parent-child relationships, and perhaps the family emotional climate, which then lead to behavior problems. For example, mothers who are depressed are more likely to use inconsistent, permissive, harsh, or coercive discipline (Gelfand & Teti, 1990; Kochanska, Kuczynski, & Maguire, 1989; Peterson, Ewigman, & Vandiver, 1994); depressed parents may be more likely to disengage from the parenting role and to neglect parenting responsibilities (Gelfand & Teti, 1990; Osofsky & Thompson, 2000). Regarding parental conflict, relations with childhood externalizing problems may be due to parental modeling of problematic behavior. However, most evidence suggests that the link is indirect through parental conflict's adverse effect on parent-child relationship quality (Harrist & Ainslie, 1998), parenting practices such as disciplinary strategies (Mann & MacKenzie, 1996), and/or child emotional insecurity (Davies & Cummings, 1994). Much empirical evidence supports links between both maternal depression (see Gotlib & Goodman, 1999 for review) and parental conflict (see Cummings, 1994 for review) and future levels of externalizing behavior, but only one study we know of documents a relation between either variable, in this case maternal depression, and growth or changes in early externalizing problems (Munson, McMahon, & Spieker, 2001). 

Early externalizing behaviors have been conceptualized as resulting from transactional processes. These typically involve reciprocal relations over time between a child's attributes or behaviors and aspects of the child's environment (Sameroff, 1975). In very young children, prior to peer exposure and formal schooling, significant and influential transactive processes likely involve aspects of the family environment, most notably parental characteristics and behaviors. Consequently, we expected the presence of cross-domain risk factors (e.g., high negative emotionality and high depressive symptoms, low acceptance and high parental conflict) to be associated with less improvement in externalizing behavior over time (anticipating that on average, externalizing behavior would decrease across the preschool period) and higher levels of externalizing problems at age 6. Furthermore, certain cross-domain interactions were expected to be predictive of externalizing growth curves because one variable might confer protection/vulnerability in the context of another. For example, infant negative emotionality might operate as a vulnerability/protective factor (increased externalizing problems and less improvement when high, and decreased problems and more improvement when low) in the context of maternal depressive symptoms (Goodman & Gotlib, 1999) or parental conflict (Cummings & Davies, 2002). Similarly, risk for externalizing problems due to maternal depression or parental conflict may be attenuated if mothers are nevertheless high on acceptance. Empirical evidence that these specific interactions predict growth or change in problem behavior is scant. However, a growing literature exists in which parenting behavior, especially discipline practices, together with child temperament (e.g., fearfulness, activity level) is associated with various aspects of child adjustment measured at particular points in time (Bates, Pettit, Dodge & Ridge, 1998; Colder, Lochman, & Wells, 1997; Lengua, Wolchik, Sandler, & West, 2000; Kochanska, 1997). This literature provides at least indirect support for our tests of interactions involving infant negative emotionality.

In sum, our goal was to test hypotheses regarding predictors of externalizing behavior growth curves across the preschool period. We examined predictors from three domains: child (infant negative emotionality), parenting (maternal acceptance), and family (maternal depressive symptoms and parental conflict). We were particularly interested in ascertaining whether cross-domain interactions explained variation in the rate of externalizing behavior change between the ages of 2 and 6. Specifically, we expected to find significant joint effects of infant negative emotionality with maternal depressive symptoms, parental conflict, and maternal acceptance, and of maternal acceptance with both maternal depression and parental conflict.



As part of an on-going longitudinal study of developmental precursors of antisocial behavior, infant boys and their mothers were recruited from Women, Infant, and Children (WIC) nutritional supplement clinics in the Pittsburgh, PA metropolitan area. Of those asked, 97% agreed to participate, and 71% (N= 310) attended the first visit at 1.5 years. 280 to 300 of the families were seen at each of the visits after 1.5 years (except for the 5.5-year visit) so that attrition at each age was less than 10%. As recognition for their contribution to our research project, at each assessment families were given between 20 and 30 dollars (depending on the length of the visit), plus 5 dollars for transportation. The analyses herein were conducted using data from the 299 boys (of the original 310) for whom mother-rated externalizing scores were available at two or more time points between ages 2 and 6.  The average 24-month externalizing score among the 11 boys not included in these analyses was slightly lower than, but not significantly different from, the average 24-month externalizing score of the 299 boys whose data were analyzed.

Fifty-eight percent of the mothers were Caucasian, 40% were African American, and 2% were of Native American, Asian, or mixed descent. All families were low-income: at the 1.5-year visit 67% of the families were living under poverty threshold, and 91% had income-to-needs ratios of 1.5 or less. Fifty-eight percent of the mothers had 12 or fewer years of education, 36% had some post-high school education, and 5% had finished college. Most mothers (76%) were not employed outside of their homes. Sixty-five percent were married or living with partner, 27% were single, and 7% were separated, divorced, or widowed.


Boys and their mothers were seen at 1.5, 2, 3.5, 5, 5.5, and 6 years of age in the home and/or in the lab for 1 ½ - 3 ½ hours at each visit. They participated in a series of developmentally appropriate interaction tasks, many of which were videotaped for later coding. At each visit mothers also completed questionnaires and interviews regarding demographic variables, their own adjustment, family functioning, and child behavior.


            Externalizing behavior. Externalizing behavior was measured using maternal report on the age 2/3 version of the Child Behavior Checklist (CBCL, Achenbach, Edelbrock, & Howell, 1987) at ages 2 and 3.5 and the age 4-16 version of the same instrument (Achenbach, 1991) at ages 5, 5.5, and 6. Both versions are psychometrically sound. Regarding the age 2/3 version, short-term and long-term retest reliability for all scales has averaged .87 and .69, respectively. Convergent validity is suggested by clinical cut-off scores that discriminated between referred and nonreferred children, and divergent validity is suggested by nonsignificant correlations between CBCL scores and measures of mental development. Scores from versions 2/3 and 4-16 are correlated to a moderately large degree, providing support for the predictive validity of the age 2/3 version (Achenbach et al., 1987). Regarding the age 4-16 version, one-week retest reliability is .89 and one-year retest reliability is .72. Convergent validity has been demonstrated by high correlations (above .80) between CBCL scores and other checklist measures of childhood behavior problems. Furthermore, suggested clinical cut-off scores discriminate between children referred and not referred for mental health services (Achenbach, 1991; Achenbach, 1994).    

            Both measures produce broad- and narrow-band factor scores reflecting child behavior over the previous six months. Because of the relatively undifferentiated nature of externalizing behavior in preschoolers, we created our dependent measure from all items loading on the broad-band Externalizing factor at each age. These Externalizing items varied across age but are considered developmentally relevant because they were obtained from age-normed versions of the CBCL that contain age-appropriate items (see Table 1). Above the dashed line are items that are virtually identical across age, whereas below the line are items that differ across age. 

            Because the T-scores typically derived from the CBCL are age normed, indexing change in relative rank over time, they are not considered optimal indicators of change (Stoolmiller, 1995). Instead, we averaged raw item scores, as recommended by Willet and Sayer (1994), to create an overall score for Externalizing behavior at each age scaled according to the original metric (0 = not true, 1 = somewhat or sometimes true, and 2 = very true or often true). T-scores of 50, 60, 70 on the age 2/3 version approximately correspond to raw scores of .54, .89, and 1.27, respectively. T-scores of 50, 60, 70 on the age 4-16 version approximately correspond to raw scores of .28, .50, and .80, respectively.

            Infant negative emotionality. Negative emotionality at 1.5 years was derived via observation of approximately 70-minute long videotapes of infants and their mothers participating in activities that varied in level of stress (e.g., free play, clean-up task, period of separation from mother). One molecular and three global ratings of negative emotionality were made. For the molecular rating, coders recorded the proportion of time spent fussing and crying. They also made global ratings on five-point scales of the amount and intensity of the infant's fussing and crying, and of overall difficulty. Interrater agreement in the form of weighted kappas were computed for each component of the Negative Emotionality measure. Across 10 randomly selected cases weighted kappas ranged from .77 to .88, with a mean of .83. The one molecular and three global scores were standardized and summed into a single observed Negative Emotionality score with a Cronbach’s alpha of .90.

            Maternal depressive symptoms. Maternal depressive symptoms were measured using the 21-item Beck Depression Inventory (BDI, Beck, Ward, Mendelson, Mock, & Erbaugh, 1961). Cronbach’s alphas when administered to nonpsychiatric populations range from .78 to .95 and retest reliability coefficients range from .60 to .90 (Beck, Steer, & Garbin 1988). The BDI has been shown to be moderately to highly correlated with other measures of depressive symptoms and disorder (Beck et al., 1988). Instructions were altered to cover depressive symptoms during the previous six months (instead of the last two weeks) in order to provide a more stable indication of maternal affect throughout her child's life. The BDI was administered at 1.5, 2, 3.5, 5, and 5.5 years, with scores from each administration averaged to produce a single score with a Cronbach’s alpha of .87. This single composite score estimated the level of maternal depressive symptoms throughout the growth period under study.

Maternal acceptance. The Acceptance of Child Behavior scale from the Home Inventory for Measurement of the Environment (HOME, Caldwell & Bradley, 1984) was administered at age 2 and used to assess maternal acceptance. Information needed to score the inventory is obtained through a combination of observational and interview methods. Items on this scale include: "Parent does not shout at child", "Parents does not interfere or restrict child more than 3 times", "Parent does not scold or criticize child during visit", and "No more than one instance of physical punishment during the past week". The HOME is widely used and psychometrically sound (Bradley & Caldwell, 1988). For example, Elardo, Bradley, and Caldwell (1975) reported an internal consistency coefficient for the total scale of .89 and a moderate degree of retest reliability from 6 to 24 months. Subscale and total scores have been found to predict child cognitive and language scores, and to distinguish the home environments of malnourished, failure-to-thrive, and developmentally delayed infants from demographically-matched, normally developing infants (Bradley & Caldwell, 1988).

Parental conflict. A total score for parental conflict was formed from two self-report measures of parental conflict: frequency scores from the Childrearing Disagreements Scale (CRD, Jouriles et al., 1991) administered at 24 and 64 months, and the Verbal and Physical aggression subscale scores from the Conflict Tactics Scale (CTS, Straus, 1979) administered at 42 and 64 months. The Cronbach’s alpha for the composited Parental Conflict measure was .60. Scores on this composited measure reflected the average level of parental conflict throughout the growth period.

The CRD assesses the frequency with which parents disagree about childrearing issues. This frequency scale has a Cronbach's alpha of .86 and some evidence of predictive and discriminative validity has been provided using relations with child behavior problems that differ from those between marital adjustment and child behavior problems (Jouriles et al., 1991). The CTS assessed the use of different conflict resolution strategies by mother and her partner. Cronbach’s alphas were .79 and .82 for the Verbal and Physical Aggression subscales, respectively (Straus, 1979) and the factor structure originally proposed by Straus has been replicated (Caulfield & Riggs, 1992). The Physical Aggression subscale and measures of family power structure that predict the use of violence as a conflict resolution strategy have shown significant correlations, as have subscale scores and measures of physical and verbal aggression obtained from interviews (Straus, 1979).

Data Analytic Strategy

            First, we computed descriptive statistics and correlations among predictor variables. We then modeled growth curves because it is a strongly recommended approach to analyzing repeated-measures data and describing developmental patterns (Boyle & Willms, 2001; Burchinal, 1999; Stoolmiller, 1995; Willet, Ayoub, & Robinson, 1991) that allows examination of individual change, average change, and predictors of individual differences in change over time. Specifically, we tested hierarchical linear models using HLM software, version 5 for Windows (Raudenbush, Bryk, & Congdon, 2000).

Our growth curve analyses involved two steps:  the first was to unconditionally model (i.e., examine without predictors) individual and group-level externalizing behavior as a linear function of time, and the second was to add predictors of variance in the Externalizing growth curve slopes and intercepts. Because we were more interested in developmental outcome at the end of the growth period than in initial status, we set the intercept at age 6 rather than at age 2, an approach that has been adopted in at least three other investigations examining growth curves of externalizing problems (Colder et al., 2002; Munson et al., 2001; Spieker et al., 1999). Therefore, in our analyses a trajectory or growth curve for each of the 299 children was represented by a slope (describing the rate of change) and an intercept (describing the level of Externalizing behavior at age 6). An average or overall growth curve was generated, and then predictors of variance around the slope and intercept of this average growth curve were examined. We examined each predictor individually, then cumulatively, and finally tested five cross-domain interactions:  Infant Negative Emotionality X Maternal Depressive Symptoms, Infant Negative Emotionality X Maternal Acceptance, Infant Negative Emotionality X Parental Conflict, Maternal Acceptance X Parental Conflict, and Maternal Acceptance X Maternal Depressive Symptoms. 


            In preparation for analyses, certain missing values were replaced and distributions of our dependent measures were examined. Replacement of missing data for between-subject predictors is necessary when using HLM software. In 6% of cases (n=19) for Maternal Acceptance, and in 2% of cases (n=6) for Infant Negative Emotionality missing values were replaced with the sample means.  For Maternal Depressive Symptoms and Parental Conflict, we first computed aggregate variables from the available raw data. Then for Parental Conflict, in 1% of cases (n=3) missing values were replaced with the Parental Conflict mean.  There were no missing values for the aggregated Maternal Depressive Symptoms variable. Missing values were not replaced for the outcome (Level 1) variables. A benefit of HLM is its ability to produce robust estimates despite missing values for the repeated dependent measure. Additionally, our use of a restricted maximum likelihood estimation procedure required that our dependent variables (the Externalizing slopes and intercepts) be normally distributed, as the slope scores were. The distribution of intercepts had a slight positive skew but did not appear to violate the assumption of normality.

Descriptive statistics are presented in Table 2.  For the predictor variables, statistics were calculated before missing data were replaced with sample means. We also computed Pearson product moment correlations among predictors. Infant Negative Emotionality was not significantly associated with any other variable (all rs less than .10). Each parenting and family variable showed small- to moderately-sized significant correlations with all of the other parenting and family variables; the smallest was between Maternal Acceptance and Parental Conflict (r = -.13, p = .016) and the largest was between Maternal Depressive Symptoms and Parental Conflict (r = .34, p = .000). The correlation between Maternal Depressive Symptoms and Maternal Acceptance was intermediary (r = -.19, p = .001).

            Figure 1 displays the actual means and the estimated mean growth curve for Externalizing behavior from ages 2 to 6. As can be seen, Externalizing scores tended to decrease over time. Given the pattern of actual Externalizing means, we considered the appropriateness of linear, quadratic, and cubic models. Ultimately we adopted a linear model both because a straight line approximated the change in Externalizing means across time, and because adding quadratic and cubic terms to our model substantially decreased the reliability of our slope estimates. However, the difference between the observed and estimated means at age 3.5 should be noted. Consistent with summaries of previous reports (Campbell, 1995), in our sample parent report of child manageability and discipline problems was highest at age 3. Despite the common belief in the existence of the "terrible twos", data seem to suggest age 3 to be the most "terrible".  Additionally, in Figure 1 the lower case letters a through d were included to provide reference points for interpretations regarding the clinical relevance of our findings. As can be seen, the actual and estimated means at ages 2 and 3.5 were quite close the normative mean. By ages 5 to 6, however, the actual and estimated means were somewhat higher than the normative mean, although not in the clinical range. Given that our participants were at elevated risk for externalizing problems (i.e., were boys from low-income urban families), the relatively high average scores at ages 5 to 6 were expected.

The linear slope of the estimated mean growth curve was -.06 and its intercept (in other words, the average Externalizing score at age 6) was .40. Both of these values were significantly different from zero, and were reasonably reliable (.45 for slope estimate and .81 for intercept estimate). The correlation between slope and intercept was .21, meaning that a small relation existed between more slowly decreasing slopes and higher age-6 Externalizing scores. The variances around the average slope and intercept were also significant (.045 for intercept, X2298 = 1545.38, p = .000; .002 for slope, X2298 = 541.05, p = .000), indicating notable diversity in children's individual trajectories and suggesting that identifying predictors accounting for variance in these estimates would be prudent. 

            Consequently, in four separate equations each independent variable was entered as a predictor of both the slope and the intercept, with results presented in Table 3. PV stands for percent of variance accounted for, a measure of effect size. As can be seen, each predictor accounted for significant variance in the age-6 intercept, with Maternal Depressive Symptoms accounting for the most variance (16%) and Infant Negative Emotionality accounting for the least (1%). When entered simultaneously, each of the three family predictors still accounted for unique variance, above and beyond the effects of the others and despite the collinearity among them, but the variance accounted for by Infant Negative Emotionality was only marginally significant. The statistics for the significant predictors in this cumulative model were as follows: Maternal Depressive Symptoms (coefficient = .011, se = .002, t294= 4.79, p = .000), Parental Conflict (coefficient = .063, se = .019, t294= 3.35, p = .001), and Maternal Acceptance (coefficient = -.017, se = .007, t294= -2.55, p = .011). All four predictors together accounted for 23% of the variance in the intercept estimate. On the other hand, no child, parenting, or family predictor accounted for significant variance in the slope. In other words, no main effects on the slope were detected. Not surprisingly, none accounted for variance above and beyond the others when entered simultaneously.

            We next computed and, in separate equations, tested five multiplicative interaction terms: Infant Negative Emotionality X Maternal Depressive Symptoms, Infant Negative Emotionality X Parental Conflict, Infant Negative Emotionality X Maternal Acceptance, Maternal Acceptance X Maternal Depressive Symptoms, and Maternal Acceptance X Parental Conflict. In order to facilitate interpretation, we centered variables around sample medians before computing interaction terms. This centering had no impact on t-ratios and their p values, PVs, or coefficients of main effects. In one of the five equations the interaction term accounted for significant variance around the intercept estimate:  Maternal Acceptance and Depressive Symptoms had a joint effect on age-6 Externalizing scores (coefficient = .003, se = .001, t = 2.52, p = .012). The term plus the component main effects accounted for 20% of the intercept variance. Regarding model fit, the variance component and X2 statistics were .036 and X2295 = 1281.69, p = .000 for the intercept and .002, X2295 = 535.64, p = .000 for the slope, suggesting a substantial improvement in model fit compared to the unconditional model. As seen in Figure 2, the effect of Maternal Acceptance was seen primarily when Maternal Depressive Symptoms were low and the effect of Maternal Depressive Symptoms was seen primarily when Maternal Acceptance was high. 

In two of the five equations, interaction terms accounted for significant variance in the slope estimate, above and beyond the component main effects. First, although the interactions between Infant Negative Emotionality and both Parental Conflict and Maternal Acceptance were not statistically significant, the interaction between Infant Negative Emotionality and Maternal Depressive Symptoms was (coefficient = .0003, se = .0001, t295= 2.32, p = .021), with the term plus its component main effects accounting for 2% of the slope variance. Regarding model fit, the variance component and X2 statistics were .0373, X2295 = 1342.79, p = .000 for the intercept and .0019, X2295 = 530.56, p = .000 for the slope, suggesting a small improvement in fit compared to the unconditional growth model. The association between the interaction term and the slope of Externalizing growth curves is displayed in Figure 3. In that figure, each line is drawn through the average child Externalizing scores when Infant Negative Emotionality and Maternal Depressive Symptom scores were high (one standard deviation above sample medians) and/or low (one standard deviation below sample medians). The effect of Maternal Depressive Symptoms is apparent (higher Externalizing scores at all ages when Depressive Symptoms are high), and at each age the average Externalizing score was the lowest when both Infant Negative Emotionality and Maternal Depressive Symptoms were low. Of note too is that when Maternal Depressive Symptoms were high, estimated Externalizing scores at ages 5 to 6, but not at ages 2 to 3.5, were in or quite near the clinically significant range (i.e., were near or at least as high as raw scores comparable to a T-score of 60 on the CBCL). When Depressive Symptoms were low, Externalizing scores decreased faster when Infant Negative Emotionality was high (slope = -.068) than when it was low (slope = -.051). On the other hand, when Depressive Symptoms were high, Externalizing scores decreased faster when Infant Negative Emotionality was low (slope = -.071), compared to when it was high (-.052).

            Second, although the cross-domain interaction involving Maternal Acceptance and Depression was not a statistically significant predictor of externalizing slope variance, the interaction between Maternal Acceptance and Parental Conflict was (coefficient = .006, se = .003, t295 = 2.25, p = .024). Regarding model fit, the variance component and X2 statistics were .0383, X2295 = 1352.16, p = .000 for the intercept and .0018, X2295 = 531.85, p = .000 for the slope, suggesting a small improvement in fit compared to the unconditional growth model. Again, the term plus its component main effects accounted for 2% of the slope variance. The association between the interaction term and the slopes is displayed in Figure 4. In that Figure, each line is drawn through the average child Externalizing scores when Parental Conflict and Maternal Acceptance scores were high (one standard deviation above sample medians) and/or low (one standard deviation below sample medians). The effect of Parental Conflict is apparent (higher externalizing scores at all ages when Parental Conflict is high).  In fact, when Parental Conflict was high and Maternal Acceptance was low, estimated Externalizing scores at ages 5 to 6 (but not at ages 2 to 3.5) were in the clinically significant range (i.e., were higher than the raw score comparable to a T-score of 60 on the CBCL). At each age the average Externalizing score was the lowest when Parental Conflict was low and Maternal Acceptance was high. The over-time decrease in Externalizing scores was also greater in this situation of low Parental Conflict and high Maternal Acceptance. When Parental Conflict was high, low Maternal Acceptance was associated with a faster decrease in Externalizing behavior than was high Acceptance (slopes = -.064 and -.051, respectively). On the other hand, when Parental Conflict was low, high Maternal Acceptance was associated with a faster decrease in Externalizing scores (slope = -.070) than was low Maternal Acceptance (slope = -.051).


            We examined both the rate of change and age-6 level of Externalizing behavior among 299 boys from low-income families and explored how factors across child, parenting, and family domains predicted the course of early externalizing behaviors. Predictors investigated included Infant Negative Emotionality, Maternal Depressive Symptoms, Maternal Acceptance, and Parental Conflict, with a special interest in cross-domain interactive effects on rate of Externalizing behavior change. Each showed a significant main effect on age-6 Externalizing behavior, and all effects were unique except that for Infant Negative Emotionality. Furthermore, the interaction between Maternal Acceptance and Depressive Symptoms was significantly associated with age-6 Externalizing behavior. On the other hand, no main effects on the rate of Externalizing behavior change were found but two of five cross-domain interactions did show significant associations with the rate of Externalizing behavior change from age 2 to 6:  Maternal Depressive Symptoms with Infant Negative Emotionality, and Parental Conflict with Maternal Acceptance.

Our unconditional growth curve model indicated that the average level of externalizing behavior in this study decreased significantly from age 2 to 6. Is this a real phenomenon or a measurement artifact? Specifically, was the decrease related to changes in items from the age 2/3 to the age 4-16 versions of the CBCL that comprised our dependent measure? It seems possible that externalizing behavior scores decreased across age because the items we used to tap such behavior at age 5 and 6 have a lower base rate than those at ages 2 and 3.5 years. There are infrequently endorsed items (e.g., stealing, truancy, vandalism) on the age 4-16 version that might have brought down the average level, but there are comparably infrequent, although somewhat fewer, items on the age 2/3 version too (e.g., rocks head or body, smears bowel movements, chews on things that aren’t edible). Furthermore, our finding of decreasing externalizing behavior across the preschool years is consistent with reports using identical items across age (e.g., Spieker et al., 1999), and one would expect this pattern given increases in self-regulation that occur throughout the preschool period. To test the idea that our decreasing average growth curve was not simply due to measurement differences across time, we examined the growth curve of externalizing behavior using only the 10 items that are identical across both CBCL versions. This growth curve also showed externalizing behavior to decrease over time. The negative slope was less steep than when all items from the Externalizing factor were used (-.03 vs. -0.6), but was nevertheless significantly different from zero. Therefore, we believe the decrease in externalizing behavior across the preschool period is likely a real phenomenon and not a measurement artifact. We speculate that this decrease is due to both biological maturation and parental socialization attempts, although we did not investigate the cause of the decreasing trajectories.

In our conditional growth curve models, in addition to a significant joint effect of maternal acceptance and depressive symptoms, all main effects tested were significantly associated in the predicted directions with age-6 externalizing behavior. This was not surprising, given accumulated evidence in the literature for associations between each child, parenting, and family predictor and later externalizing problems. However, no main effects were associated with the rate at which externalizing behavior changed. This pattern may be due to the average growth curve intercept being more reliably measured than the slope. In other words, differences among slopes were more random than differences among intercepts (according to the reliability estimates), making slope variance harder to predict. It is also possible that our measurement strategy precluded significant predictors of the slope. Some predictors were measured at one point in time and some were aggregated from measures at different points in time; but in all cases a static predictor was used. Perhaps relations between changes in predictors (e.g., rate of change in maternal depressive symptoms across time, rather than the average level across time) and changes in externalizing behavior would have been statistically significant. It is also possible that the predictors tested as main effects are simply not associated with change over time, despite their associations with externalizing behavior at a particular time point in this and many other studies.

On the other hand, slope variance was accounted for by interactions, suggesting perhaps that over-time behavioral change is a complicated phenomenon that requires a more specific and elaborate explanation than one suggested by main effects.  In fact, the transactional model (Sameroff, 1975) suggests that interactions or cross-domain effects should better predict behavior development than do simple main effects, as we report. Our findings are also important because in few studies to date have predictors of the rate of change in childhood behavior problems been identified. We, along with a few others (Colder et al., 2002; Keiley, Bates, Dodge, & Pettit, 2002; McFayden-Ketchum et al., 1996; Munson et al., 2001; Nagin & Tremblay, 2001; Spieker et al., 1999), are some of the first to generate evidence relevant to understanding childhood behavior problem change over time, rather than simply predicting the level of problems at a particular point in time.

In the two cases in which interactive terms were associated with the growth of externalizing behavior, the nature of these associations was only partially expected. In the first case, infant negative emotionality and maternal depressive symptoms together accounted for significant variance in the slope of the externalizing behavior growth curves. This finding is consistent with the growing literature regarding associations between child temperament X parenting behavior interactions and child adjustment (e.g., Bates et al., 1998; Colder et al., 1997; Lengua et al., 2000; Kochanska, 1997), and the more general theory concerning the bidirectionality of parent and child effects on child developmental outcomes (Bell, 1968).  Not surprisingly, when depressive symptoms were high, low infant negative emotionality was associated with greater improvement in externalizing behavior over time than was high infant negative emotionality. This finding suggests a protective effect of low negative emotionality when children are at risk for externalizing problems due to high levels of maternal depressive symptomatology.  Others too have found positive child temperamental attributes (e.g., positive emotionality, Lengua et al., 2000;  low activity level, Colder et al., 1997) to protect children from adjustment problems in high-risk parenting contexts. 

However, when depressive symptoms were low the opposite was true. High, not low, negative emotionality was associated with a greater improvement in externalizing behavior. It could be that under "normal" circumstances (i.e., low levels of maternal depressive symptoms), the association between infant negative emotionality and externalizing behavior simply fades over time. This fading effect is represented by the convergence of the two growth curves when maternal depressive symptoms were low. Consistent with a non-specific, cumulative risk hypothesis (Rutter, Cox, Tupling, Berger, & Yule, 1975), the plot of this interaction also suggests that the presence of cross-domain risk factors (high negative emotionality and high depressive symptomatology) are maintaining externalizing problems over time whereas the level of externalizing behavior starts and stays low or declines more rapidly in the presence of only one or neither risk factor.

The finding that parental conflict and maternal acceptance jointly accounted for significant variance in the slopes of the externalizing behavior growth curves is somewhat more difficult to explain. Not surprisingly, the fastest decrease in externalizing behavior (i.e., most improvement) and the lowest level of externalizing behavior at each age were found in what is arguably the most optimal situation: low parental conflict and high maternal acceptance. And when parental conflict was low but maternal acceptance was also low, externalizing behavior decreased at a slower rate than when acceptance was high. Yet unexpectedly, a relatively large decrease in externalizing behavior was also found in the least optimal situation: low maternal acceptance and high parental conflict. Here we invoke a regression to the mean explanation, i.e., over time initially high externalizing scores moved toward the more typical scores of children in the other groups (although externalizing scores for these children exposed to cross-domain risks began and remained higher than for all others). Additionally, among the children experiencing high parental conflict, the effect of maternal acceptance (measured at age 2) seemed to fade over time because externalizing scores in the high versus low acceptance conditions were more divergent at age 2 than at age 6. 

In addition to displaying the significant interaction, Figure 4 also shows the joint effect of parental conflict and maternal acceptance on the level of externalizing behavior at each age, an effect which is consistent with a non-specific, cumulative risk hypothesis (Rutter et al., 1975). When neither risk factor was present, externalizing scores were lowest at each age. When both risk factors were present, externalizing scores were highest at each age. And when one risk factor was present, externalizing scores were always intermediate. It must be noted, however, that unlike in Figures 3 and 4, this non-specific, cumulative risk pattern was not evident in Figure 2 in which the joint effect of maternal acceptance and depressive symptoms on age-6 externalizing behavior is displayed. There, although the absence of both risk factors was clearly associated with the lowest levels of externalizing behavior, whether one or both risk factors were present was not as predictive as the presence of maternal depressive symptoms.

            The primary limitations of our methodology are our exclusively male, low SES sample (which limits generalizability of our findings) and shared method variance between certain predictors (maternal depressive symptoms, parental conflict) and our dependent measure. Additionally, as noted above, our statistical approach did not allow the testing of relations between changes in predictors and the change or growth in externalizing behavior. Because HLM 5 does not allow for the modeling of time-varying Level 2 predictors (even though for two of our predictors we had repeated measures), we needed to model all of our predictors as fixed effects.  This misspecification of our model likely inflated the effects of our Level 2 variables to some degree. There are also potentially important differences in when each predictor was measured.  In particular, infant negative emotionality and maternal acceptance were each measured once during infancy; parental conflict and maternal depressive symptoms were aggregated from scores taken across ages 1.5 to 5.5 years. However, these procedures did not seem to have a notable impact on our findings: earlier-measured predictors and those measured across time all produced significant results. It should also be noted that the variances accounted for by the interaction terms that were identified as significant predictors of externalizing problem change were small. Additionally, our use of multiplicative interaction terms only approximated the transactive processes we wished to assess.

            In conclusion, we used a recommended and relatively new statistical approach to analyze our repeated-measures data that offers distinct advantages when one is interested in understanding the rate of behavior problem change as well as the level of behavior problems at a particular point in time. We predicted the ultimate level of externalizing behavior from infant negative emotionality, maternal depressive symptoms, maternal acceptance of the child, and parental conflict. But more important, we predicted rates of externalizing behavior change using combinations of these child, parenting, and family factors. Our results add to a small but growing body of literature regarding predictors of behavior problem change in young children, an understudied area of research with potential to inform the science and practice of developmental and clinical child psychology.





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Table 1

Externalizing factor items from age 2/3 and age 4-16 versions of the CBCL

Age 2/3                                                                        Age 4-16                                                        

Destroys own things                                                      Destroys own things

Destroys things belonging to others                                Destroys things belonging to others

Demands must be met immediately                                Demands a lot of attention

Disobedient                                                                  Disobedient at school/disobedient at home

Easily jealous                                                                Easily jealous

Gets in many fights                                                        Gets into many fights

Screams a lot                                                                Screams a lot

Sudden changes in mood or feelings                              Sudden changes in mood or feelings

Temper tantrums or hot temper                         Temper tantrums or hot temper

Unusually loud                                                  Unusually loud


Hits others                                                                    Does not feel guilty after misbehaving

Can’t concentrate or pay attention                                 Hangs with others who get in trouble

Cruel to animals                                                            Lying or cheating

Gets into everything                                                      Teases a lot

Defiant                                                                         Sets fires

Easily frustrated                                                            Steals at home, Steals outside of home

Angry moods                                                                Swears a lot

Punishment doesn’t change behavior                             Threatens people

Selfish or won’t share                                                   Truancy, skips school

Table 1 (con't)

Age 2/3                                                                        Age 4-16                                                        

Whining                                                                        Vandalism

Quickly shifts from one activity to another                      Argues a lot

Repeatedly rocks head or body                                    Bragging, boasting

Smears bowel movements                                             Cruelty, bullying, meanness to others

Gets hurts a lot, accident-prone                         Physically attacks people

Chews on things that aren’t edible                                 Showing off or clowning

Eats or drinks things that are not food                            Talks too much

                                                                                    Stubborn, sullen, or irritable

                                                                                    Thinks about sex too much


Note. Items above dotted line are identical across age. Items below dotted line vary across age.





Table 2

Descriptive Statistics

Predictor variables                                            n          M                     SD

Infant Negative Emotionality                              293      13.21               5.44

Maternal Acceptance                                        280      5.0                  2.0

Maternal Depressive Symptoms                        299      7.8                  5.5

Parental Conflict                                               296      -.01                 .70


Outcome variables                                            n          M                     SD

Externalizing score 24 months                           275      .64                   .28

Externalizing score 42 months                           275      .61                   .30

Externalizing score 60 months                           275      .42                   .24

Externalizing score 64 months                           231      .40                   .25

Externalizing score 72 months                           253      .40                   .24

































Figure Captions

Figure 1.  Unconditional growth curve.

Figure 2.  Age-6 externalizing behavior at different levels of maternal acceptance and depressive symptoms.

Figure 3.  Average growth curves at different levels of infant negative emotionality and maternal depressive symptoms.

Figure 4. Average growth curves at different levels of parental conflict and maternal acceptance.