Trajectories Leading to School-Age Conduct Problems

Recently, there has been an increased interest in studying the developmental trajectories of children who show high levels of early conduct problems (CP, Aguilar, Sroufe, Egeland, & Carlson, 2000; Shaw et al., 1998). The reasons for this interest are clear.  First, both epidemiological and developmental studies beginning as early as age 2 have found aggressive behavior to be highly stable, particularly among males (Cummings, Iannotti, & Zahn-Waxler, 1989; Olweus, 1979; Shaw, Gilliom, & Giovannelli, 2000).  From longitudinal studies that have traced the developmental course of child disruptive behavior, it is estimated that approximately 50% continue to show these difficulties throughout the school-age period and into early adolescence (Campbell, 1994, 1995; McGee, Silva, & Williams, 1984; Richman, Stevenson, & Graham, 1982).  Second, CP, especially in their more serious forms occurring during school-age and adolescence, are extremely costly to society in terms of damaged property and disruption of normal patterns of living.  Third, in school-age children and adolescents serious forms of CP have been found to be highly resistant to change -- few interventions have proven to be consistently effective (Kazdin, 1995).  Fourth, the period from infancy to preschool is one of the most critical in development.  During these years, many developmental trajectories leading to adaptive or maladaptive outcomes begin (Campbell, 1995).  Furthermore, past research on treatment of CP has shown that interventions implemented prior to school-age have a higher probability of success (Dishion & Patterson, 1992).  For these reasons, delineating developmental trajectories of early CP may suggest important targets and appropriate timing for intervention, particularly if mapping of trajectories is accompanied by identification of risk factors associated with divergent pathways.  This study extends our knowledge base by identifying patterns of CP and correlates of these trajectories among a sample of high-risk children from toddlerhood to middle childhood.

Modeling Developmental Trajectories of Conduct Problems

 Tremblay and colleagues (1999) have suggested that the developmental trajectory of overt antisocial behavior is a negative function of age.  Overt forms of CP include oppositional and aggressive behaviors that occur in the presence of adults.  Tremblay points to research demonstrating that oppositional and aggressive behavior peaks at the end of the second year, and diminishes thereafter due to socialization effects and children’s increasing capacity for using alternative conflict-resolution strategies.  The few longitudinal studies that have traced trajectories of physical aggression during middle childhood and adolescence support Tremblay’s contention, consistently noting a decrease in physical aggression with age (Cairns, Cairns, Neckerman, Ferguson, & Gariepy, 1989; Patterson, Shaw, Snyder, & Yoerger, 2001; Tremblay et al., 1996).  Less recent research on younger children’s rates of oppositionality also suggest a decrease with age.  Goodenough (1931) showed frequency of anger outbursts decreased from about .13 per hour at 18 months to .07 per hour by 8 years.  Similarly, a home observation study by Fawl (1963) showed a correlation of -.76 between age and child frequency of conflict bouts.

Despite children’s decreasing use of overt forms of antisocial behavior with age, there is also a body of evidence to suggest that not all children follow this descending trajectory.  Using ad hoc categorization procedures such as chronicity of CP to create groups of antisocial children, researchers have shown that a significant minority of children follow a stable pattern of overt CP from middle childhood through adolescence.  In all, four trajectories have been consistently identified, ranging from persistently high or low rates of overt antisocial behavior, to initially  high or moderate levels followed by later desistance  (Haapasalo & Tremblay, 1994; Loeber, Tremblay, Gagnon, & Charlebois, 1989; Moffitt, 1993; Patterson, DeBaryshe, & Ramsey, 1989).

In the past decade, several methodological advances have occurred that have allowed researchers to move beyond the use of ad hoc categorization procedures for studying developmental trajectories, including hierarchical modeling (Bryk & Raudenbush, 1987, 1992) and growth curve modeling (McArdle & Epstein, 1987; Willett & Sayer, 1994).  More recently, Nagin (1999) introduced a semiparametric, group-based approach for modeling developmental trajectories, which has the advantage of identifying clusters of individuals who share common pathways.  In this approach, classification of homogeneous groups occurs based on the pattern of trajectories over time rather than using an a priori criterion. Whereas hierarchical and latent growth curve modeling assume a continuous distribution of trajectories within the population, the semiparametric method is categorical, allowing one to ascertain if certain types of people follow unique developmental trajectories (Nagin & Tremblay, 1999).

In one of the first studies to apply the semiparametric method to identify pathways of CP, Nagin and Tremblay (1999) identified four similar developmental trajectories for three different forms of overt antisocial behavior: physical aggression, oppositionality, and hyperactivity.  Teacher reports on children’s behavior were gathered beginning at age 6 and at one-year intervals between ages 10 and 15, for which the following four trajectories were identified: a chronic persistence trajectory, a high level near-desister trajectory, a moderate level desister trajectory, and a no problem trajectory.  In a follow-up of this study, Nagin and Tremblay (2001) also identified risk factors that accounted for the differences in trajectories of physical aggression among groups.  Controlling for other child and family factors, low maternal age and maternal education were the only factors to discriminate those children who showed a pattern of persistent antisocial behavior from those in the high desister group.

To date, modeling of children’s antisocial behavior has been limited to studying developmental trajectories beginning at school-age or early adolescence (Fergusson, Horwood, & Nagin, 2000; Nagin, 1999; Nagin & Tremblay, 1999).  Moreover, evaluation of child and family risk factors that has been used to test differences among trajectories has been limited to questionnaires and interviews.  Specifically, Nagin and Tremblay (2001) find that socioeconomic risk factors may be significant in discriminating trajectories of antisocial behavior among school-age children and adolescents. However, more proximal indicators, such as the child’s early behavioral style, the mother’s psychological resources, and quality of the caregiving environment may provide potentially more useful data on the mechanisms underlying the relationship between socioeconomic risk and trajectories of persistent antisocial behavior.

Risk Factors Associated with Early Starter Trajectories

The examination of risk factors associated with persistent trajectories of CP is of particular interest because of the increased risk status of children who display CP prior to adolescence.  “Early starters” show a more persistent and chronic course of antisocial behavior from middle childhood through young adulthood (Moffitt, 1990; Patterson, Reid, & Dishion, 1992).  Moffitt (1993) has suggested that early starters are characterized by neuropsychological deficits in the child that compromise verbal and executive functioning.  Psychosocial risk factors are hypothesized to interact with child characteristics to place children at further risk for a persistent course of CP.  Moffitt’s model is also consistent with recent formulations of how early child characteristics, such as negative emotionality or fearlessness, may moderate the effects of parenting on the course of children’s CP (Bates, Dodge, Pettit, & Ridge, 1998).

Like Moffitt, Patterson and colleagues’ (1992) research suggests that early starters are at greater risk for more serious criminal offending, but places a greater emphasis on the role of parenting than on child characteristics.  Patterson acknowledges that specific types of child characteristics are more likely to elicit inept parenting strategies (e.g., irritability, hyperactivity), but postulates that patterns of coercive parenting potentiate the onset of more serious CP.  In a coercive cycle, the parent and child each behave in a way that is aversive to the other in an attempt to control the other's behavior.  As the child's aversive behaviors increase in intensity and frequency, the parent eventually acquiesces, unwittingly reinforcing the child’s behavior.  As the child becomes increasingly irritating, the parent further escalates power assertion techniques and presumably, the level of hostility she displays toward the child.

Unfortunately, few studies have been initiated prior to preschool age to examine the relative influence of child and caregiving factors in relation to persistence of CP.  In the one study to examine this issue from infancy through adolescence, Aguilar et al. (2000) found that persistently antisocial children were distinguished from never antisocial and/or adolescent-onset antisocial children by the following group of family life and psychosocial risk factors assessed in the first three years: avoidant attachment, stress, caregiver sensitivity, caregiver depression, quality of caregiving and the home environment, and socioeconomic status.  In an earlier follow-up of the present cohort, similar results were found in differentiating children with clinically-significant CP at school entry from those with subclinical scores (Shaw, Owens, Giovannelli, & Winslow, 2001).  Of child, family, and neighborhood risk factors assessed at ages 1.5 and 2, only rejecting parenting, overall quality of the home environment (HOME scale), and neighborhood dangerousness differentiated clinically-elevated CP identified by teacher reports.

Based on the results of the Aguilar and Shaw studies and coercion theory (Patterson, 1982), we chose to focus on proximal factors in three domains: child characteristics, parental psychological resources, and parenting.  We hypothesized that risk factors in each of these three domains, in the form of high fearlessness, high maternal depressive symptomatology, and high rejecting parenting, would likely increase rates of coercive parent-child interaction during the first two years, which in turn, would likely differentiate subsequent CP trajectories into the school-age period.

 

Fearlessness and Child Conduct Problems

Individual differences have been noted in children’s propensities to approach or avoid novel situations.  Some children experience high levels of negative arousal when confronted with such challenging situations, leading to a tendency to escape, avoid, or alleviate the stress associated with the novel stimuli (Kagan, 1989).  Other children are relatively fearless and are quick to approach new situations or people (Kagan, 1997), and children falling in the extremes of these opposing profiles show moderately stable trajectories from late infancy to adolescence (Schwartz, Snidman, & Kagan, 1996).  Accordingly, fearful toddlers, because of their tendency to minimize exposure to new people and environments, retreat to caregivers, and eliminate opportunities to develop proactive coping skills.  In contrast, fearless toddlers, more likely to approach the unfamiliar, would more often test limits.  From an interactionist perspective, such fearless toddlers would also be more likely to stress caregiver patience because of their eagerness to explore more challenging and potentially dangerous situations, and their lesser fear of consequences for misbehavior.  The latter hypothesized pathway is supported by a few prospective studies, finding that more fearless children appear to be at risk for CP in middle childhood and adolescence (Raine, Reynolds, Venables, Mednick, & Farrington, 1998; Schwartz et al., 1996), but few studies have traced this pathway with an at-risk sample from toddlerhood to the school-age period.  While assessments of behavioral inhibition with young children have traditionally employed procedures to test for children’s approach/avoidance in both social and nonsocial contexts (e.g., approach to playing with a strange adult or peer coupled with exposure to a novel and/or scary toy or robot), because of our interest in toddlers who would approach potentially dangerous situations and those that would stimulate parental intervention and coercive interaction, we limited the assessment of inhibition to a nonsocial stimulus.

 

Maternal Depressive Symptoms and Child Conduct Problems

Several researchers have attempted to identify psychological resources in the family that may interfere with the optimal functioning of the parent, including social support (Crnic, Greenberg, Ragozin, Robinson, & Basham, 1983), life events (Aguilar et al., 2000), and parenting hassles (Crnic & Greenberg, 1990).  One of the most proximal indices of maternal psychological resources is the mother’s level of depressive symptomatology.  From an interactionist perspective, features common to adult depressives, such as high irritability and criticalness, and low positive affect are hypothesized to compromise caregiving quality in two ways.  First, high negativity should increase parent’s tendencies to be harsh and rejecting.  Second, the parent’s low positivity should increase demands on the child to gain the mother’s attention, thereby increasing the probability of disruptive behavior on the part of the child and subsequently, greater negativity on the part of the parent.  Results from several studies are consistent with this formulation, documenting that mothers of young children with CP report more depressive symptomatology than those who endorse fewer symptoms (Aguilar et al., 2000; Mash & Johnston, 1983; Shaw, Vondra, Dowdell Hommerding, Keenan, & Dunn, 1994; Spieker et al., 1999; Zahn-Waxler, Iannotti, Cummings, & Denham, 1990), differences that persist longitudinally (Campbell, March, Pierce, Ewing, & Szumowski, 1991; Webster-Stratton, 1990).

Rejecting Parenting and Child Conduct Problems

 

The second year is a transitional period for parents as they must simultaneously cope with children’s increasing mobility and quest for autonomy.  Unfortunately, these developments are accompanied by toddlers’ limited understanding of the world around them, which results in normative increases in the expression of anger and physical aggression (Goodenough, 1931; Maccoby, 1980).  It is only recently that researchers have begun to investigate how the toddler period may be critical to the development of early CP, depending to a considerable degree on how parents respond to these normative changes in child behavior (Belsky, Woodworth, & Crnic, 1996; Shaw et al., 1998).  Recent studies have documented that parental hostility in the second and third years is predictive of later CP (Campbell, Pierce, Moore, Marakovitz, & Newby, 1996; Shaw et al., 1998), following similar results among school-age children and adolescents (see Loeber & Dishion, 1983; McCord, McCord, & Zola, 1959).  In fact, in a meta-analysis of studies examining relations between juvenile delinquency and parenting, parental rejection emerged as one of the most powerful and consistent predictors (Loeber & Stouthamer-Loeber, 1986).  In the present study, a measure of rejecting parenting was composited from observations recorded in the lab and the home based on structured and unstructured tasks, respectively. 

In summary, our first goal was to extend the use of the semiparametric mixture model to early childhood by tracing trajectories of overt CP from ages 2 to 8 using data on 284 boys from ethnically diverse, low-income urban families.  Based on recent research that documented a similar pattern of decreasing growth of overt CP between the school-age period and adolescence, and between the toddler and school-age period (Patterson, Shaw, Snyder, & Yoerger, 2001), we hypothesized that similar developmental trajectories would be identified from ages 2 to 8 as that found between ages 6 to 15 (Nagin & Tremblay, 1999).  Specifically, it was expected that four groups would be identified and include a persistent chronic and a persistent low problem group, a high desister group, and a moderate desister group. 

A second goal was to advance our understanding of risk factors that differentiate developmental trajectories of CP in early childhood, including those groups that show initially high versus low CP, and those that maintain a high rate of CP throughout the period of study in contrast to those who desist from initially high levels. Following up the recent work of Nagin and colleagues (1999) that showed that parental sociodemographic factors differentiated CP pathways, we tested the effects of more proximal child and family measures, relying heavily on observational measurement.  However, to ensure that effects were not attributable to socioeconomic influences, these risk factors were also included in analysis.  Finally, child IQ was also included based on previous research showing modest but consistent effects of low verbal IQ on child CP.  It was hypothesized that children characterized by high fearlessness with family environments marked by high maternal depressive symptoms and elevated rejecting parenting would more likely follow the persistent CP trajectory, and that these effects would continue to be demonstrable after accounting for the influences of socioeconomic factors and child IQ.  Based on transactional models of CP in early childhood ( Bates et al., 1998; Shaw & Bell, 1993), we also anticipated the interaction between children with high fearlessness and high rejecting parenting to differentiate persistent CP children from other groups.  

Method

Participants

The source for subject recruitment was low-income families who use the Allegheny County's Women, Infants, and Children (WIC) Program in the Pittsburgh metropolitan area (Shaw et al., 1998).  WIC provides nutritional food supplements for income-eligible participants from pregnancy until children are 5 years old.  Three-hundred and ten participants were recruited from WIC sites throughout the Pittsburgh metropolitan area over the course of 2 years.  Since the intent of the original investigation was to examine the developmental precursors of antisocial behavior, the sample was restricted to boys. Participants were recruited when target children were between 6 and 17 months old.  At the time of the first assessment, at which time infants were 1.5 years old, mothers ranged in age from 17 to 43 years, with a mean age of 28.  Fifty-three per cent of participants were Caucasian, 36% were African American, 5% were biracial, and 6% were other (e.g., Hispanic). At the age 1.5 visit, 65% were either married or living together, 26% were single, 7% were divorced, and 2% were other.  Mean per capita family income was $241 per month ($2,892 per year), and the mean Hollingshead socioeconomic status score was 24.8, indicative of a working class sample.

Initially, 421 families were approached at WIC sites.  Fourteen (3.3%) declined to participate at the time of recruitment and an additional 97 declined before the first assessment.  Thus, of the 421 families asked, 310 (71%) participated in the first assessment at 1.5 years.  Of the 310 families seen at the age 1.5 assessment, data were available on 302 at the age 2 assessment. Subsequent lab or home assessments were convened when children were ages 3.5, 5, 6, and 8, during which time retention rates ranged from 86-91% per assessment.  For the purposes of modeling individual trajectories, measures of CP were required at three or more time points, resulting in a sample of 284 boys.  To examine whether attrition may have biased the sample selection, we compared families whose data were used in the present study (i.e., > three assessments) to those with fewer than three assessment points.  Families who were included versus excluded in the analyses did not differ on any variables used in the study.

Procedures

At ages 1.5 and 2, mothers and target children were seen in our laboratory for approximately 2 hours.  These visits included structured parent-child interactive tasks, free play, and maternal interviews.  Assessment tasks in the lab were selected to vary in stress level so that mother and child behavior could be observed across a broad spectrum of conditions.  All tasks conducted in the lab were recorded on videotape for future coding. The age-2 laboratory visit was preceded by a 1.5-hour-long home visit (i.e., occurred on the same day) to observe the quality of the home environment and parent-child interaction during structured tasks and during an interview with the mother.  As part of both lab visits, mothers completed inventories about depressive symptomatology and were observed with their sons in a clean-up task. At the age-2 lab visit, children were also observed in the inhibition paradigm. 

The clean-up task is widely used in research on parenting behavior with young children.  After a 15-minute warm-up period in which boys played with a variety of toys while mothers completed questionnaires with an examiner, mothers were told to instruct their child to put the toys in a basket. Mother-child dyads were allowed five minutes to complete the task. 

A measure of nonsocial behavioral inhibition (i.e., fearlessness/fearfulness), adapted from the work of Kagan (1997), was administered midway through the lab assessment. After the lab room was cleared of toys and mothers were given several questionnaires to complete, a tape recording of gorilla noises was played intermittently for 2 minutes.  The audio recording was a compilation of scenes from the movie, “Gorillas In the Mist,” in which gorillas howled in a threatening manner while being chased by hunters.  The tape recorder was stationed in an enclosed cabinet on the opposite side of the room from the mother and child so that the child could identify the source of the sounds and choose to approach or stay away.  To facilitate coding the child’s proximity to the cabinet, tape was placed on the floor to mark the perimeter one foot around the cabinet.

Measures

Maternal age and education.  As part of a demographic interview conducted at the age 2 assessment, information about maternal age and educational attainment was gathered.  It should be noted that because families were required to have another sibling living at home at the time of the recruitment, relatively few of the mothers were under 20 years of age at the time the target child was born (n = 17).

Child IQ.  When children were age 5.5 years old, a home assessment was conducted on a subset of families (n = 235), which included an assessment of child IQ using a short form of the widely used Wechsler Preschool and Primary Scale of Intelligence-Revised (Wechsler, 1989). The Block Design (BD), Geometric Design (GD), Information (I), and Vocabulary (V) subtests were administered because of their factor loadings, split-half reliability coefficients (BD: r = .85; GD: r = .79; I: r = .84; V: r = .84), the high reliability and validity coefficients of this set of subtests (r tt = .92 and r = .91, respectively), and ease of administration (Sattler, 1990).  Based on previous research demonstrating more consistent effects of Verbal IQ (VIQ) on CP, scaled scores for I and V were converted to VIQ scores according to procedures described by Sattler (1990).

Child Fearlessness.  Coders rated boys’ behavior during the Gorilla Task on two molecular and two global scales. The molecular codes included latency to approach the cabinet and time in close proximity to mother. The global ratings included distress and approach/avoidance. Distress was defined as facial or vocal expressions of fear and anxiety (e.g., crying; whimpering; statements indicating distress, such as “I’m scared”). Coders took into account both the duration and intensity of distress cues. Ratings of approach/avoidance were based on the extent to which they approached and investigated the cabinet. The global ratings were made on 4-point scales. Inter-rater reliability was .9 or greater on all scales based on 20% of cases coded by two raters. To create a single index of behavioral inhibition, the four ratings were subjected to principal-components analysis. One factor emerged with an eigenvalue greater or equal to one. This factor accounted for 49.22% of the total variance.     

Maternal Depressive Symptoms

Beck Depression Inventory (BDI).  The BDI, a well-established and widely used measure of depressive states (Beck & Beamesderfer, 1974; Beck, Ward, Mendelon, Mock, & Erbaugh, 1961), was administered at the age 1.5- and 2-year assessments.  Split-half reliability of the scale is high (.86 to .93).  A composite was formed based on the scores at ages 1.5 and 2.  Empirically, this was justifiable given that correlations between composited BDI scores were equal to r =.66, p <.0001.  Previous research has identified maternal depression to be associated with CP in early childhood (Shaw, Keenan, et al. 1994; Zahn-Waxler et al., 1990).  In order to make the instrument more trait-like, directions for the BDI were altered so mothers reported about depressive symptoms experienced in the past six months rather than the past week. 

Rejecting Parenting

 Maternal rejecting parenting was measured in two ways at ages 1.5 and 2: from

videotapes of the clean-up task using the Early Parenting Coding System (EPCS, Winslow & Shaw, 1995) and from examiner report using the Home Observation for Measurement of the Environment (age 2 only; HOME; Caldwell & Bradley, 1984). The EPCS was designed to capture a range of parenting behavior typically exhibited in interactions with young children. This coding system consists of nine molecular and six global ratings. The EPCS measure of harsh parenting included two molecular ratings– verbal/physical approval and critical statement–and three global ratings–hostility, warmth, and punitiveness. Hostility was defined as the expression of anger by the mother toward the child as indicated by tone of voice and mannerisms. The warmth rating was an evaluation of positive affect directed toward the child. Punitiveness was defined as the extent to which the mother was too strict or harsh, considering the child’s behavior. For molecular ratings, Cohen’s kappa coefficients were .87 for approval and .79 for critical statement. For global ratings, kappa coefficients were .94, .83, and .94 for hostility, warmth, and punitiveness, respectively. Principal-components analysis yielded a single factor with an eigenvalue greater than one.  For the present study, a composite rating was created by averaging rejecting factor scores from the age 1.5 and 2 assessments.

The HOME assesses the quality and quantity of support and stimulation in the child’s home environment using semi-structured observation and parent interview. The eight-item Acceptance of Child’s Behavior subscale taps parent’s responses to child misbehavior or distress (e.g., “parent does not express annoyance with or hostility to the child,” “parent does not shout at child”). The HOME has demonstrated good reliability and validity properties (Caldwell & Bradley, 1984). Trained graduate student research assistants completed the HOME during home visits when boys were 2 years old. The HOME Acceptance scale and EPCS rejecting parenting factor were negatively correlated r = -.33, p < .01). To create a single measure of rejecting parenting, HOME Acceptance standard scores were reverse scored and added to standard scores derived from the EPCS rejecting composite at ages 1.5 and 2 years.

Child Conduct Problems                                                                                                                         

Child Behavior Checklist (CBCL; Achenbach, 1991, 1992). The Child Behavior Checklist is a widely used parent-report measure of childhood adjustment problems. There are two versions of the CBCL, one designed for children ages 2-3 and a second for children ages 4-18. Both versions contain items tapping externalizing and internalizing problems, although the content of some  items varies across versions to capture developmental change within these domains.  We selected five items that appear on both versions to create a measure of overt CP that could be used across time points: “cruel to animals,” “disobedient,” “gets in many fights,” “physically attacks people,” and “temper tantrums or hot temper.”  Cronbach’s alpha was used to evaluate the internal consistency of the scale and ranged from a low of .56 at age 2 to a high of .71 at age 8

Analyses

Analyses proceeded in two stages. In the first stage, a semiparametric, group-based

modeling strategy was used to identify distinct groups of individual trajectories. In the second stage, multivariate analyses were performed to identify early child and parent characteristics that distinguish membership in the divergent trajectory groups.

Like other approaches to analyzing individual trajectories, including hierarchical and latent growth curve modeling, the semiparametric, group-based method uses a polynomial function to model the relationship between an attribute (e.g., CP) and age (Nagin, 1999; Nagin & Tremblay, 1999). The function takes the form

y_it^*j = β₀^j + β₁^jAge_it + β₂^jAge²_it + ε,                  (1)

where y_it^*j is a latent variable characterizing the level of the attribute for participant i at time t given membership in group j, Age_it is participant i’s age at time t, Age²_it is the square of subject i’s age at time t, and ε is a disturbance assumed to be normally distributed with zero mean and constant variance σ². The model’s coefficients, β₀^j, β₁^j, and β₂^j, determine the shape of the trajectory and are superscripted by j to denote that the coefficients are free to vary across groups.

This flexibility is a key feature of the model because it allows for easy identification of population heterogeneity not only in the level of behavior at a given age but also in its development over age. A single peaked trajectory is implied if _₁ > 0 and _₂ < 0. Alternatively, if behavior remains constant over age, this trajectory is implied if _₁ = 0 and _₂ = 0.  Other interesting possibilities include trajectories in which growth is either steadily accelerating or decelerating. The former would be characterized by a trajectory in which both _₁  and _₂  are positive and the latter by both being negative. Thus, the method allows for the identification of unusual mixtures of trajectories within the population.

As discussed in Nagin (1999) and Raudenbush (2001), conventional hierarchical modeling (Bryk &Raudenbush, 1987, 1992; Goldstein, 1995), and latent curve analysis (McArdle &Epstein, 1987; Meredith &Tisak, 1990; Muthen,1989; Willett &Sayer, 1994) methods are designed to analyze developmental processes such as language acquisition that vary regularly within the population. By contrast they are ill-suited for identifying the sorts of unusual mixtures of trajectories that are commonly postulated in taxonomic theories of development.  While these two classes of methodology differ in very important respects, they also have important commonalities (MacCallum, Kim, Malarkey, & Kiecolt-Glaser, 1997; Raudenbush, 2001; Willett & Sayer, 1994). For our purposes one is key: Both model the unconditional and conditional population distribution of growth curves based on continuous distribution functions which makes it very difficult to use them for testing theories postulating distinctive developmental courses of psychopathology. Raudenbush (2001, p. 513) observes:  “It makes no sense to assume that everyone is increasing (or decreasing) in depression¼¼many persons will never be high in depression, others will always be high, while others will become increasingly depressed.” 

Because conventional growth curve modeling methods were ill-suited to identifying unusual mixtures of trajectories, developmental researchers have commonly resorted to using assignment rules based on subjective categorization criteria to construct categories of developmental trajectories. While such assignment rules are generally reasonable, there are limitations and pitfalls attendant to their use. One is that the existence of the various developmental trajectories that underlie the taxonomic theory cannot be tested; they must be assumed a priori. A second related pitfall is the risk of simultaneously  “over- and under- fitting” the data —creating trajectory groups that reflect only random variation and failing to identify unusual but still real developmental patterns. Third, ex ante specified rules provide no basis for calibrating the precision of individual classifications to the various groups that comprise the taxonomy. 

            Trajectory parameters are estimated with maximum likelihood. The essential function of maximum likelihood is to choose estimates of the parameters for which the likelihood of observing the actual data, Y, is maximized. In this study, as in many developmental investigations that rely on psychometric scale data, the distribution of y_it is censored. That is, at any given age, a significant number of participants exhibit none of the problem behaviors measured by the scale, resulting in a cluster of data at the scale minimum. The likelihood function linking y_it to the latent variable y_it^*j incorporates established results on the censored normal distribution to accommodate this censoring problem. It is also specified to accommodate missing data under the assumption that it is missing at random. Thus, individuals with incomplete assessment histories do not have to be dropped from the analysis.

A derivation of the likelihood may be found in Nagin (1999) but intuitively, the estimation procedure works as follows: Suppose unbeknownst to us there were two distinct groups in the population: One group who over the observation period started low but had rising conduct problems and another group who started high but subsequently had declining conduct problems.  Further suppose that each group comprised 50% of the population.  If data from this population were analyzed under the assumption that the relationship between age and behavior was identical across all individuals, we would mistakenly conclude that the rate of conduct problems is invariant with age.  If the data were analyzed using the approach described here which specifies the likelihood function as a mixing distribution, no such mathematical "compromise" would be necessary.  The parameters of one component of the mixture would effectively be used to accommodate (i.e., match) the individuals with rising conduct problems and another component would accommodate the individuals with declining problems.  

Final model selection requires a determination of the number of groups that best describes the data. D’Unger, Land, McCall, and Nagin (1998) recommend the Bayesian Information Criterion (BIC) as a basis for selecting the optimal group.  This index rewards parsimony in model specification by imposing penalty functions on the log likelihood for increasing the number of model parameters to be estimated. Thus, for two models with equivalent likelihoods, the model with fewer groups is preferred. For this application, model fitting is conducted using a customized SAS procedure. This procedure is available on request from the fourth author.

Model estimation produces two key outputs: parameter estimates that demarcate the shape of the trajectories and posterior probabilities of group membership for each individual in the estimation sample. The posterior probabilities estimate the probability of belonging to each of the trajectory groups. In the case of an individual who receives high CP ratings throughout childhood, for example, the probability of belonging to the chronic group would be high while the probability of belonging to the low trajectory group would be near zero. The posterior probabilities provide a basis for assigning individuals to trajectory groups: the largest probability for each individual indicates the trajectory that best conforms to that individual’s behavior over time.

The group membership designations set the stage for the second phase of analyses. Logit models were estimated to identify child and parent variables that discriminate among boys with divergent developmental trajectories, including those with initially high versus low levels of CP, as well as those with initially high levels of CP that persist versus desist over time. In the prediction of trajectory groups, we considered first the main effects of child fearlessness, maternal rejecting parenting, and maternal depression, controlling for maternal age and education and child verbal IQ (at age 5 ½). We then examined the interaction of maternal rejecting parenting with child fearlessness.

 

Results

The presentation of results follows the data analysis plan outlined above. After presenting descriptive statistics and correlations among independent variables, we report BIC scores for three alternative models and present the trajectories identified by the optimal model. Finally, we describe relations between early risk factors and trajectory group membership.

Descriptive statistics for all study variables are presented in Table 1.  Scores for child fearlessness and maternal rejection were converted to factor scores; hence, means for both indicators are zero. Of note are the relatively high scores for maternal depressive symptoms on the Beck Depression Inventory (BDI) at 18 and 24 months, for which the means approached levels of mild depression (i.e., scores of 9 are considered to reflect mild depressive symptomatology on the BDI).  Maternal age is relatively high because of the requirement that another sibling be present in the home at the time of recruitment of the target child.  The pattern of descending overt conduct problems from ages 2 to 8 is in accord with past research documenting this decreasing trajectory from todddlerhood to the school-age period (Tremblay et al., 1999).

                                                        

Insert Table 1 about here

                                                         

Correlations among independent variables are presented in Table 2. While child fearlessness was unrelated to all other predictors except rejecting parenting, rejecting parenting was positively  associated with maternal depressive symptoms, and negatively related to maternal age and education, and child IQ.  Maternal age, education, and child IQ were also modestly intercorrelated.

                                                        

Insert Table 2 about here

 

To determine the optimal number of trajectories for overt CP from ages 2 to 8, we estimated models with three, four, and five groups. This range coincides with the number of groups posited by trajectory theories of antisocial behavior and found in a prior application of the semiparametric, group-based approach (Nagin & Tremblay, 1999). The BIC score was -2326.50 for three groups; -2320.69 for four groups, and -2338.79 for five groups. Based on the selection rule provided by D’Unger and colleagues (1998), the four group model fit the data best.

Inspection of the parameter estimates revealed that the constant term (i.e., levels of overt CP at age 2) was significant (i.e., differed from 0) for all four groups.  For three of the four groups, the linear term was also significant, indicating that, for these groups, levels of overt CP changed over time.  The quadratic term did not reach significance for any of the groups, indicating that the rate of change remained constant over time.  Based on these results, a new four-group model was estimated in which the trajectories for three groups were defined by the constant and linear terms, while the trajectory for the fourth group was constrained to be constant over time. The BIC score for this final model, -2312.72, marked an improvement over previous models.

Figure 1 plots the predicted versus actual trajectories by group for overt CP. As noted above, the parameter estimates determine the shape of the predicted trajectories.  The actual trajectories reflect mean overt CP scores for participants assigned to each group based on their posterior probabilities. Although measures of goodness of fit between predicted and actual trajectories are not available presently, the degree of correspondence evident in Figure 1 suggests that the model approximates the data reasonably well.

Overall, the trajectories reveal reductions in overt CP for most boys between ages 2 and 8. One group, accounting for 14% of the sample, exhibits low levels of problematic behavior at age 2 that virtually disappear by age 8 (constant = 1.38, SE = 0.14, p < .0001; slope = -0.17, SE = .08, p < .05).  A second, larger group, comprising 42% of the sample, may be described as “moderate desisters.” This group engages in slightly higher levels of CP than the low group and shows a steady decline to the end of the observation period (constant = 2.72, SE = 0.23, p < .0001; slope = -0.24, SE = .04, p < .0001). On average, mothers of the moderate desisters endorse a single overt symptom at age 8. A third group, which comprises 38% of the sample, follows a trajectory that is similar in shape to the first two groups but at a slightly higher level (constant = 4.22, SE = 0.19, p < .0001; slope = -0.27, SE = .04, p < .0001). We designate this group as the “high desisters.” A fourth group, accounting for approximately 6% of the sample, exhibits relatively severe and persistent behavior problems across the observation period (constant = 5.24, SE = 0.22, p < .0001; slope was nonsignificant in the original four-group model [slope = .60, SE = .47, p = .20 ] and was constrained to be constant in the revised model). We identify boys who follow this high,

non-descending trajectory as members of the “chronic” group.

                                                         

Insert Figure 1 about here

                                                        

In Table 3 scores on risk factors are presented by trajectory group membership. An ANOVA was conducted to examine if trajectory group membership was associated with higher levels of individual risk factors.  In the case of child fearlessness, rejecting parenting, and maternal depressive symptoms, risk factor scores showed greater elevations in the high desister and chronic groups, with significant differences for child fearlessness and maternal depressive symptoms, and a nonsignificant trend for rejecting parenting. Results were less consistent for maternal age and education, as well as child IQ.

                                                        

Insert Table 3 about here

                                                          

Tables 4 and 5 contain coefficients and their associated statistics estimated in the multivariate logit analyses. Logit coefficients indicate the direction, strength, and reliability of the relationship between predictor variables.  Their exponentiated value of the coefficient measures the odds ratio—the relative change in odds of belonging to the target group attendant to a one unit change in the risk factor.  Table 4 summarizes an analysis aimed at distinguishing boys who followed the two high trajectories (high desister and chronic) from those in the two low trajectory groups (low and moderate desister). The results show that higher levels of child fearlessness and maternal depression increased the likelihood of following a high trajectory. After accounting for the other variables in the model, a one unit increment in fearlessness (1 SD) increased the odds of being in the high group by 63%; a one unit increase in maternal depression (1 point on the BDI scale) increased the odds by 6%.

                                                        

Insert Table 4 about here

                                                         

In a second logit analysis, summarized in Table 5, we tested the capacity of child and maternal variables to discriminate between the chronic and high desister groups. Child fearlessness and maternal rejecting parenting reliably distinguished these two trajectories. A one unit increase in fearlessness increased the odds of belonging to the chronic group by 86%, while a one unit increase in maternal rejection (1 SD) raised the odds by 67%.

                                                         

Insert Table 5 about here

                                                        

Discussion

The present findings fill in some significant holes in our understanding of the early developmental trajectories of overt CP.  Many of the results are consistent with recent work on developmental trajectories of overt antisocial behavior during the school-age period and adolescence.  Nagin and Tremblay (1999) and Patterson and colleagues (2001) have recently shown that boys demonstrate a decrease in overt antisocial behavior as a function of age.  Our results suggest that decreases in boys’ oppositional and aggressive behavior begin well before school-age, as the vast majority of the boys in the present sample showed a gradual decline in overt CP from ages 2 to 8.

Despite the general decrease in overt antisocial behavior with age, in accord with research on older children, there was also clear evidence that not all children follow this trajectory (Haapasalo & Tremblay, 1994; Loeber et al., 1989).  Applying Nagin’s semiparametric mixture model method, we identified four developmental trajectories of overt antisocial behavior: a persistently high group, a high desister group, a moderate desister group, and persistently low group.  While there was diversity in the starting point of overt CP among toddlers, three of the four groups showed a marked decrease from ages 2 to 8.  Only a small group of 16 children continued to show a comparably high rate of oppositional and aggressive through the preschool and early school-age periods, representing 5.6% of the sample. 

Most pertinent to the present findings is Nagin and Tremblay’s (1999) recent paper that used the same semiparametric mixture model to trace developmental trajectories of aggressive and oppositional behavior from ages 6 to 15.  This study was based on teacher reports of 1,037 boys from low socioeconomic areas in Montreal.  Mapping separate models for aggressive and oppositional behavior, they also found that a 4-trajectory model fit the data most optimally for both aggressive and oppositional trajectories, as well as hyperactivity.  Moreover, the patterning of the four trajectories for both aggressive and oppositional behavior was similar to our findings.  Perhaps even more significantly, Nagin and Tremblay found 5 and 6% of their children to be in the persistent aggressive and oppositional groups, respectively.  This is the same percentage of children identified in our persistent overt group (5.6%).  It also is close to the figure of 7% reported by Moffitt, Caspi, Dickson, Silva, and Stanton (1996) of children who persisted in showing high rates of antisocial behavior from ages 3 to 18 in the Dunedin study, and the 7% of children found to show a pattern of chronic aggression by Dodge and Laird (1999) from ages 6 to 10. Thus, the current results suggest that a descent in overt antisocial behavior begins for most children around age 2 despite heterogeneity in initial levels.  Furthermore, a small percentage of toddlers persist in demonstrating high rates of overt CP through the early school-age period despite the decrease in overt CP shown by most of their peers.

A second major objective of the study was to examine risk factors assessed in the first two years of life that differentiated membership in trajectory groups.  Risk factors were selected to include facets of the child behavior, the parent’s psychological resources, and parenting in the form of child fearlessness, maternal depressive symptomatology, and rejecting parenting.  Despite the fact that all measurement occurred when children were between ages 1.5 and 2, and that the influences of preschool child Verbal IQ, maternal age, and maternal education were accounted for, factors from each domain discriminated the developmental trajectories of children. Specifically, children who were more fearless and whose mothers reported higher rates of depressive symptoms in the toddler period were more likely to be in the persistent or high desister groups versus the moderate desister or persistently low problem group.  Child fearlessness and rejecting parenting differentiated children who remained in the persistent CP group from those who showed initially high CP but later desisted.

At the level of individual risk factors, the results corroborate previous research that has demonstrated individual associations between low inhibition (Schwartz et al., 1996), maternal depressive symptoms (Zahn-Waxler et al., 1990), rejecting parenting (Loeber & Stouthamer-Loeber, 1986), and later CP.  That early indices of these factors would discriminate the developmental trajectories of children over a six-year period even when controlling for the influence of these factors and maternal age and education, and child IQ is significant.  While several research groups studying older children and adolescents have identified risk factors that differentiate persistently low versus persistently high CP children (Haapasalo & Tremblay, 1994; Loeber et al., 1989; Moffitt, 1993; Nagin & Tremblay, 1999), it is only recently investigators have attempted to discriminate trajectories of persisters versus high desisters, and this research has been limited to the inclusion of less proximal indices of children’s caregiving environment (Nagin & Tremblay, 2001). These findings are consistent with our emphasis on factors that are most proximal to the child, both child attributes and caregiving the child receives.  On the one hand, the longitudinal relations may reflect the moderate stability of fearlessness, maternal depressive symptoms, and rejecting parenting.  Indeed, in the present cohort, stability of maternal depressive symptoms was r = .51 from when children were 2 to 6 years old, and short-term stability of rejecting parenting was .40 between ages 1.5 and 2.  While test-retest data for child fearlessness are unavailable from the current data set, Kagan (1989) reports that stability of behavioral inhibition is moderate from 21 months to 7.5 years, ranging from r = .39 to r = .67 in two independent cohorts.   Thus, there is reason to believe that all three factors are relatively stable over time.  From a prevention viewpoint, these risk factors’ moderate stability also suggests that identification of high-risk dyads may be possible by age two.

The nonsignificant effects found for maternal age in differentiating persisters from high desisters may also reflect the relative homogeneity of this factor within the sample compared to other investigations (Nagin & Tremblay, 2001).  In particular, because we required families to have another child living in the home at the time of recruitment, relatively few mothers (17) were in their teens.  We also believe that the factors measured in this study were more proximal in tapping the characteristics of the child and his caregiving environment.

From a transactional perspective, as hypothesized by Patterson and colleagues (1992), Martin (1981), and Shaw, Bell, and Gilliom, (2000), the combination of these proximal risk factors is likely to set in motion coercive processes between parents and children that result in a trajectory of persistent CP for children and continued maternal depressive symptoms and rejecting parenting.  Child fearlessness and maternal depressive symptoms appear critical in distinguishing initial levels of overt CP at age 2, but child fearlessness and rejecting parenting appear to be more salient in distinguishing the developmental course of children with both initially-high CP in early childhood.  In response to the behavior of a fearless toddler, parents may grow weary of attempting to thwart the child’s  to tendency to explore unknown and potentially dangerous situations.  They may increase the intensity of their responses both behaviorally and affectively, eventually demonstrating low levels of positivity and involvement towards the child.  Data from earlier stages of this project also support the notion that child CP at ages 2 and 3.5 are predicted by observations of earlier forms of aversive child behavior (i.e., persistent negative emotionality) in conjunction with unresponsive maternal behavior at age 1, and noncompliant toddler and rejecting parenting behavior at age 2 (Shaw, Winslow et al., 1998), findings that have been replicated in two other independent cohorts (Martin, 1981; Shaw, Keenan et al., 1994). Alternatively, the findings regarding fearlessness are also consistent with research by Kochanska (1997) and Frick and Ellis (1999).  Such a temperament could inhibit the development of conscience and a child’s ability to internalize parental norms, leading to higher levels of CP. 

It is also interesting to decompose the components of the rejecting parenting measure given its ability to differentiate group status over a six-year period.  In constructing it, we hypothesized that its longitudinal generalizability would be increased by having it based on observations in multiple contexts (i.e., home and lab), using a combination of structured and unstructured tasks (clean-up in the laboratory versus unstructured time at home), and by including items that tapped active rejecting behaviors (clean-up) and the absence of warmth and involvement (home visit).  In fact, neither individual measure was found to differentiate trajectory group status on its own, but when these modestly-correlated measures were combined, it was one of two variables that discriminated the course of initially-high CP children.  The strategy of aggregating measures across context, method, and content may prove fruitful for other researchers desiring to extend the predictive validity of parenting and other observationally-based data in relation to children’s CP.

Limitations

There are several significant methodological limitations of the study.  First, participants were limited to low-income European American and African American boys living in an urban setting.   Future work with boys and girls from other socioeconomic strata and ethnic backgrounds is recommended to replicate or disconfirm these results.  Measurement error could have influenced the findings, as predictor variables were assessed on only one or two occasions.  Relatedly, while many of the relations cannot be attributed to shared reporter or method variance because of the reliance on observations to measure child behavioral inhibition and rejecting parenting and the use of parent report to assess overt antisocial behavior, the linkage between early maternal depressive symptoms and persistence of child CP is confounded by shared informant and method variance.  Maternal depression has been consistently found to inflate relations with child behavior problems (Fergusson, Lynskey, & Horwood, 1993).   The concern about reporting bias is tempered by corroboration of the finding using the same composite of maternal depressive symptoms at ages 1.5 and 2 and teacher’s report of age 8 CP (Shaw et al., 1999).  Report of child CP was limited to maternal report.  Ideally, this would be supplemented by a second parent, teacher, and youth reports.  However, because use of the same items are currently a prerequisite for using Nagin’s semiparametric method (i.e., he is currently working on methods to permit the use of different item pools that tap the same underlying construct -- heterotypic continuity), alternative caregiver,  teacher, and youth reports available only at later ages could not be used.  Regarding the identification of trajectory groups, it should be emphasized that such groups’ are probabilistic in nature and that a single trajectory group may include individuals with relatively high and low probability of membership in that group. However, our analysis revealed such probabilities were

generally very high, which suggests little classification error.

As noted earlier, our measure of child fearlessness did not include both social and nonsocial components; the nonsocial stimulus was limited to an aural versus an aural and visual presentation.  As such, our measure of fearlessness was not optimal and the findings using this and more refined measures require further validation. Despite the crudeness of the measure, the gorilla sounds procedure may be tapping a tendency to approach unfamiliar, even noxious stimuli, perhaps reflecting individual differences in physiological arousal (Raine et al., 1998).  If the findings are generalizable and similar stimuli in the child’s environment trigger approach responses, one could imagine how they would tax parent’s patience and lead to persistence in disruptive behavior.  In contrast to a child high on negative emotionality, whose persistent crying and whining would be expected to challenge caregiver’s patience by the end of the first year, a tendency to explore unknown and potentially dangerous stimuli would be expected to impact parenting only later during the second year of life when the child has gained sufficient mobility to gain quick access to such stimuli (e.g., crossing a street, walking away from the parent at a crowded shopping mall).   Finally, this study examined developmental trajectories and covariates associated with overt versus covert CP.  Research that examines trajectories and covariates associated with covert CP is also recommended.  Although covert CP likely follow a different developmental sequence than overt CP (i.e., later starting period), it likely involves many of the same children previously exhibiting high rates of overt CP in early childhood.

Implications for Early Intervention

The present research extends previous research by documenting how specific factors across risk domains are associated with persistence versus desistance in overt antisocial behavior beginning when children were 1.5 to 2 years old, for which few other longitudinal data are available (Aguilar et al., 2000).  They suggest that successful interventions will need to address the multiple risk factors facing families in the persistent high group.  While parent training may be helpful in improving consistency and decreasing the use of harsh and hostile discipline practices, the current results suggest that it will need to be tailored to the demands of children who are uninhibited in approaching provocative or even scary stimuli.  It also needs to be reiterated that the vast majority of families in the present study face the implicit challenges associated with poverty.  These include low parental educational and occupational attainment, poor resources for social support and child care, poor housing, unsafe neighborhoods and schools marked by exposure to high rates of deviant peer behavior, and a high frequency of parental transitions.  Thus, it is clear that the development of antisocial behavior in children is embedded within a context of child characteristics, parental psychological resources and childrearing practices, and  the family’s social adversity.  One must take seriously the reservations of others who have tried to intervene with high-risk families and failed because they neglected to address contextual factors (Kazdin, 1995).  For instance, Salvador Minuchin abandoned working with low-income, high-risk families because he concluded it was analogous to putting band-aids on people who require surgery.  Interventions are recommended that are multi-systemic (Henggeler, Schoenwald, Borduin, Rowland, & Cunningham, 1998), geared to the developmental challenges and transitions of early childhood (Shaw & Bell, 1993), and tailored to the issues that compromise individual parent’s abilities to provide safe and caring environments for their offspring.

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Footnotes

¹ y_it^*j is described as a latent variable because it is not fully observed. This use of the term latent differs from that in the psychometric literature, where the term latent factor refers to unobservable construct that is assumed to give rise to multiple manifest variables.

 

 

Table 1

Mean Scores and Standard Deviations of Study Variables

Child’s Age               M                SD               Range

Fearlessness                                                   2                       0                     1          -1.62 - 3.09

Maternal rejecting parenting                

Observed maternal rejection               1½                     0                .58           -1.11 - 3.99        

Observed maternal rejection                2                       0                .64           -1.12 - 2.81

HOME acceptance                                2                  5.01              1.92                      0 - 8

Maternal depression                                                         

Beck depression inventory                   1½                8.95              6.90                    0 - 45

Beck depression inventory                    2                  7.49              6.22                    0 - 33

Maternal age                                                  2                 28.04             5.36                  17 - 43

Maternal education (years)                             2                 12.58             1.50                    8 - 18

Child verbal IQ                                             5½                   93              14.9                51 - 135

Overt conduct problems

CBCL-overt CP                                     2                  2.75              1.61                      0 - 8

CBCL-overt CP                                    3½                2.62              1.73                      0 - 9

CBCL-overt CP                                     5                  2.16              1.73                    0 - 10

CBCL-overt CP                                     6                  1.92              1.66                      0 - 8

CBCL-overt CP                                     8                  1.52              1.57                      0 - 9

 

Table 2

Correlations Among Risk Factors

* p < .05. ** p < .01.

 

 

Table 3

Risk factors by trajectory group

Note. Entries in first four columns are means and (standard deviations); means with different subscripts are significantly different based on Tukey HSD post-hoc comparisons

⁺ p < .10, * p < .05. *** p < .001.

 

 

Table 4

Logit Analysis: Predicting Membership in Initially High versus Initially Low Groups

* p < .05.

 

 

Table 5

Logit Analysis: Predicting Membership in Chronic versus High Desister Groups

* p < .05.

                                                                              

Figure 1.  Trajectories of Overt Antisocial Behavior