Examining Longitudinal Associations between Externalizing and Internalizing Behavior Problems at Within- and Between-Child Levels

Abstract

Externalizing and internalizing behavior problems are known to often co-occur, but mechanisms underlying this co-occurrence remain unclear: whether the associations are due to causal influences of one domain on the other or due to common risk processes influencing both domains. This study aimed to better understand the sources of co-occurring behavior problems by disentangling within- and between-child levels of associations between the two across the five years of childhood, from pre-kindergarten to Grade 3. We analyzed a longitudinal sample of 1,060 children from non-urban settings in the U.S. using random-intercept cross-lagged panel models (RI-CLPMs) as an alternative to the commonly-used standard CLPMs. Results indicate that co-occurring externalizing and internalizing problems can be explained partly by a unidirectional influence from externalizing to internalizing problems operating within children and partly by stable differences between children that influence both domains of problems. Further analyses indicate that an executive function deficit in early childhood is an important shared risk factor for both problems, suggesting the utility of executive function interventions in preventing or addressing externalizing and internalizing problems in childhood.

Externalizing and internalizing problems at young ages are significantly associated with a range of negative outcomes later in life, including education, social functioning, and health-related quality of life (Bradshaw, Schaeffer, Petras, & Ialongo, 2010; Capaldi & Stoolmiller, 1999; Dodge, Malone, Greenberg, & The Conduct Problems Prevention Research Group, 2008; Duprey, Oshri, & Liu, 2019). Although classified as distinct forms of behavioral maladjustment, externalizing problems encompassing aggression and noncompliance and internalizing involving anxiety and depressed mood, these problems often co-occur in young children, as well as in older children and adolescents (Angold, Costello, & Erkanli, 1999; Boylan, Vaillancourt, Boyle, & Szatmari, 2007). Studies that have examined externalizing-internalizing co-occurrence in preschool- and early school-aged children reported prevalence rates between 2 – 10% in general population or community samples (Basten et al., 2016; Hinnant & El-Sheikh, 2013; Wiggins, Mitchell, Hyde, & Monk, 2015). Rates are much higher in high-risk samples. For example, in the analyses of a sample of high-risk kindergarteners, 61% of whom screened high on aggressive/oppositional behaviors, Willner, Gatzke-Kopp, and Bray (2016) identified nearly half of the sample as having co-occurring externalizing and internalizing problems.

Children with co-occurring problems, compared to those with either problem alone, tend to display more severe symptoms, are more likely to continue to have these difficulties through adulthood, and are at increased risk of experiencing more adverse outcomes (Basten et al., 2016; Fanti & Henrich, 2010; Wolff & Ollendick, 2006). Externalizing and internalizing co-occurrence may be particularly detrimental if experienced in the early school years, when children are exposed to new settings and opportunities to learn fundamental cognitive, social, and regulatory skills needed for later life (Huston & Ripke, 2006). Externalizing and internalizing problems in the early school years impede children to benefit from this window of opportunity, likely resulting in other developmental difficulties including learning and social problems (Burt & Roisman, 2010; van Lier & Koot, 2010). If externalizing and internalizing problems are sequentially linked to each other and other domains of functioning, as hypothesized in cascade or transactional models, specific symptoms early in development can snowball into multiple functional impairments over time (Masten & Cicchetti, 2010; Dodge et al., 2008). Failing to intervene earlier will make the problems more difficult to change later in life.

Consequently, there has been an increasing demand for intervention programs that can prevent or address externalizing and internalizing problems early in school (Mclntosh, Ty, & Miller, 2014). However, many existing interventions target either externalizing or internalizing problems, and ignore the role of one domain in the development of the other (Granic, 2014). If externalizing and internalizing problems are causally related, then interventions failing to take into account this relationship may be less effective in addressing or preventing children’s behavior problems. An enhanced understanding of mechanisms of co-occurrence is essential to develop more targeted and effective intervention strategies. This article aimed to provide insights into how externalizing and internalizing problems are interrelated by clarifying the directional and temporal relations between the two constructs over the early school years, from pre-kindergarten (pre-K) to 3^rd grade. We investigate whether increases in externalizing problems at one point in time lead to increases in a child’s internalizing problems at a subsequent point in time and/or vice versa or whether the observed relationship between the two is due to common risk processes rather than causal influences of one domain on the other.

Most previous studies have examined only unidirectional flows of influence, either the effect of externalizing on internalizing problems or the effect of internalizing on externalizing problems (e.g., Capaldi & Stoolmiller, 1999; Lahey, Loeber, Burke, Rathouz, & McBurnett, 2002). In more recent years, researchers have used cross-lagged panel modeling (CLPM) to simultaneously model bidirectional and temporal processes between the two and thereby more fully evaluate alternative hypotheses (e.g., Klostermann, Connell, & Stormshak, 2016; Morin et al., 2017). However, this approach has also some potential methodological drawbacks, e,g., aggregation of within- and between-person effects which might compromise the validity of research findings (Berry & Willoughby, 2016; Curran & Bauer, 2011; Hamaker, Kuiper, & Grasman, 2015). Here, we applied random-intercept cross-lagged panel modeling (RI-CLPM: Hamaker et al., 2015) as an alternative approach to address methodological concerns associated with the standard CLPM, and examined within-child relationships of over-time changes in externalizing and internalizing problems separate from stable between-child differences.

Relations between Externalizing and Internalizing Problems

There are several well-known theoretical explanations for how externalizing and internalizing problems might co-develop over time (for a review, Bubier & Drabick, 2009; Caron & Rutter, 1991). The first claims that externalizing problems lead to later internalizing problems through the mechanism of failure experiences in social and educational areas (e.g., peer rejection, academic difficulties, poor family processes), which is often referred to as a failure hypothesis (Capaldi, 1991, 1992; Patterson & Capaldi, 1990). There are also theoretical explanations for the opposite effect, i.e., internalizing problems leading to later externalizing problems. One explanation is the acting-out model: children with internalizing problems tend to express their depressive or anxious feelings through minor acting-out behaviors, which increase conflicts with family and peers that, over time, contribute to elevating the risk for externalizing problems (Carlson & Cantwell, 1980; Glaser, 1967). Another proposed mechanism focuses on regulatory processes: sustained anxiety induces the depletion of children’s inhibitory control capacity that leads to aggressive behaviors (Drabick, Ollendick, & Bubier, 2010; Granic, 2014). While these perspectives focus on either causal route from externalizing to internalizing or from internalizing to externalizing, others suggest bidirectional or reciprocal relationships between the two, integrating unidirectional perspectives. For example, the adjustment erosion hypothesis suggests that both externalizing and internalizing problems have negative influences on children’s social and academic competence, contributing to the onset or maintenance of the other domain of problems (Moilanen, Shaw, & Maxwell, 2010). As an alternative to the causal perspectives, a shared-risk hypothesis states that externalizing and internalizing co-occurrence is due to common risk factors that are simultaneously related to both externalizing and internalizing problems, rather than direct causal processes (Angold et al., 1999).

Which of these competing claims has received the most empirical support? Our review of empirical research identified a little over a score of studies that used the CLPM to examine the reciprocal or bidirectional relations between externalizing and internalizing problems during childhood and/or adolescence (e.g., Morin et al., 2017; Poirier et al., 2016; Stone, Otten, Engels, Kuijpers, & Janssens, 2015; Wiggins et al., 2015). These studies vary in terms of developmental stages covered (e.g., childhood, adolescence), informants of children’s functioning (e.g., teachers, parents, self), sample characteristics (e.g., clinical sample, community sample), and constructs under examination (e.g., broadband constructs like internalizing and externalizing problems, specific symptoms such as anxiety). Despite these differences, one common finding across the studies is that both domains of problems remain quite stable from one time to next, indicated by significant and substantial autoregressive effects.

With respect to cross-lagged paths, studies have yielded mixed results. Some found a positive unidirectional relation from externalizing to internalizing problems, but not vice versa, providing support for the failure model (Gooren, van Lier, Stegge, Terwogt, & Koot, 2011; Hipwell et al., 2011; Moilanen et al., 2010; van der Giessen et al., 2013; van Lier & Koot, 2010; van Lier et al., 2012). In contrast, several studies reported the opposite pattern with internalizing problems predicting later externalizing problems, but not the opposite (Bornstein, Hahn, & Haynes, 2010; Burt, Obradović, Long, & Masten, 2008; Loukas, Ripperger-Suhler, & Horton, 2009; Poirier et al., 2016). Other findings suggests bidirectional, mutually-reinforcing processes, in which the level of one problem is positively associated with the subsequent level of the other (Hipwell et al., 2011; Lee & Stone, 2012; van der Ende, Verhulst, & Tiemeier, 2016; Wiggins et al., 2015). Finally, some studies showed unidirectional negative associations from internalizing to externalizing problems (Englund & Siebenbruner, 2012; Rogosch, Oshri, & Cicchetti, 2010) or reciprocally (Lee & Bulowski, 2012; Morin et al., 2017).

Several studies have tested the shared-risk hypothesis by estimating the models with and without a few potential risk factors that might be common to both domains, but the findings are inconclusive (Bornstein et al., 2010; Burt et al., 2008; Burt & Roisman, 2010; Moilanen et al., 2010; Stone et al., 2015). For example, in a study that followed at-risk boys from 6 to 12 years of age, the addition of three early risk factors (i.e., parenting quality, intelligence, and neighborhood adversity) did not result in substantive changes in the findings (Moilanen et al., 2010). In a study of normative sample of 4-year-olds followed through age 14 years, the significant suppressing effects of internalizing on externalizing problems held after controlling for three potential common factors, i.e., child IQ, maternal education, and social desirability (Bornstein et al., 2010). In contrast, a study of Dutch children found that significant bidirectional pathways existed from clinical problems in one domain leading to the onset of problems in the other domain, but these relationships dropped to nonsignificance with the addition of four early risk factors (i.e., inadequate parenting, parenting stress, maternal health, and peer social preference), providing evidence for the shared-risk hypothesis (Stone et al., 2015).

Although these conflicting findings may be attributed to differences in study populations and the type of measures used, they occur even within studies of similar populations using equivalent teacher-report measures (e.g., van Lier & Koot, 2010; Wiggins et al., 2015). As such, the relationship between externalizing and internalizing problems remains unclear.

Methodological Concerns

Cross-lagged panel modeling (CLPM) has been considered the most suitable analytical approach to clarify the directionality and temporal precedence of associations between variables because it estimates cross-lagged effects of one variable on the other and vice versa after controlling for concurrent associations between the two variables as well as stability of each variable (i.e., autoregressive effect) (van der Ende et al., 2016; Wiesner, 2003). However, CLPM has been recently criticized for failing to disaggregate within-person variation from between-person variation and consequently yielding cross-lagged estimates that might be biased as well as uninterpretable (Berry & Willoughby, 2017; Hamaker et al., 2015).

According to these critiques, the inclusion of autoregressive paths controls for only “temporal stability” from one time point to the next but does not adjust for “trait-like stability” that may persist (Hamaker et al., 2015, p. 104). As a result, effects of time-stable differences between individuals are inseparable from those of time-to-time fluctuations within individuals. This suggests that the significant cross-lagged effects of internalizing on externalizing problems (or vice versa) resulting from the standard CLPM may be due, in part, to time-general, trait-like characteristics shared by both domains. Two simulation studies have demonstrated that the cross-lagged results of the standard CLPM can be spurious, suggesting the need to disaggregate within- and between-person relations (Berry & Willoughby, 2017; Hamaker et al., 2015). This is particularly true in the presence of unmeasured or unspecified time-invariant confounders. Although some previous studies controlled for potential causes of externalizing and internalizing problems, such as intellectual ability and parenting (Bornstein et al., 2010; Moilanen et al., 2010; Stone et al., 2015), these are far from an exhaustive list of confounders, and it would be unrealistic to adequately measure and include all possible confounders in a model.

To address the methodological problem mentioned above, new modeling strategies have been proposed including random-intercept CLPM (RI-CLPM: Hamaker et al., 2015). The RI-CLPM partials out time-general, trait-like components from total variance in each construct by adding random-intercepts representing systematic, enduring differences between individuals. By doing so, it focuses on capturing within-person processes, i.e., how an individual’s time-specific deviations from their typical or expected score in one variable predict subsequent temporal deviations from their underlying score in another variable (See Berry & Willoughby, 2017; Hamaker et al., 2015 for technical details)

Recently, empirical studies have applied RI-CLPM or similar strategies to examine longitudinal associations between constructs, including parental monitoring and adolescent behaviors (Dietvorst, Hiemstra, Hillegers, & Keijsers, 2018), student perceptions of classroom environments and motivation (Ruzek & Schenke, 2019), adolescent empathy and prejudice development (Miklikowska, 2018), and child executive function and academic achievement (Willoughby, Wylie, & Little, 2019). Some studies compared results obtained by the RI-CLPM versus standard CLPM and found that cross-lagged effects from the standard CLPM tended to be stronger than those from the RI-CLPM (Ruzek & Schenke, 2018). Furthermore, one study demonstrated that in the presence of a Simpson’s paradox, the sign of cross-lagged estimates became reversed after controlling for between-person differences (Dietvorst et al., 2018).

The Present Study

Here, we use the RI-CLPM to more rigorously evaluate the relations between externalizing and internalizing problems and compare the results from this newer strategy to those from the standard CLPM approach. We analyze a longitudinal sample of U.S. children from non-urban settings to address the following research questions. At the within-child level, does an increase in a child’s level of problems in one domain lead to a subsequent increase or decrease in his or her level of problems in the other domain? At the between-child level, are children’s trait-like tendencies to engage in externalizing and internalizing problems related to each other? If so, what early childhood factors explain this relationship? Which of the competing hypotheses best explains externalizing-internalizing co-occurrence between pre-K and Grade 3? We expect to find weaker cross-lagged effects in the RI-CLPM, relative to the standard CLPM, as it focuses on estimating within-child associations after partialling out between-child variances and thereby controlling for all time-invariant, unobserved confounders. Thus if significant cross-lagged parameter estimates were found from the RI-CLPM, it may provide stronger support for a causal interpretation of our results.

Methods

Data and Analytic Sample

Data are drawn from the Family Life Project (FLP), a large-scale longitudinal study following a 2003–04 birth cohort of 1,292 children and their families representative of six high-poverty, rural counties in Pennsylvania and North Carolina. Using a two-stage random sampling procedure, families of newborns in the sampled hospitals were recruited between September 15, 2003 and September 14, 2004. About 58% of eligible and consenting families were randomly selected and formally enrolled in the study by completing their first home visit at 2 months of child age. The University of North Carolina at Chapel Hill Internal Review Board provided approval and continuing oversight of the FLP research. Details about initial recruitment are provided by Burchinal et al. (2008).

The analytic sample for the current study consists of 1,060 children who were assessed by teachers on at least one occasion across five measurement time points (i.e., pre-K, kindergarten, Grades 1, 2, and 3). The sociodemographic characteristics of the sample are presented in Table 1. Approximately 56% of children were White and 44% were African American and about half were boys. The average income-to-needs ratio was 1.81 (SD=1.39; range=0.04 – 13.60). About 51% of mothers were not married at the time of the child’s birth. About 14% of mothers had a 4-year college degree. We compared sociodemographic characteristics between children retained in our analytic sample (n = 1,060) and those who were in the full sample at the base-year data collection but not retained in our analytic sample (n = 232). Analyses found no significant group differences in gender, ${\chi }^2$(1)=.02, p =.882, race/ethnicity, ${\chi }^2$(1)=.13, p =.717, parent marital status, ${\chi }^2$(1)=.98, p =.323, and maternal education, ${\chi }^2$(1)=1.09, p =.297. Income-to-needs ratio was significantly higher for those not retained in our analytic sample, t(1101) =2.094, p =.042. Of the 1,060 children in our analytic sample, 46.8% (n=496) had complete behavior outcome data across all five time points, and 31.8% (n=337), 14.2% (n=151), 5.1% (n=54), and 2.1% (n=22) had missing data at one, two, three, and four time points, respectively. We compared sociodemographic characteristics across groups of children who had the data at one, two, three, four, and five time points. Chi-square analyses indicated no significant group differences in gender, ${\chi }^2$(4)=1.28, p =.864, race/ethnicity, ${\chi }^2$(4)=2.06, p =.724, parent marital status, ${\chi }^2$(4)=2.45, p =.654, and maternal education, ${\chi }^2$(4)=1.37, p =.850. A one-way analysis of variance (ANOVA) indicated no significant group differences in income-to-needs ratio F(4, 1,054) =2.206, p=.066.

Table 1.

Descriptive statistics and correlations

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
1. Externalizing at PK	1.00
2. Externalizing at K	.53	1.00
3. Externalizing at G1	.42	.55	1.00
4. Externalizing at G2	.44	.49	.62	1.00
5. Externalizing at G3	.36	.45	.54	.61	1.00
6. Internalizing at PK	.15	.05	.01	.02	.01	1.00
7. Internalizing at K	.08	.13	.00	.03	−.03	.19	1.00
8. Internalizing at G1	.08	.09	.22	.10	.09	.12	.19	1.00
9. Internalizing at G2	.14	.13	.19	.32	.19	.21	.17	.31	1.00
10. Internalizing at G3	.11	.13	.15	.15	.27	.14	.17	.30	.32	1.00
11. State is NC (vs. PA)	−.18	−.16	−.21	−.21	−.28	−.08	.09	.01	.03	−.07	1.00
12. Male (vs. female)	.16	.07	.15	.17	.15	.00	−.07	−.07	.04	−.02	.00	1.00
13. White (vs. Black)	.08	.05	.06	.10	.16	.03	−.07	.02	−.02	.10	−.64	−.06	1.00
14. Center-based care	.01	.02	.02	−.01	.01	−.02	−.01	−.07	−.04	−.02	−.04	−.01	.03	1.00
15. Income-needs ratio	−.12	−.18	−.16	−.21	−.25	−.11	−.03	−.06	−.11	−.16	.40	.02	−.28	.01	1.00
16. Parent unmarried	.16	.19	.22	.22	.27	.06	.00	.09	.15	.09	−.39	.01	.20	.07	−.45	1.00
17. Mother college graduate	−.13	−.14	−.16	−.18	−.21	−.10	−.06	−.13	−.11	−.15	.26	.02	−.17	.01	.58	−.37	1.00
18. Prenatal smoking	.03	.09	.08	.11	.09	.06	.08	.11	.18	.06	.13	−.03	−.14	.04	−.15	.19	−.20	1.00
19. Maternal depression	.08	.10	.11	.05	.08	.12	.08	.03	.03	.10	−.10	−.04	.01	.05	−.19	.13	−.17	.10	1.00
20. Parenting quality	−.24	−.24	−.26	−.26	−.28	−.13	−.01	−.03	−.12	−.14	.38	−.07	−.18	.02	.42	−.41	.34	−.08	−.19	1.00
21. Child executive function	−.24	−.23	−.20	−.23	−.22	−.11	−.08	−.09	−.16	−.16	.34	−.14	−.32	−.01	.29	−.23	.28	−.07	−.10	.33	1.00
Mean	.23	.27	.28	.30	.30	.23	.29	.31	.33	.31	.59	.51	.56	.47	1.81	.51	.14	.24	.40	.84	−.13
SD	.37	.40	.42	.43	.41	.33	.37	.40	.40	.40	−	−	−	−	1.39	−	−	−	.46	.11	.52
Missing data proportion	.25	.08	.14	.14	.22	.25	.08	.14	.14	.22	0	0	0	.06	0	0	0	0	0	.01	.09

Note. N=1,060. PK = prekindergarten; K = kindergarten; G1 = Grade 1; G2 = Grade 2; G3 = Grade 3. Bold values indicate p < .05.

Measures

Externalizing & Internalizing Problems.

Children’s externalizing and internalizing problems were assessed by teachers using the Strengths and Difficulties Questionnaire (SDQ; Goodman, 1997) during the spring semester of pre-K (mean age = 4.99 years, SD = .28), kindergarten (mean age = 6.02 years, SD = .36), 1^st grade (mean age = 7.07 years, SD = .45), 2^nd grade (mean age = 8.11 years, SD = .44), and 3^rd grade (mean age = 9.10 years, SD = .42). The SDQ is a widely used brief screening questionnaire for assessing psychological attributes of children aged 4–16 years. The SDQ consists of 25 items on a 3-point scale (0 = not true, 1 = somewhat true, 2 = certainly true) that capture five dimensions: emotional symptoms, conduct problems, prosocial behavior, peer relationship problems, and hyperactivity/inattention. The SDQ has demonstrated construct validity (i.e., 5-factor structure) and concurrent validity with clinical diagnoses of psychiatric disorders, as well as good internal consistency (mean $\alpha =$ .73) and test-retest reliability (mean = .73) (Goodman, 2001). For the current analyses, we used the measure’s 5-item conduct problems subscale (e.g., lose temper, fight) to represent externalizing behavior problems and 5-item emotional symptoms subscale (e.g., worried, depressed, nervous) to represent internalizing behavior problems. In the current data, internal consistency reliability ranged from .79 to .82 for conduct problems and from .71 to .76 for emotional symptoms.

Covariates.

Our analyses also included a range of early childhood individual and environmental characteristics and experiences as predictors of between-child associations of externalizing and internalizing problems, including maternal depression, quality of parenting, child executive function, and other child- and parent/family-level background characteristics. Maternal depressive symptoms were measured with the Brief Symptoms Inventory-18 (BSI-18: Derogatis, 2000), which is an 18-item questionnaire of psychological distress, each rated on a scale of 0 (not at all) to 4 (extremely) and consists of three scales including depression, somatization, and anxiety. Mothers completed the BSI questionnaire at the 2-, 6-, 15-, 24-month home visits. Internal consistency reliability for the measure’s 6-item Depression subscale at each time point ranged from .81 to .86. We used the average of the depression subscale scores across 2- to 24-month data collections. Parenting quality was assessed using the HOME inventory (Caldwell & Bradley, 1984), which is a semi-structured interview/observation instrument designed to assess the quality and quantity of support available to young children in their home environment. Trained home visitors administered the infant/toddler version of the inventory at the 6-, 15-, and 24-month visits and the preschooler version at the 36-month visit. We used two subscales of the HOME, i.e., parent responsiveness and acceptance of the child, to create the measure of parenting quality. All items of the two subscales (19 and 11 items for the infant/toddler and preschooler versions, respectively), each rated on yes=1/no=0, were averaged to create a composite of parenting quality at each time point ($\alpha$ = .64 to .74). We then calculated the average of the composite scores across 6- to 24-month data collections. Child executive function (EF) was measured using a common EF battery that consisted of six tasks including three inhibitory control tasks (i.e., Simon-like spatial conflict task, Stroop-like silly sounds task, and farm animal go/no-go task), two working memory tasks (i.e., span-like task and self-ordered pointing task), and one attention shifting task (i.e., item-selection task similar to the Dimensional Change Card Sort task). A composite measure of EF ability was calculated by averaging the item-response-theory-based scores (expected a posteriori scores) across the tasks. Full details of task administration protocols, psychometric properties of each task, and scoring methods are provided elsewhere (Willoughby, Blair, Wirth, Greenberg, & The Family Life Project Key Investigators, 2010). In the current study, we used composite EF scores obtained at the 48-month assessment. The scores ranged from −2.14 to 1.23 with mean of −.13 (SD=.52). Child background factors included gender (male =1), race (non-Hispanic White = 1 vs. African American), and child care experience (attended center-based care for 10 or more hours per week = 1). Parent/family background factors included family’s income-to-needs ratio, maternal education (4-year college or higher = 1), parent marital status at the child’s birth (unmarried = 1), and prenatal smoking (smoked at least once during pregnancy = 1 vs. never smoked). These measures were obtained from parent reports at the 2-month home visit. Only two exceptions were: family’s income-to-needs ratio was calculated as the average across 6, 15, 24, 35, and 48-month data collections; and child care experience was based on parent reports completed at the 58-month visit. State of residence (NC = 1 vs. PA) was additionally included as a control.

Analysis Plan

We first estimated unconditional RI-CLPM presented in Figure 1. Similar to the standard CLPM, the RI-CLPM contains autoregressive paths representing the stability of each measure from one occasion (t) to the next (t+1) (i.e., E_t,t+1 & I_t,t+1 ), cross-lagged paths indicating the predictive effects of externalizing problems (E) at each time point on internalizing problems (I) at the immediately subsequent time point and vice versa (i.e., EI_t,t+1 & IE_t,t+1), correlations between the two constructs at the first time point (i.e., EI_pp), and correlated residuals between the two constructs at subsequent time points (i.e., EI_kk, EI_11, EI_22, EI₃₃) (Selig & Preacher, 2009). In contrast to the CLPM, the RI-CLPM estimates all of these parameters based on within-child variances in externalizing and internalizing problems separated from between-child variances. As shown in the Figure 1, the total variance in each observed outcome (“E^p” to “E³” and “I^p” to “I³”) is disaggregated into a within-child component (“LE^p” to “LE³” and “LI^p” to “LI³”) and a between-child component (alpha & eta). The latent factors, “alpha” and “eta,” represent trait-like stability or persistence of E and I over the entire study period that differs across children. These are identical to random intercepts in latent growth curve modeling, in which loadings from the intercept factor to repeated measures are constrained to 1. The time-specific latent factors, “LE^p” to “LE³” and “LI^p” to “LI³,” capture within-child variation at each time point, i.e., each child’s time-specific deviations from his or her own expected scores. The variances of the observed measures were constrained to zero and the factor loadings to 1. The time-specific latent variables were then used to estimate the cross-lagged (i.e., EI_t,t+1 & IE_t,t+1) and autoregressive effects (i.e., E_t,t+1 & I_t,t+1 ) as well as the concurrent associations (i.e., EI_tt). For the comparison purpose, we also estimated the standard CLPM.

Figure 1.

RI-CLPM of relationship b/w externalizing and internalizing problems

Note. The letters “E” and “I” indicate externalizing and internalizing problems, respectively. The superscripts and subscripts p, k, 1, 2, and 3 denote pre-k, kindergarten, 1^st, 2^nd, and 3^rd grade, respectively. The “E^p” to “E³” and “I^p” to “I³” indicate time-specific observed variables for E and I, respectively. The “alpha” and “eta” represent underlying latent stability/trait of over-time E and I, respectively, and their correlation is denoted by $\mathrm{\phi }$. The “LE^p” to “LE³” and “LI^p” to “LI³” indicate time-specific latent variables for E and I, respectively. The paths, E_p to E₃ and I_p to I₃, denote factor loadings of observed E and I scores on the latent stability/trait of over-time E and I, respectively. The loadings are constrained to 1. The paths “E_pk” to “E₂₃” and “I_pk” to “I₂₃” indicate autoregressive paths from one occasion to the next. The paths “IE_pk” to “IE₂₃” indicate cross-lagged effects of I on E. The paths “EI_pk” to “EI₂₃” indicate cross-lagged effects of E on I. The double-headed arrow “EI_pp” indicates correlations between E and I at pre-k and the double-headed arrows “EI₁₁” to “EI₃₃” indicate correlated residuals at subsequent time points. The “e_k” to “e₃” indicate time-specific residuals.

We started with a fully restricted model that imposed across-time equality constraints on all of autoregressive parameters, cross-lagged parameters, and time-specific covariances, and then progressively released constraints one by one. Because our preliminary data screening revealed slight evidence of non-normality in externalizing and internalizing behavior measures, all models were estimated using the maximum likelihood estimation with robust standard errors (MLR). Model fit was evaluated using several common indices including CFI, TLI, RMSEA and SRMR. We considered CFI $\ge \mathrm{ }$.95, TLI $\ge \mathrm{ }$.95, RMSEA $\le$ .06, and SRMR $\le \mathrm{ }$.05 as criteria for indicating good to excellent fit, and CFI and TLI $\ge$.90, RMSEA $\le$.08, and SRMR $\le$ .08 as acceptable fit (Brown & Cudeck, 1992; Hu & Bentler, 1999). We compared a more constrained model to a less constrained model using the Satorra-Bentler scaled chi-square test statistic (S–B${\chi }^2$: Satorra & Bentler, 1994).

The final RI-CLPM model was re-estimated with potential predictors of latent traits of externalizing and internalizing problems, including individual and parental background characteristics, maternal depression, parenting quality, and child EF ability. All analyses were implemented in Mplus 8.1 (Muthén, & Muthén, 1998–2017). Missing data were handled via full information maximum likelihood (FIML) method. The results presented below were not adjusted for complex sampling design because the FLP-provided weight and strata variables were specific to the baseline sample and our analyses used multiple waves of data. We also analyzed the data using sampling weights and strata variables and found the results consistent with and without taking into account complex sampling design (See Appendix Tables A3 and A4 for the results).

Results

Descriptive statistics and correlations

Table 1 presents the descriptive statistics and correlations for all study variables. Within-domain correlations across time were higher for externalizing (.36 ~.62) than internalizing problems (.14 ~ 32). Cross-time correlations within each domain tended to be stronger in the later grades, with one-year lagged correlations increasing from .53 between the pre-K and kindergarten to .61 between the 2^nd and 3^rd grades for externalizing problems and from .19 to .32 for internalizing problems. Cross-domain correlations were also somewhat greater in the later grades: within-time correlations between externalizing and internalizing problems ranged from .15 and .13 at pre-K and kindergarten to .32 and .27 in the 2^nd and 3^rd grades. As expected, both within- and cross-domain correlations diminished with increasing time lags.

Model Fits

Model fit statistics for each of five unconditional RI-CLPMs are shown in Table 2. The fully constrained model (Model 1) had an acceptable fit (${\chi }^2$(44) = 141.66, CFI = .94, TLI = .94, RMSEA = .05). Relaxing the across-time equality constraints on occasional covariance (Model 2) significantly improved the model fit (ΔS-B${\chi }^2$(3) = 11.69, p = .009). Model 3 additionally freed the constraint of equal cross-lagged paths across time. Comparison of this model with Model 2 yielded a non-significant S-B${\chi }^2$ difference test (ΔS-B${\chi }^2$(6) = 9.58, p = .144) with little change in other fit statistics, supporting the equivalence of cross-lagged paths across time. Instead, a model with free estimates for autoregressive paths (Model 4) provided a significant fit improvement over Model 2 (ΔS-B${\chi }^2$(6) = 15.22, p = .019), while displaying a comparable fit with the least constrained model (Model 5) with all paths being free to vary across time (ΔS-B${\chi }^2$(6) = 10.81, p = .095). Accordingly, Model 4 was retained as the final RI-CLPM. Model fit statistics for the equivalent standard CLPMs are provided in Appendix Table A1. The RI-CLPMs showed better model fit than did the standard CLPMs. The chi-square difference test between the final RI-CLPM and its equivalent CLPM indicated that the RI-CLPM was a significantly better fit to the data than the standard CLPM (ΔS-B${\chi }^2$(3) = 121.54, p < .001).

Table 2.

Model fit statistics of unconditional RI-CLPMs

Model	AR Paths	CL Paths	Occasional Covariance	χ2	p-value	df	CFI	TLI	RMSEA [90% CI]	SRMR	CM	S-B Δχ2	Δdf	S-B Δχ2 p-value
1	Constrain	Constrain	Constrain	141.66	< .001	44	0.94	0.94	0.05 [0.04, 0.05]	0.06
2	Constrain	Constrain	Free	129.77	< .001	41	0.94	0.94	0.05 [0.04, 0.05]	0.06	1	11.69	3	0.009
3	Constrain	Free	Free	119.19	< .001	35	0.95	0.93	0.05 [0.04, 0.06]	0.05	2	9.58	6	0.144
4	Free	Constrain	Free	115.63	< .001	35	0.95	0.93	0.05 [0.04, 0.06]	0.05	2	15.22	6	0.019
5	Free	Free	Free	104.17	< .001	29	0.95	0.92	0.05 [0.04, 0.06]	0.05	4	10.81	6	0.095

Note. AR = Autoregressive; CL = Cross-lagged; CFI = Comparative Fit Index; TLI = Tucker-Lewis Index; RMSEA = Root Mean Square Error of Approximation ; CI = Confidence Interval; SRMR = Standardized Root Mean Square Residual; CM = comparison model; S-B Δχ² = Satorra–Bentler adjusted chi-square difference test

Relationships between Externalizing and Internalizing Problems

The standardized parameter estimates and their standard errors from the final unconditional RI-CLPM are presented in Figure 2 (only significant paths shown) and Table 3 (full results shown). With respect to within-child associations, the cross-lagged effects from internalizing to externalizing problems were not statistically significant (β = −.02, p = .330). However, the cross-lagged effects from externalizing to internalizing problems were significantly positive ($\beta$ = .07 to .08, p < .01), indicating that a child displaying a higher level of externalizing problems at a given year, relative to his or her underlying, trait-like level of problems, tended to experience a higher level of internalizing problems at the immediately following year. The autoregressive effects were stronger for externalizing problems (β = .18 to .40) than for internalizing problems (β = .01 to .16), indicating higher temporal stability in externalizing than internalizing problems. For both domains, the autoregressive effects tended to be stronger in later grades ($\beta$ = .38 to .40, ps < .001 for externalizing; $\beta$ = .16 to .15, ps < .01 for internalizing) than in earlier grades ($\beta$ = .18 to .24, ps < .01 for externalizing; $\beta$ = .01 to .04, ps > .05 for internalizing). With respect to between-child associations, the latent trait factors of externalizing and internalizing problems were significantly and positively correlated (φ = .21, p < .01). This indicates that children who were typically higher in one domain of behavior problems across pre-K to Grade 3 tend, to some degree, to display higher overall levels of problems in the other domain over this developmental period.

Figure 2.

Model estimates from the final unconditional RI-CLPM

Note 1. Values are standardized parameter estimates with their standard errors in the parentheses. Significant estimates are only shown. Dashed arrow indicates non-significant path. Bolded values indicate the cross-lagged effects of externalizing on internalizing problems. See Table 3 for full results.

Note 2. The letters “E” and “I” indicate externalizing and internalizing problems, respectively. The superscripts and subscripts p, k, 1, 2, and 3 denote pre-k, kindergarten, 1^st, 2^nd, and 3^rd grade, respectively. The “E^p” to “E³” and “I^p” to “I³” indicate time-specific observed variables for E and I, respectively. The “alpha” and “eta” represent underlying latent stability/trait of over-time E and I, respectively. The “LE^p” to “LE³” and “LI^p” to “LI³” indicate time-specific latent variables for E and I, respectively. The “e_k” to “e₃” indicate time-specific residuals.

Table 3.

Results of the final unconditional RI-CLPM

	Parameter Estimates
Loadings
Ep, Ek, E1, E2, E3	.66(.03), .64(.03), .61(.03), .59(.03), .61(.03)a
Ip, Ik, I1, I2, I3	.45(.03), .41(.03), .38(.03), .39(.03), .38(.03)a
Autoregressive Paths
Epk, Ek1, E12, E23	.18(.06)**, .24(.07)***, .38(.06)***, .40(.06)***
Ipk, Ik1, II2, I23	.01(.05)ns, .04(.04)ns, .16(.06)**, .15(.04)***
Cross-lagged Paths
IEpk, IEk1, IE12, IE23	−.02(.02)ns, −.02(.02)ns, −.02(.02)ns, −.02(.02)ns
EIpk, EIk1, EI12, EI23	.07(.03)**, .07(.03)**, .08(.03)**, .08(.03)**
Occasion Covariance
EIpp	.16(.05)**
EIkk, EI11, EI22, EI33	.13(.04)**, .25(.04)***, .31(.04)***, .26(.04)***
Correlation b/w alpha & eta (φ)	.21(.07)**

Note 1. Values are standardized coefficients with standard errors in parentheses. Superscript a indicates that all the coefficients in the row are statistically significant at p <. 001. Superscript ns indicates no statistical significance.

^***p < .001,

^**p < .01,

^*p <.05.

Note 2. The subscripts p, k, 1, 2, and 3 denote pre-k, kindergarten, 1^st, 2^nd, and 3^rd grade, respectively. The E_p to E₃ and I_p to I₃ denote factor loadings of observed externalizing and internalizing scores on the latent stability/trait of over-time externalizing and internalizing problems, respectively. The E_pk to E₂₃ and I_pk to I₂₃ indicate autoregressive paths from one time to the next for externalizing and internalizing problems, respectively. The IE_pk to IE₂₃ indicate cross-lagged effects of internalizing problems at each time point on externalizing problems at the immediately subsequent time point. The EI_pk to EI₂₃ indicate cross-lagged effects of externalizing problems at each time point on internalizing problems at the immediately subsequent time point. The EI_pp indicates correlations between externalizing and internalizing at pre-k. The EI₁₁ to EI₃₃ indicate correlated residuals at subsequent time points.

For comparison, the parameter estimates from the equivalent standard CLPM are provided in Appendix Figure A1 and Table A2. The autoregressive and cross-lagged parameter estimates from the standard CLPM were generally larger than those from the RI-CLPM. In particular, unlike in the RI-CLPM, the cross-lagged paths from internalizing to externalizing problems were statistically significant although their magnitudes were small ($\beta$ = −.04, p < .01).

Predictors of Latent Traits of Externalizing and Internalizing Problems

We re-estimated the final RI-CLPM adding a set of potential predictors of the latent trait factors of externalizing and internalizing problems. The model fit showed acceptable fit indices (${\chi }^2$= 214.15, df = 97, p < .001; RMSEA = .03; CFI = .95; TLI = .91; SRMR = .03). The results of within-child associations were consistent with those without predictors, including significant, positive cross-lagged paths from externalizing to internalizing problems ($\beta$ = .08, p < .01) and no effects the other way around ($\beta$ = −.01, p = 0.587). With the addition of the covariates, however, the correlation between the two latent traits reduced from .21 (p < .01) to .06 (p = .627). This suggests that most of the shared variance between the two latent trait factors was explained by early childhood predictors added in the model. Also, about 32.4% and 28.5% of the variance in the latent trait factors of externalizing and internalizing problems, respectively, was accounted for by the set of covariates included in the model.

Table 4 presents the standardized regression coefficients for these variables. Both child gender and race were differentially associated with externalizing and internalizing domains. Being male was significantly predictive of higher levels of trait-like externalizing behaviors while associated with lower levels of trait-like internalizing problems. Compared to African-Americans, White children showed higher levels of internalizing problems but lower levels of externalizing problems. Income-to-needs ratio was not a significant predictor of both domains net of the other covariates. Parents’ marital status at the child’s birth was a significant predictor of between-child trait-like differences in both domains adjusting for the other covariates, with children of unmarried parents displaying significantly higher levels of trait-like problems in both domains. Having mothers with a 4-year college degree or more was a protective factor against internalizing behavior only. In contrast, mothers’ prenatal smoking tended to be a common risk factor for both domains of behavior problems although its association with externalizing problems did not reach statistical significance. Maternal depression was not significantly associated with both externalizing and internalizing problems after controlling for the other covariates in the model. Positive parenting was a protective factor against externalizing problem only: more responsive and accepting parenting practices were associated with lower levels of trait-like externalizing problems. Child EF ability was a significant shared predictor of both domains of behavior problems such that higher executive function was related to lower levels of externalizing and internalizing problems.

Table 4.

Predictors of latent trait of externalizing and Internalizing problems from the conditional RI-CLPM

	Latent Trait of Externalizing Problems		Latent Trait of Internalizing Problems
Predictors	β(SE)	p-value	β(SE)	p-value
Male	0.17 (0.04)	0.000	−0.13 (0.06)	0.022
White	−0.22 (0.06)	0.000	0.31 (0.08)	0.000
State is NC	−0.11 (0.05)	0.040	0.05 (0.07)	0.505
Center-based child care	0.02 (0.04)	0.577	−0.08 (0.06)	0.156
Income-needs ratio	−0.05 (0.04)	0.171	−0.04 (0.07)	0.561
Parents unmarried	0.14 (0.05)	0.008	0.13 (0.07)	0.050
Mother college graduate	−0.04 (0.03)	0.232	−0.14 (0.06)	0.012
Prenatal smoking	0.09 (0.05)	0.081	0.16 (0.07)	0.012
Maternal depression	0.03 (0.04)	0.435	0.09 (0.06)	0.122
Parenting quality	−0.18 (0.05)	0.001	−0.04 (0.07)	0.515
Executive function	−0.16 (0.05)	0.000	−0.31 (0.06)	0.000
Explained Variance	R2 = 0.324		R2 = 0.285

Note. Reported are standardized regression coefficients (β) with standard errors (SE) in parentheses.

Discussion

Here we examined the bidirectional associations between children’s externalizing and internalizing problems over the five-year period spanning pre-K to 3^rd grade in a longitudinal sample of non-urban children. We used the RI-CLPM designed to improve upon the standard CLPM by partialing out the effects of time-invariant, trait-like characteristics between individuals, and compared the resulting parameter estimates to those obtained from the standard CLPM. While the CLPM found the significant bidirectional effects with opposite signs, positive from externalizing to internalizing and negative the other way around, the latter effect did not remain significant in the RI-CLPM. Instead, the RI-CLPM demonstrated that a significant positive correlation existed between the two trait-like factors of externalizing and internalizing problems and this shared variance was explained by a set of individual and parental/familial characteristics, especially child EF skills at age 4 and parental marital status at the child’s birth.

Methodological and Substantive Implications

Methodologically, the present study adds to the small but emerging body of research that demonstrated the added-value of the RI-CLPM model for understanding developmental pathways (e.g., Dietvorst et al., 2018; Ruzek & Schenke, 2018). Our findings demonstrate the importance of separating between- and within-person effects in examining reciprocal processes between constructs over time. Even with the relatively small amount of shared variance at the between-child level, the standard CLPM and RI-CLPM generated different results that could lead to different explanations of how externalizing and internalizing problems co-develop over time. With the standard CLPM, we would have concluded that internalizing problems were negatively predictive of subsequent externalizing problems. This result, although in agreement with some previous studies suggesting that internalizing problems act as a protective or buffering factor against the development of externalizing problems (Burt et al., 2008; Englund, & Siebenbruner, 2012; Masten et al., 2005; Morin et al., 2017; Rogosch, Oshri, & Cicchetti, 2010; van der Ende et al.2016), did not hold in the RI-CLPM. The autoregressive effects also became considerably smaller in the RI-CLPM. These findings suggest that the cross-lagged and autoregressive parameter estimates reported in some studies of externalizing and internalizing problems likely reflect confounds of within- and between-person effects. Overall, our findings support the use of the RI-CLPM as a valid statistical approach to clarifying bidirectional relationships between variables.

Substantively, our finding suggests that externalizing problems increase risk for internalizing problems above and beyond the influences of common risk factors that are time-invariant and might dispose children to both problems. Our finding echoes some previous studies (Burt & Roisman, 2010; Gooren et al., 2011; Hipwell et al., 2011; Moilanen et al., 2010; van Lier & Koot, 2010), providing supportive evidence for the failure model that views externalizing problems as a causal antecedent of the development of internalizing problems (Capaldi, 1991, 1992; Patterson & Capaldi, 1990). From an intervention perspective, this finding highlights the importance of identifying and intervening with children at risk of externalizing problems because children exhibiting externalizing problems are also more likely vulnerable to the future development of internalizing problems.

Our findings also support the shared-risk hypothesis (Angold et al., 1999). We found a significant correlation between the time-invariant components of externalizing and internalizing problems, suggesting that co-development of these behavior problems is partly attributable to stable, trait-like characteristics or tendencies that are commonly related to both externalizing and internalizing problems. Common risk factors associated with trait-like externalizing and internalizing problems included maternal prenatal smoking, single marital status at the child’s birth, and lower child EF skills. In particular, our result indicated that EF skills in early childhood were the strongest common antecedent that might dispose children to risk in both domains of problems over the pre-K to primary school period. Previous studies have shown that EF deficits were cross-sectionally and longitudinally related to broad psychopathology during childhood, including externalizing and internalizing problems (Hughes & Ensor, 2011; Kusche, Cook, and Greenberg, 1993; Riggs, Blair, & Greenberg, 2004). Furthermore, several studies of intervention programs for childhood social-emotional development have reported that beneficial impacts of interventions on reducing behavior problems were mediated by improvements in EF skills (Bierman, Nix, Greenberg, Blair, & Domitrovich, 2008; Riggs, Greenberg, Kusché, & Pentz, 2006). Consistent with these studies, our findings provide empirical support for interventions targeting EF skills as one component of an effective strategy for preventing or addressing both externalizing and internalizing problems in childhood.

It is also worth noting that year-to-year stability within each domain, after adjusting for trait-like stability, was much higher in later grades than in earlier grades. For externalizing problems, an average stability coefficient across 1^st to 2^nd grades and 2^nd to 3^rd grades (0.39) was nearly two times higher than the average of pre-K to kindergarten and kindergarten to 1^st grade (0.21). For internalizing problems, the average stability coefficient of the latter two periods (0.155) was over six times higher than that of earlier two periods (0.025). This finding suggests that externalizing and internalizing problems likely become increasingly stable as children mature, demonstrating a cascading effect that may make them more resistant to changes in later childhood (Dodge et al., 2008). This leads to the important implication that intervention programs might be more effective when delivered earlier rather than later in childhood. Another noteworthy finding is that the year-to-year stability was considerably lower for internalizing than externalizing problems. This might be attributable to relatively low prevalence and/or low observability of internalizing symptoms in young children (Grietens et al., 2004).

Limitations and Future Research

The present study has several limitations that should be addressed in future studies. First, although our analysis indicated the significant, positive cross-lagged effects from externalizing to internalizing problems, we did not further investigate possible mediating pathways of this association. The failure hypothesis suggests failure experiences in academic and social settings as mediating mechanisms through which externalizing problems lead to later internalizing problems (Capaldi, 1991, 1992; Dodge et al., 2008), which was supported by some previous empirical studies using the standard CLPM (Burt & Roisman, 2010; Gooren et al., 2011; Moilanen et al., 2010; van Lier & Koot, 2010; van Lier et al., 2012). The previous findings on these mediating mechanisms should be replicated in future research with the RI-CLPM or similar approaches. Second, our analytic approach accounted for the effects of all time-invariant confounders, but not for potential time-varying confounders. Thus, the results are still open to bias due to the potential for the presence of time-varying confounders. Another limitation concerns the use of teacher-reported behavior problems. Teacher reports may provide unique information reflecting true differences in children’s behavior in classroom contexts, but it is also possible that they are biased due to teachers’ personal beliefs and standards and other characteristics (Grietens et al., 2004; Mason, Gunersel, & Ney, 2014), raising the need to use and compare the results of ratings from different informants. It should be noted as well that the measures of behavior problems used in the present study are based on small sets of items tapping conduct problems and emotional symptoms. Future research may use alternative measures that better represent the broad spectrums of externalizing and internalizing behaviors while also considering specific symptoms of externalizing (e.g., oppositional-defiant, disruptive, antisocial behaviors) and internalizing (e.g., depression, anxiety) problems.

Finally, the present study does not address whether the results hold for different population groups and for different developmental stages. There is evidence of subgroup disparities in the prevalence of externalizing and internalizing problems as well as mental health service utilization (Bitsko et al., 2018; Lu, 2017). This suggests that the patterns of associations between externalizing and internalizing problems may differ across population subgroups defined by, for example, gender, race/ethnicity, socioeconomic status, clinical status, birth conditions. The patterns of associations may also change as children age and transition into adolescence. For example, the socio-developmental milestone hypothesis proposed by Oland and Shaw (2005) suggests that the directional influences from internalizing to externalizing problems might emerge only with the development of more complex and intimate peer relationships in adolescence. It also suggests that the deleterious effects of externalizing problems in the development of internalizing problems might become stronger as children’s cognitive capacity to self-evaluate or self-reflect increases with age. Examinations of potential subgroup and age differences are important extensions of the present work that are left for future research. Despite several limitations noted above, the present study makes a unique contribution to the literature on the relationships between externalizing and internalizing problems in childhood by disentangling the levels of associations into the between- and within-child levels. We hope that our study provides a starting point for future research endeavors to more comprehensively and rigorously evaluate the mechanisms of co-occurring externalizing-internalizing problems.