Evaluating differential effects using regression interactions and regression mixture models.

Research increasingly emphasizes understanding differential effects. This paper focuses on understanding regression mixture models, a relatively new statistical methods for assessing differential effects by comparing results to using an interactive term in linear regression. The research questions which each model answers, their formulation, and their assumptions are compared using Monte Carlo simulations and real data analysis. The capabilities of regression mixture models are described and specific issues to be addressed when conducting regression mixtures are proposed. The paper aims to clarify the role that regression mixtures can take in the estimation of differential effects and increase awareness of the benefits and potential pitfalls of this approach. Regression mixture models are shown to be a potentially effective exploratory method for finding differential effects when these effects can be defined by a small number of classes of respondents who share a typical relationship between a predictor and an outcome. It is also shown that the comparison between regression mixture models and interactions becomes substantially more complex as the number of classes increases. It is argued that regression interactions are well suited for direct tests of specific hypotheses about differential effects and regression mixtures provide a useful approach for exploring effect heterogeneity given adequate samples and study design.

Asymmetry in children's salivary cortisol and alpha-amylase in the context of marital conflict: links to children's emotional security and adjustment.

Recent research supports the promise of examining interactive models of physiological processes on children's adjustment. The present study investigates interactions between children's autonomic nervous system activity and adrenocortical functioning in the context of marital discord; specifically, testing models of concurrent responses proposed by Bauer et al. ([2002] Developmental and Behavioral Pediatrics 23:102-113) in the prediction of children's behavioral responses to conflict and adjustment. Asymmetry and symmetry in children's salivary alpha-amylase and cortisol were examined in 195 children (M age = 8 years) in response to viewing conflict vignettes. Results were partially consistent with an interactive model in the context of high marital discord; asymmetry among higher alpha-amylase and lower cortisol related to higher emotional insecurity and concurrent and subsequent maladjustment. In contrast, patterns of symmetrical responses were related to greater maladjustment for children exposed to lower levels of marital discord, supporting an additive model. Findings support the importance of a multisystem approach to investigating the adaptiveness of children's physiological stress responses, while also highlighting the value of considering physiological responses in the context of family risk.

Finite Mixtures for Simultaneously Modelling Differential Effects and Non-Normal Distributions.

Regression mixture models have been increasingly applied in the social and behavioral sciences as a method for identifying differential effects of predictors on outcomes. While the typical specification of this approach is sensitive to violations of distributional assumptions, alternative methods for capturing the number of differential effects have been shown to be robust. Yet, there is still a need to better describe differential effects that exist when using regression mixture models. The current study tests a new approach that uses sets of classes (called differential effects sets) to simultaneously model differential effects and account for non-normal error distributions. Monte Carlo simulations are used to examine the performance of the approach. The number of classes needed to represent departures from normality is shown to be dependent on the degree of skew. The use of differential effects sets reduced bias in parameter estimates. Applied analyses demonstrated the implementation of the approach for describing differential effects of parental health problems on adolescent body mass index using differential effects sets approach. Findings support the usefulness of the approach which overcomes the limitations of previous approaches for handling non-normal errors.

Using regression mixture models with non-normal data: Examining an ordered polytomous approach.

Mild to moderate skew in errors can substantially impact regression mixture model results; one approach for overcoming this includes transforming the outcome into an ordered categorical variable and using a polytomous regression mixture model. This is effective for retaining differential effects in the population; however, bias in parameter estimates and model fit warrant further examination of this approach at higher levels of skew. The current study used Monte Carlo simulations; three thousand observations were drawn from each of two subpopulations differing in the effect of X on Y. Five hundred simulations were performed in each of the ten scenarios varying in levels of skew in one or both classes. Model comparison criteria supported the accurate two class model, preserving the differential effects, while parameter estimates were notably biased. The appropriate number of effects can be captured with this approach but we suggest caution when interpreting the magnitude of the effects.

Interparental conflict in kindergarten and adolescent adjustment: prospective investigation of emotional security as an explanatory mechanism.

Advancing the long-term prospective study of explanations for the effects of marital conflict on children's functioning, relations were examined between interparental conflict in kindergarten, children's emotional insecurity in the early school years, and subsequent adolescent internalizing and externalizing problems. Based on a community sample of 235 mothers, fathers, and children (Ms=6.00, 8.02, 12.62years), and multimethod and multireporter assessments, structural equation model tests provided support for emotional insecurity in early childhood as an intervening process related to adolescent internalizing and externalizing problems, even with stringent autoregressive controls over prior levels of functioning for both mediating and outcome variables. Discussion considers implications for understanding pathways between interparental conflict, emotional insecurity, and adjustment in childhood and adolescence.

Understanding children's emotional processes and behavioral strategies in the context of marital conflict.

Marital conflict is a distressing context in which children must regulate their emotion and behavior; however, the associations between the multidimensionality of conflict and children's regulatory processes need to be examined. The current study examined differences in children's (N = 207, mean age = 8.02 years) emotions (mad, sad, scared, and happy) and behavioral strategies to regulate conflict exposure during resolved, unresolved, escalating, and child-rearing marital conflict vignettes. Children's cortisol levels were assessed in relation to child-rearing and resolved conflict vignettes. Anger and sadness were associated with escalating and child-rearing conflicts, fearfulness was related to escalating and unresolved conflicts, and happiness was associated with resolution. Anger was associated with children's strategies to stop conflict, whereas sadness was associated with monitoring and avoidant strategies. Cortisol recovery moderated the link between fearfulness and behavioral regulation. These results highlight the importance of children's emotions and regulatory processes in understanding the impact of marital conflict.

Parental Depressive Symptoms and Adolescent Adjustment: Responses to Children's Distress and Representations of Attachment as Explanatory Mechanisms.

OBJECTIVE: This study seeks to extend the investigation of parenting as an explanatory mechanism for relations between parental depressive symptoms and adolescent adjustment in the context of a four-wave longitudinal study. DESIGN: Participants were cohabiting parents and their 320 children (156 boys, 164 girls). Parental depressive symptoms were assessed in kindergarten (T1), parental negative responses to children's emotional distress in first grade (T2), children's representations of attachment with parents in second grade (T3), and adolescent adjustment in seventh grade (T4). RESULTS: Multiple pathways were identified in predicting adolescent conduct problems, including links involving (1) mothers' depressive symptoms, mothers' negative responses to children's distress and insecure father-child attachment representations; (2) fathers' depressive symptoms and insecure father-child attachment representations; and (3) fathers' depressive symptoms and negative responses to children's distress. A pathway was also found among mothers' depressive symptoms, mothers' negative responses to children's distress, insecure mother-child attachment representations, and peer problems in adolescence. CONCLUSION: The findings support a role of parents' negative responses to children's distress and representations of father-child and mother-child attachment in relations between children's early experience with parental depressive symptoms and socioemotional outcomes in early adolescence.

Patterns of children's adrenocortical reactivity to interparental conflict and associations with child adjustment: a growth mixture modeling approach.

Examining children's physiological functioning is an important direction for understanding the links between interparental conflict and child adjustment. Utilizing growth mixture modeling, the present study examined children's cortisol reactivity patterns in response to a marital dispute. Analyses revealed three different patterns of cortisol responses, consistent with both a sensitization and an attenuation hypothesis. Child-rearing disagreements and perceived threat were associated with children exhibiting a rising cortisol pattern, whereas destructive conflict was related to children displaying a flat pattern. Physiologically rising patterns were also linked with emotional insecurity and internalizing and externalizing behaviors. Results supported a sensitization pattern of responses as maladaptive for children in response to marital conflict, with evidence also linking an attenuation pattern with increased family risk. The findings of the present study support children's adrenocortical functioning as one mechanism through which interparental conflict is related to children's coping responses and psychological adjustment.

Positive Aspects of Fathering and Mothering, and Children's Attachment in Kindergarten.

Past research suggests that maternal and paternal parenting processes differentially contribute to children's adjustment. However, the contribution of paternal warmth and responsiveness, to childhood attachment security is less understood, especially beyond the preschool years. The current study examined relations between parenting and attachment among 236 families with children in kindergarten. Parental warmth was virtually unrelated to attachment security and avoidance with mothers and fathers, while paternal and maternal responsiveness to children's emotional distress were uniquely predictive of father- and mother-child attachments, respectively. Although less responsive parenting was related to insecure attachment for both mothers and fathers, the parenting mechanisms associated with insecure attachment differed. Low paternal responsiveness was linked with continuous and categorical assessments of insecure-avoidant attachment, while low maternal responsiveness was associated with insecure-ambivalent attachment. Further research is needed to delineate why these patterns differ for fathers and mothers in order to understand fathers' unique effects on childhood attachment.