A goal of developmental research is to examine individual changes in constructs over time. The accuracy of the models answering such research questions hinges on the assumption of longitudinal measurement invariance: The repeatedly measured variables need to represent the same construct in the same metric over time. Measurement invariance can be studied through factor models examining the relations between the observed indicators and the latent constructs. In longitudinal research ordered-categorical indicators such as self- or observer-report Likert scales are commonly used, and these measures often do not approximate continuous normal distributions. The present didactic paper extends previous work on measurement invariance to the longitudinal case for ordered-categorical indicators. We address a number of problems that commonly arise in testing measurement invariance with longitudinal data including model identification and interpretation, sparse data, missing data, and estimation issues. We also develop a procedure and associated R program for gauging the practical significance of the violations of invariance. We illustrate these issues with an empirical example using a subscale from the Mexican American Cultural Values scale. Finally, we provide comparisons of the current capabilities of three major latent variable programs (lavaan, Mplus, OpenMx) and computer scripts for addressing longitudinal measurement invariance.

This study evaluated the efficacy of 2 theory-based preventive interventions for divorced families: a program for mothers and a dual component mother-child program. The mother program targeted mother-child relationship quality, discipline, interparental conflict, and the father-child relationship. The child program targeted active coping, avoidant coping, appraisals of divorce stressors, and motherchild relationship quality. Families with a 9-to 12-year-old child (N = 240) were randomly assigned to the mother, dual-component, or self-study program. Postintervention comparisons showed significant positive program effects of the mother program versus self-study condition on relationship quality, discipline, attitude toward father-child contact, and adjustment problems. For several outcomes, more positive effects occurred in families with poorer initial functioning. Program effects on externalizing problems were maintained at 6-month follow-up. A few additive effects of the dual-component program occurred for the putative mediators; none occurred for adjustment problems.

Three models of the relations of coping efficacy, coping, and psychological problems of children of divorce were investigated. A structural equation model using cross-sectional data of 356 nine- to twelve-year-old children of divorce yielded results that supported coping efficacy as a mediator of the relations between both active coping and avoiding coping and psychological problems. In a prospective longitudinal model with a subsample of 162 of these children, support was found for Time 2 coping efficacy as a mediator of the relations between Time 1 active coping and Time 2 internalizing of problems. Individual growth curve models over four waves also found support for coping efficacy as a mediator of the relations between active coping and psychological problems. No support was found for alternative models of coping as a mediator of the relations between efficacy and symptoms or for coping efficacy as a moderator of the relations between coping and symptoms.

The family stress model represents a common framework through which to examine the effects of environmental stressors on adolescent adjustment. The model suggests that economic and neighborhood stressors influence youth adjustment via disruptions to parenting. Incorporating integrative developmental theory, we examined the degree to which parents’ cultural value orientations mitigated the effects of stressors on parenting disruptions and the degree to which environmental adversity qualified the effect of parenting on adolescent adjustment. We tested the hypothesized Integrative Family Stress Model longitudinally in a sample of mother-youth dyads (N = 749) and father-youth dyads (N = 467) from Mexican origin families, across three times points spanning early to middle adolescence. Providing the first longitudinal evidence of family stress mediated effects, mothers’ perceptions of economic pressure were associated with increases in adolescent externalizing symptoms five years later via intermediate increases in harsh parenting. The remaining findings supported the notion that integrative developmental theory can inform family stress model hypothesis testing that is culturally and contextually relevant for wide range of diverse families and youth. For example, fathers’ perceptions of economic pressure and neighborhood danger had important implications for adolescent internalizing, via reductions in paternal warmth, but only at certain levels of neighborhood adversity. Mothers’ familism value orientations mitigated the effects of economic pressure on maternal warmth, protecting their adolescents from experiencing developmental costs associated with environmental stressors. Results are discussed in terms of identifying how integrative developmental theory intersects with the family stress model to set diverse youth on different developmental pathways.

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