Interest in mediation analysis has increased over time, with particular excitement in the social and behavioral sciences. A mediator is defined as an intermediate in the causal sequence between an independent and dependent variable. Previous research has demonstrated that the cross-sectional form of mediation analysis is inherently flawed, evidenced by the inability of the cross-sectional mediation model to account for temporal precedence and estimation of the indirect effect being biased in nearly all situations. For these reasons, a longitudinal model is recommended. However, a method for determining the exact time points to measure the variables used in mediation analysis has not been adequately examined. In this study, we examined methods for determining an appropriate time lag when designing a mediation study. The methods implemented include correlation analysis, the quadratic and exponential forms of the lag as a moderator approach, and knot estimation using basis splines. The data for the study was simulated for three distinct trends generated using a linear piecewise model, a sigmoid model, and a sigmoid piecewise model. Additionally, two sampling approaches, an intense sampling approach and a three-measure approach, were examined as well as six sample sizes and three effect sizes for the total effect on the outcome. The estimation methods were additionally compared by considering different types of error structures used in data generation as well as by examining equal and unequal time lag lengths between the predictor and mediator, and the mediator and outcome. The intent of the study is to provide methods so that researchers can estimate the best time to evaluate mediator and outcome measurements that will be used in mediation analysis. The results from this study showed that the best estimation method varied depending on the lag being estimated, the sampling approach, and the length of the lag. However, the knot estimation approach worked reasonably well in most scenarios considered even with small sample sizes of 5 or 10 per group. The findings from this study have the potential to improve study design for research implementing longitudinal mediation analysis by reducing bias in the estimate of the indirect effect when adequate time points are used.

The purpose of this study was to take a multidimensional perspective to prosocial behavior and self-regulation by analyzing longitudinal, bidirectional relations between prosocial behavior toward strangers, friends, and family members and behavioral, cognitive, and emotional dimensions of self-regulation across adolescence. Participants included reports from 500 adolescents (age Time 1 = 12, Time 2 = 14, Time 3 = 16, Time 4 = 18; 52% female, 77% European American) taking part in the Flourishing Families Project. Nine cross-lagged panel models were conducted analyzing longitudinal associations between each target of prosocial behavior and each dimension of self-regulation. Results revealed that in early adolescence, prosocial behavior toward strangers and cognitive self-regulation were bidirectionally related. Prosocial behavior toward strangers was significantly associated with cognitive self-regulation from age 12 to age 18 and cognitive self-regulation was significantly associated with prosocial behavior toward friends across adolescence. Further, behavioral and emotional self-regulation were significantly related to prosocial behavior toward family from age 12 to age 18. Gender was significantly associated with initial levels of study variables but was not significantly relate to patterns of association. Discussion focuses on how findings fit into existent theory and research.