**Research**

The goal of our research is to develop and evaluate quantitative methods for the social and behavioral sciences. We draw inspiration from a variety of literatures and approaches, including structural equation modeling, longitudinal modeling, mixed-effects (multilevel) modeling, statistical learning (data mining/machine learning), Bayesian methods, and many more. The methods we create help address limitations social science researchers face, including small sample sizes, measurement error, missing data, and so on. Below are a few lines of research we've pursued.

## Exploratory mediation analysis

Mediation analysis is the study of systems in which an independent variable transmits its effect to an outcome through a mediating variable. Our work on exploratory mediation analysis uses techniques from the data mining literature to help us identify mediators in an exploratory way. We've developed an approach called XMed, which conducts exploratory mediation analysis via regularization (Serang, Jacobucci, Brimhall, & Grimm, 2017). This work has been extended to accommodate dichotomous outcomes, both mediators and dependent variables (Serang & Jacobucci, 2020). It has also been used to identify potential mediators in the relationship between childhood maltreatment and attempted suicide (Ammerman, Serang, Jacobucci, Burke, Alloy, & McCloskey, 2018).

## Latent change score modeling

The latent change score model is a form of longitudinal structural equation model that allows for dynamic change to unfold over time. Our work on this model attempts to understand its properties. For example, we've studied how model fit indices and their corrections break down in small samples between N=20 and N=100 (Serang, 2018) and proposed a test for model fit and comparison in these situations (Serang, in press). We've also demonstrated the conditions under which the latent change score model is equivalent to the latent growth curve model (Serang, Grimm, & Zhang, 2019), as well as how unintended correlations between parameters can form when lacking measurement occasions (Jacobucci, Serang, & Grimm, 2019). We have used these models to understand how mathematical reasoning changes over time in both children and older adults.

## Heterogeneity in nonlinear change

Change over time often follows a nonlinear trajectory, and people often change in different ways. Our work in this area involves developing and evaluating methods to identify subgroups of people who follow similar change patterns to each other, but have different patterns than those in other subgroups. We've sought to understand how well mixed-effects mixture models can accomplish this, both from the frequentist and Bayesian perspectives (Serang, Zhang, Helm, Steele, & Grimm, 2015). We've extended this work to individually varying time metrics (e.g. age as opposed to grade) to understand how this can influence results (Serang, Grimm, & McArdle, 2016). We've also used recursive partitioning to construct decision trees where nonlinear mixed-effects models (Stegmann, Jacobucci, Serang, & Grimm, 2018) and/or structural equation models (Serang, Jacobucci, Stegmann, Brandmaier, Culianos, & Grimm, in press) are fit within each node. These approaches have been used to identify subgroups of children whose reading ability changes in similar ways across time.