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Longitudinal data are necessary to study how individuals change over time. Latent change score (LCS) models are a collection of longitudinal models used to study within-person change and dynamics. This chapter reviews the LCS framework, describes its specification in the structural equation modeling framework, and discusses how to specify LCS models in the nonlinear multilevel modeling framework using NLMIXED, and in the Bayesian hierarchical framework using JAGS. Using NLMIXED or JAGS for LCS models enables researchers to be more precise about the time metric, which allows for the idiosyncracies of each longitudinal dataset. When discussing time metrics, there are some time metrics whose values are discrete, where the time metric takes on a relatively small number of distinct values. One of the main advantages of the LCS model framework is the flexibility of which it can be adapted to the idiosyncracies of both research questions and datasets.

This chapter focuses on exploring and examining additional extensions of the latent change score (LCS) framework. It introduces multiple ways for regularization to be used with the LCS model. The chapter proposes the incorporation of regularization for constraining parameters within the LCS model to allow for simpler, more flexible model testing. With longitudinal data, although a number of statistical frameworks are available for analysis; the use of structural equation modeling has become increasing popular. Hypotheses about change trajectories, determinants of change, along with other components can be formulated as a sequence of models, each representing a specific theoretical formulation. Regularization allows for more flexibility, in both simplifying the model testing process, while promoting the incorporation of more complex specifications. Across both univariate and bivariate LCS models, using both frequentist and Bayesian regularization allowed for a simplified process in choosing a best model, while also increasing the plasticity of the LCS model to incorporate additional parameterizations.