Three Essays on the Modeling of Development

This dissertation is intended for the advancement of methodology and techniques used in the modeling of development. There are three loosely tied essays of which this contribution is comprised. The first chapter is entitled ‘Finite Sample Effects in Group-Based Trajectory Models." It analyses a very intricate and specific aspect of the broader body of work credited to Daniel Nagin regarding group-based trajectory models. These models, which are an application of finite mixture modeling, are used to model population heterogeneity in the development of various types of behavior such as physical aggression or anxiety over age or time. The second chapter is entitled "Consequences of a Violation of the Conditional Independence Assumption in Group-Based Trajectory Models." This chapter again addresses another nuance of the group-based trajectory model, which, in particular, is often a criticism of the methodology. Specifically, in the specification of these groupbased models trajectory models, the following assumption is made. The third chapter is entitled "Accounting for Selection to Understand the Effects of Group Daycare on the Development of Physical Aggression." This chapter considers the problem of estimating casual effects of a treatment on an outcome of interest, which is a problem often addressed by researchers.