Advanced finite mixture modeling with Trajer: methods and applications for trajectory analysis

This thesis presents trajeR , an innovative R package designed for advanced finite mixture modeling in longitudinal trajectory analysis. trajeR addresses the challenge of identify- ing latent subgroups in heterogeneous longitudinal data by integrating specialized distribu- tions, including Zero-Inflated Poisson (ZIP), Censored Normal (CNORM), Logit, and Beta models, to capture diverse trajectory patterns. A dedicated chapter on multivariate finite mixture models extends the framework to handle complex, multi-dimensional longitudinal data, enabling joint analysis of multiple outcomes and their interdependencies. Method- ological contributions include enhanced Expectation-Maximization (EM) algorithms, robust standard error estimation, and rigorous identifiability criteria for mixture models, supported by numerical techniques such as Iteratively Reweighted Least Squares and quasi-Newton op- timization. Applied to real-world datasets in fields like criminology, medicine, and finance, trajeR uncovers meaningful subgroups and predictors of trajectory group membership. Model selection criteria, including AIC and BIC, ensure optimal clustering, while techniques like dynamic time warping enhance trajectory analysis accuracy. trajeR provides a flexible and computationally efficient tool for researchers, with broad applications in epidemiologi- cal studies, behavioral trajectory modeling, and multivariate longitudinal data analysis.