A Theoretical Investigation of Identifiability and Estimation in Mixture Models for Heterogeneous Populations in Nigerian Longitudinal Studies

Finite mixture models for latent population heterogeneity offer a flexible statistical framework for characterising subgroup structure in Nigerian longitudinal study data, yet identifiability conditions, estimation convergence, and model selection theory specific to the small-cluster, high-missingness longitudinal data structures common in Nigerian panel surveys have not been established. This dissertation investigates identifiability and estimation theory for mixture models applied to heterogeneous populations in Nigerian longitudinal studies, making original theoretical contributions. New identifiability conditions for finite mixture models under non-random dropout missingness are derived, extending existing complete-data identifiability results. Conditions under which the EM algorithm achieves consistent parameter recovery in mixture models under missing-at-random and missing-not-at-random assumptions are established theoretically and verified by simulation. A novel penalised BIC criterion for mixture component number selection accounting for Nigerian panel data effective sample sizes is proposed. Group-based trajectory mixture models are applied to three Nigerian longitudinal datasets: child anthropometric growth trajectories from the NDHS panel, agricultural income trajectories from the LSMS-ISA Kano panel, and HIV viral load trajectories from the PEPFAR Nigeria cohort. Four-component trajectory models provided the best-fitting representations in all three applications. Theoretically derived standard errors for trajectory class membership probabilities were 22 percent wider than bootstrap estimates, indicating asymptotic over-precision. The dissertation establishes theoretical foundations for valid mixture model inference in Nigerian longitudinal data. Keywords: mixture models, identifiability theory, longitudinal data, EM algorithm, Nigerian panel studies