Statistical Theory and Application of Penalised Longitudinal Models for Analysing Socioeconomic Mobility Trajectories Across Nigerian States

Socioeconomic mobility trajectories in Nigeria exhibit complex non-linear patterns over time and heterogeneity across states that standard linear random effects longitudinal models cannot adequately characterise, necessitating penalised flexible modelling approaches with rigorous statistical theory. This dissertation develops the statistical theory and application of penalised longitudinal models for analysing socioeconomic mobility trajectories across Nigerian states, contributing to semiparametric longitudinal methods. A penalised spline mixed effects model for individual longitudinal trajectories is extended to incorporate between-state and between-zone random trajectory variation. Theoretical results on consistency and convergence rates of penalised likelihood estimators under correlated longitudinal data and group-based heterogeneity are derived. Optimal penalty selection using generalised cross-validation extended to longitudinal settings is theoretically justified. Variable selection for time-varying covariate effects uses group LASSO with theoretical oracle properties established. The framework is applied to 10-year household consumption expenditure trajectories from the NBS panel survey for 4,200 households across 12 states spanning all geopolitical zones. Four distinct mobility trajectory classes were identified by penalised mixture modelling: upwardly mobile (22 percent), stagnant low-income (38 percent), volatile (28 percent), and declining (12 percent). Trajectory class membership was significantly predicted by initial education level, land ownership, and North-South zone classification after controlling for initial welfare. The study provides a statistically rigorous mobility analysis framework and recommends class-targeted social investment programme design. Keywords: penalised longitudinal models, socioeconomic mobility, Nigerian states, penalised spline, semiparametric statistics