Design-Based Generalized Linear Mixed Model For Binomial Outcome Two-Stage Survey Using Laplace Approximation With Application To 2021 Nigeria Malaria Indicator Survey Data

Applied statistical analyses have increasingly incorporated complex survey designs, though generalized linear mixed models (GLMMs) remain scarce. This study developed a GLMM for two-stage samples using integrated nested Laplace approximation (INLA) on the 2021 Nigeria Malaria Indicator Survey (NMIS) data. A binomial outcome GLMM was fitted, treating design sampling weights as a Gaussian latent model, and posterior estimates were obtained using INLA. Simulation and real data applications compared classical, weighted, MCMC, and INLA approaches, evaluated through accuracy and model diagnostics. Results indicated that incorporating design weights improved model fits, with the INLA GLMM showing superior performance. INLA also required the least computational time, highlighting its advantage for large survey datasets. The study recommends the design-based GLMM approach using INLA for analyzing large-scale survey data