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 featured model-based inference for complex survey design including multistage sampling. Taking into account the survey design information in the analysis of the resulting data have seen implementations with regression and generalized linear model, with scarcity with generalized linear mixed models (GLMMs). This study aimed at GLMMs for complex survey design of a two-stage sample using integrated nested Laplace approximation (INLA) with application to the dataset from the 2021 Nigeria Malaria Indicator Survey (NMIS). A binomial outcome GLMM was presented using the design sampling weights as a Gaussian latent model leading to posterior estimation using INLA. Simulation study and application to NMIS data were carried out to compare classical, weighted and MCMC approaches with the INLA approach. The model performances were evaluated using accuracy metrics and model comparison diagnostics. The results showed that incorporating design weights gave better fits in both classical and Bayesian cases and the INLA GLMM with survey design information was the best-fitting model reported by the simulation and NMIS data. The time taken to run the models was the least for the INLA model which is of great merit especially when analysing large datasets from survey studies. Therefore the design-based approach for GLMM binary outcome using INLA is advocated for large survey data.