A New Unit‐Lindley Mixed‐Effects Model With an Application to Electricity Access Data

ABSTRACT This paper introduces a novel unit‐Lindley mixed‐effects model (NULMM) within the generalized linear mixed model (GLMM) framework, designed for analyzing correlated response variables bounded within the unit interval. Parameter estimation was conducted via maximum likelihood, using Laplace approximation and adaptive Gaussian‐ Hermite quadrature (AGHQ). Simulation studies revealed that the Laplace approximation yielded biased estimates, while AGHQ with 5 or 11 quadrature points produced unbiased results. The proposed model was applied to rural electricity access data from South Asian countries, with covariates including time, log(GDP), log(Rural Population), and income level. Results show that time and log(GDP) are positively associated with rural electricity access, whereas log(Rural Population) has a negative association but is not statistically significant. Additionally, significant disparities were observed between low‐income and upper‐middle‐income countries. Model comparisons demonstrated that NULMM provides a better fit to the data than the beta mixed model and the unit‐Lindley (UL) mixed model.