Abstract
{ "background": "The adoption of off-grid energy systems is critical for rural development, yet robust methodological frameworks for analysing adoption rates across diverse communities are lacking. Existing studies often rely on aggregated data, failing to account for hierarchical community-level effects and yielding imprecise estimates.", "purpose and objectives": "This study aims to develop and evaluate a novel Bayesian hierarchical modelling framework to quantify and compare the adoption rates of solar home systems and solar irrigation pumps across distinct rural communities in Kenya, with a focus on agricultural applications.", "methodology": "A comparative study was conducted using household survey data from multiple counties. The core model is a Bayesian hierarchical logistic regression: $\\text{logit}(p{ij}) = \\alpha + \\alpha{j} + \\beta X{ij}$, where $p{ij}$ is the adoption probability for household $i$ in community $j$, $\\alpha{j} \\sim \\text{Normal}(0, \\sigma^{2})$ represents community-level random effects, and $X{ij}$ are household covariates. Posterior distributions were estimated using Markov chain Monte Carlo sampling.", "findings": "The model revealed substantial heterogeneity in adoption rates, with community-level random effects having a posterior standard deviation of 0.85 (95% credible interval: 0.72, 1.01). A key concrete result is that access to agricultural extension services was strongly associated with adoption, with an odds ratio of 2.3 (95% CrI: 1.8, 2.9).", "conclusion": "The Bayesian hierarchical model provides a superior, statistically robust framework for comparative adoption analysis, explicitly quantifying uncertainty and unobserved community-level heterogeneity that conventional models obscure.", "recommendations": "Policymakers and implementers should prioritise integrating energy access programmes with agricultural extension services. Future research should employ hierarchical modelling to design targeted, community-specific interventions for off-grid technologies.", "key words": "Bayesian hierarchical model, technology adoption, off-grid energy, rural