A Bayesian Hierarchical Model for the Adoption Rate of Industrial Machinery Fleets in Nigeria: A Methodological Evaluation, 2000–2026

{ "background": "The adoption of modern industrial machinery is a critical driver of structural engineering and construction productivity in developing economies. However, reliable, high-resolution measurement of adoption rates across diverse sectors and regions remains a significant methodological challenge, hindering effective policy and investment.", "purpose and objectives": "This study presents a methodological evaluation of a novel Bayesian hierarchical model designed to estimate and forecast the adoption rate of industrial machinery fleets. The objective is to provide a robust framework that quantifies uncertainty and integrates sparse, multi-source data.", "methodology": "A Bayesian hierarchical model was developed, formalised as $y{it} \\sim \\text{Beta}(\\mu{it}\\phi, (1-\\mu{it})\\phi)$, with $\\text{logit}(\\mu{it}) = \\alpha{j[i]} + \\beta{k[i]} + \\gamma t$, where $\\alphaj$ and $\\betak$ represent sector and region-specific random effects. The model was fitted using Hamiltonian Monte Carlo, with data synthesised from national industrial surveys, customs records, and industry reports.", "findings": "The methodological evaluation demonstrates that the model successfully integrates heterogeneous data sources, producing probabilistically coherent estimates. A key finding is the model's identification of a pronounced regional disparity, with posterior estimates indicating adoption rates in the south-west were, with 95% credible probability, between 1.4 and 2.1 times higher than in the north-east for heavy lifting equipment. Forecasts suggest a gradual convergence in rates.", "conclusion": "The proposed Bayesian hierarchical model offers a statistically rigorous and flexible methodological framework for tracking machinery adoption. It effectively handles data limitations common in developing contexts and provides a probabilistic foundation for decision-making.", "recommendations": "Adoption of this modelling approach by national statistical agencies and industry bodies is recommended to generate consistent, sub-national indicators. Future research should focus on incorporating real-time sensor data from telematics to enhance model fidelity.", "key words": "Bay