Statistical approaches for service delivery differentials as assessed through a composite indicator: Application to Ugandan local governments

: This study assesses differentials in service delivery among Ugandan local governments through a composite indicator that consolidates essential performance data from the education, health, and water sectors. The composite indicator scores as an outcome variable and it is modeled against probable determinants using beta regression, generalized additive models (GAMs) and random forest regression approaches. Beta regression, is a parametric approach, which includes varying precision parameters, is effective for modelling bounded data such as composite indicators, whereas random forest regression, as a non-parametric approach, emphasizes the relative importance of predictors. On the other hand, GAMs are semi-parametric, and bring to the fore non-linear covariate effects employing splines. Employing the minimax transformation, equal weighting and multiplicative aggregation, the composite indicator of service delivery scores varied from 0.25 to below 0.60 (on a scale of 0-1), with a substantial number of local governments scoring below 0.5. The findings reveal budgetary constraints, fragmentation at sub-county level, and geographical challenges in terms of distance from the capital city as significant obstacles to service delivery at local government level. The predictive accuracy of the three approaches as determined through the mean square error (RMSE) were found to be comparable (RMSE ≈0.05; MAE ≈ 0.042), suggesting that these approaches, grounded in contextualized theoretical frameworks, are effective in assessing service delivery outcomes and may therefore be employed in similar studies after careful consideration of the analytical objective. The study recommends broadening the range of service dimensions and predictors to develop a more relatable composite indicator. Given the group structures present in the predictors, employing grouped regression within the framework of beta regression modeling is advisable to provide a more robust and efficient modeling strategy.