Structural equation modeling with time dependence: an application comparing Brazilian energy distributors

This study proposes a Bayesian structural equation model (SEM) to explore financial and economic sustainability indicators, considered by the Brazilian energy regulator (ANEEL), to evaluate the performance of energy distribution companies. The methodology applies confirmatory factor analysis for dimension reduction of the original multivariate data set into few representative latent variables (factors). In addition, a regression structure is defined to establish the impact of the factors over the response “indebtedness” of the companies; this is a central aspect regularly discussed within ANEEL to identify whether a distributor may have difficulty to manage the concession. Most of the variables in this study are collected for 8 different years (2011–2018); therefore, a time dependence is inserted in the analysis to correlate observations. The SEM approach has several advantages in this context: it avoids using criticized deterministic formulations to measure non-observable aspects of the distributors, it allows a broad statistical analysis exploring elements that cannot be investigated through the simple descriptive studies currently developed by the regulator, and finally, it provides tools to properly rank and compare distances between companies. The Bayesian view is a powerful option to handle the SEM fit here, since convergence issues, due to sample size and high dimensionality, may be experienced via classical alternatives based on maximization.