Revisitando a estimação de coeficiente de determinação

Abstract

The coefficient of determination (R2) is a widely used metric to analyze the quality of adjustment of linear models. This coefficient assumes values in the range between 0 and 1, so that the closer to 1, most of the capacity variation is being explained by the model. R2 is treated with caution in the literature, as it can be biased in models with few observations or inflated when covariates are added to the model. In this sense, authors suggest treating it as a statistic that estimates a population parameter ( 2), which is understood as the quality of fit that a model would have if the infinite observations of the phenomenon were to be collected. Thus, we study the estimation of the parametric coefficient of determination ( 2) from five parametric interval estimators. For comparison, a Monte Carlo simulation study was performed, computing precision and accuracy in the different combinations to model the number of model variables (k), sample size (n) and the value of the parameter ( 2). The results allowed the recommendation of the best estimator for each region of the parametric space. Thus, it was found that the proposed estimators presented similar quality to those indicated in the literature in the parametric space. Finally, an R package was built, allowing the user to estimate the quality of the model using the best performing estimator.