Ridge-Type Shrinkage Estimators in Low and High Dimensional Beta Regression Model with Application in Econometrics and Medicine

Beta regression model is useful in the analysis of bounded continuous outcomes such as proportions. It is well known that for any regression model, the presence of multicollinearity leads to poor performance of the maximum likelihood estimators. The ridge type estimators have been proposed to alleviate the adverse effects of the multicollinearity. Furthermore, when some of the predictors have insignificant or weak effects on the outcomes, it is desired to recover as much information as possible from these predictors instead of discarding them all together. In this paper we proposed ridge type shrinkage estimators for the low and high dimensional beta regression model, which address the above two issues simultaneously. We compute the biases and variances of the proposed estimators in closed forms and use Monte Carlo simulations to evaluate their performances. The results show that, both in low and high dimensional data, the performance of the proposed estimators are superior to ridge estimators that discard weak or insignificant predictors. We conclude this paper by applying the proposed methods for two real data from econometric and medicine.