Comparison of the Performance of the Gradient and Newton-Raphson Method to Estimate Parameters in Some Zero-Inflated Regression Models

Abstract

This paper compares the performance of the gradient and Newton-Raphson (N-R) method to estimate parameters in some zero-inflated (ZI) regression models such as the zero-inflated Poisson (ZIP) model, zero-inflated Bell (ZIBell) model, zero-inflated binomial (ZIB) model and zero-inflated negative binomial (ZINB) model. In the present work, firstly, we briefly present the approach of the gradient and N-R method. We then introduce the origin, formulas and applications of the ZI models. Finally, we compare the performance of two investigated approaches for these models through the simulation studies with numerous sample sizes and several missing rates. A real data set is investigated in this study. Specifically, we compare the results and the execution time of the R code for two methods. Moreover, we provide some important notes on these two approaches and some scalable research directions for future work.

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