Semiparametric Additive Beta Regression Models

Inference and Local Influence Diagnostics

Authors

  • Germán Ibacache-Pulgar Universidad de Valparaíso
  • Jorge Figueroa-Zuñiga Universidad de Concepción
  • Carolina Marchant Universidad Católica del Maule

DOI:

https://doi.org/10.57805/revstat.v19i2.342

Keywords:

beta distribution, diagnostic techniques, maximum penalized likelihood estimates, penalized likelihood function, semiparametric additive mode

Abstract

In this paper, we study a semiparametric additive beta regression model using a parameterization based on the mean and a dispersion parameter. This model is useful for situations where the response variable is continuous and restricted to the unit interval, in addition to being related to other variables through a semiparametric regression structure. First, we formulate the model and then estimation of its parameters is discussed. A back-fitting algorithm is derived to attain the maximum penalized likelihood estimates by using natural cubic smoothing splines. We provide closed-form expressions for the score function, Fisher information matrix and its inverse. Local influence methods are derived as diagnostic tools. Finally, a practical illustration based on real data is presented and discussed.

Published

2021-06-08

How to Cite

Ibacache-Pulgar , G., Figueroa-Zuñiga , J., & Marchant , C. (2021). Semiparametric Additive Beta Regression Models: Inference and Local Influence Diagnostics. REVSTAT-Statistical Journal, 19(2), 255–274. https://doi.org/10.57805/revstat.v19i2.342