Inference on zero inflated ordinal models with semiparametric link

Abstract

In socioeconomics or in Biological studies, observations on individuals are often observed longitudinally on a Likert-type scale with substantially large proportion of zeros. This leads to a special case of mixture structured data where extra-variation occurs. Obviously the standard ordinal data analysis fails to provide appropriate statistical inference. We propose a suitable zero inflated semiparametric ordinal model that takes into account the non linear link between the ordinal response and a covariate. A sieve maximum likelihood estimator(MLE) is proposed for the regression parameter of interest. We also propose a test for the zero proportion in this semiparametric model. A simulation study has been carried out to investigate the performance of the estimator as well as the test. We illustrate the methodology using data from a survey on Tuberculosis patients in and around Kolkata, India.