Unified computational methods for regression analysis of zero-inflated and bound-inflated data

Authors:
Yan Yang;Douglas Simpson
Affiliations:
Department of Mathematics and Statistics, Arizona State University, Wexler Hall, Tempe, AZ 85287, USA;Department of Statistics, University of Illinois, Illini Hall, 725 South Wright Street, Champaign, IL 61820, USA
Venue:
Computational Statistics & Data Analysis
Year:
2010

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Abstract

Bounded data with excess observations at the boundary are common in many areas of application. Various individual cases of inflated mixture models have been studied in the literature for bound-inflated data, yet the computational methods have been developed separately for each type of model. In this article we use a common framework for computing these models, and expand the range of models for both discrete and semi-continuous data with point inflation at the lower boundary. The quasi-Newton and EM algorithms are adapted and compared for estimation of model parameters. The numerical Hessian and generalized Louis method are investigated as means for computing standard errors after optimization. Correlated data are included in this framework via generalized estimating equations. The estimation of parameters and effectiveness of standard errors are demonstrated through simulation and in the analysis of data from an ultrasound bioeffect study. The unified approach enables reliable computation for a wide class of inflated mixture models and comparison of competing models.