Simultaneous confidence bands in a zero-inflated regression model for binary data

Aba Diop (1, 2) , Aliou Diop (2) , Jean-François Dupuy (3)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement
3 IRMAR - Institut de Recherche Mathématique de Rennes

The logistic regression model has become a standard tool to investigate the relationship between a binary outcome and a set of potential predictors. When analyzing binary data, it often arises however that the observed proportion of zeros is greater than expected under the postulated logistic model. Zero-inflated binomial (ZIB) models have been developed to fit binary data that contain too many zeros, and maximum likelihood estimators in these models have been proposed and their asymptotic properties recently established. In this paper, we use these asymptotic properties to construct simultaneous confidence bands for the probability of a positive outcome in a ZIB regression model. Simultaneous confidence bands are especially attractive since they allow inference to be made over the whole predictor space. We construct two types of confidence bands, based on: i) the Scheffé method for the linear regression model, ii) Monte Carlo simulations to approximate the distribution of the supremum of a Gaussian field indexed by the regressor. The finite-samples properties of these two types of bands are investigated and compared in a simulation study.

Mots clés: simultaneous inference; mixture model; Logistic regression model; simulations

Domaines: Méthodologie [stat.ME]

Aba Diop, Aliou Diop, Jean-François Dupuy. Simultaneous confidence bands in a zero-inflated regression model for binary data. Random Operators and Stochastic Equations, 2022, 30 (2), pp.85-96. ⟨10.1515/rose-2022-2073⟩. ⟨hal-00762446⟩