Statistical Modelling 15 (1) (2015), 1–23

Semi-parametric Bayesian analysis of binary responses with a continuous covariate subject to non-random missingness

Frederico Z Poleto
Instituto de Matemática e Estatística,
Universidade de São Paulo,
São Paulo,
Brazil
e-mail: fpoleto@ime.usp.br

Carlos Daniel Paulino
Instituto Superior Técnico,
Universidade de Lisboa (and CEAUL-FCUL),
Av. Rovisco Pais,
Lisboa,
Portugal


Julio M Singer
Instituto de Matemática e Estatística,
Universidade de São Paulo,
São Paulo,
Brazil


Geert Molenberghs
I-BioStat,
Universiteit Hasselt,
Diepenbeek,
Belgium,
and

Katholieke Universiteit Leuven,
Leuven,
Belgium


Abstract:

Missingness in explanatory variables requires a model for the covariates even if the interest lies only in a model for the outcomes given the covariates. An incorrect specification of the models for the covariates or for the missingness mechanism may lead to biased inferences for the parameters of interest. Previously published articles either use semi-/non-parametric flexible distributions for the covariates and identify the model via a missing at random assumption, or employ parametric distributions for the covariates and allow a more general non-random missingness mechanism. We consider the analysis of binary responses, combining a missing not at random mechanism with a non-parametric model based on a Dirichlet process mixture for the continuous covariates. We illustrate the proposal with simulations and the analysis of a dataset.

Keywords:

Dirichlet process mixture; incomplete data; non-ignorable missingness mechanism; missing not at random; MNAR

Downloads:

Example data in zipped archive
back