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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. 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