Analysis of Mixed Outcomes: Misclassified Binary Responses and Measurement Error in Covariates

Abstract

The focus of this paper is on regression models for mixed binary and continuous outcomes, when the true predictor is measured with error and the binary responses are subject to classification errors. Latent variable is used to model the binary response. The joint distribution is expressed as a product of the marginal distribution of the continuous response and the conditional distribution of the binary response given the continuous response. Models are proposed to incorporate the measurement error and/or classification errors. Likelihood based analysis is performed to estimate the regression parameters of interest. Theoretical studies are made to find the bias of the likelihood estimates of the model parameters. An extensive simulation study is carried out to investigate the effect of ignoring classification errors and/or measurement error on the estimates of the model parameters. The methodology is illustrated with a data set obtained by conducting a small scale survey.