Researchers in the medical, health, and social sciences routinely encounter ordinal variables such as self-reports of health or happiness. When modelling ordinal outcome variables, it is common to have covariates, for example, attitudes, family income, retrospective variables, measured with error. As is well known, ignoring even random error in covariates can bias coefficients and hence prejudice the estimates of effects. We propose an instrumental variable approach to the estimation of a probit model with an ordinal response and mismeasured predictor variables. We obtain likelihood-based and method of moments estimators that are consistent and asymptotically normally distributed under general conditions. These estimators are easy to compute, perform well and are robust against the normality assumption for the measurement errors in our simulation studies. The proposed method is applied to both simulated and real data.

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Keywords Instrumental variable, latent predictors, likelihood method, measurement error, ordinal dependent variable, probit model
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Journal Canadian Journal of Statistics
Guan, J. (Jing), Cheng, H. (Hongjian), Bollen, K.A. (Kenneth A.), Thomas, R, & Wang, L. (Liqun). (2019). Instrumental variable estimation in ordinal probit models with mismeasured predictors. Canadian Journal of Statistics. doi:10.1002/cjs.11517