Every few days, we will be publishing layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.
The article featured today is from the Canadian Journal of Statistics, with the full article now available to read here.
Guan, J. , Cheng, H. , Bollen, K. A., Thomas, D. R. and Wang, L. (2019), Instrumental variable estimation in ordinal probit models with mismeasured predictors. Can J Statistics. doi: 10.1002/cjs.11517
Researchers in the medical, health, and social sciences routinely encounter ordinal data such as self-reports of health or happiness. The data are usually recorded in the form of a sequence of numerical values of increasing or decreasing order and the statistical analysis of this type of data requires different methodologies than commonly used ones for continuous data. When modelling ordinal outcome variables, it is common to have covariates (e.g., attitudes, family income, retrospective variables) that either cannot be measured directly or are measured with substantial error. It is well known that ignoring even random error in covariates can bias coefficients in a downward or upward direction and hence undermine correct estimates of their effects.
The authors study this issue in the context of regression models with ordinal dependent variables. They show how additional variables called “instrumental variables” enable researchers to use standard statistical estimation procedures such as the maximum likelihood and moments estimation to deal with the biases in coefficients caused by measurement errors. They provide theoretical results on the large sample properties of the proposed estimators. They also investigate the performance of their estimators through numerical simulation studies and applied their method to a health survey data set. The numerical computation is straightforward and the computer algorithms are provided.