She, X. and Wu, C. (2020), Validity and efficiency in analyzing ordinal responses with missing observations. Can J Statistics, 48: 138-151. doi:10.1002/cjs.11523

Ordinal responses are one of the most widely collected and analyzed types of data in many scientific fields. Examples of ordinal responses include variables measuring performance (poor, average, excellent), attitude (strongly disagree, disagree, neutral, agree, strongly agree), severity of disease (mild, moderate, severe, life-threatening), and many others. It is often the case that a set of baseline variables can be observed for all units in the sample while the ordinal response variable is subject to missingness. Statistical analyses involving ordinal responses often focus on the estimation of category probabilities or regression analysis on how the response variable is related to the baseline variables. The authors propose an efficient fractional imputation procedure and show that it is an ideal tool for handling missing ordinal responses and creating a single imputed data file that can be analyzed by different data users with different scientific objectives. The authors address the two most critical aspects of statistical analyses using the imputed data set: validity and efficiency. Validity refers to the approximate unbiasedness of the point estimators for unknown population quantities or model parameters while efficiency is assessed by the relative variance of the estimators as compared to existing methods. There has been debate among researchers on the practical and theoretical merits of single imputation versus multiple imputation, with the former lacking of efficiency and the latter requiring the creation and maintaining of multiple copies of the data files. The authors demonstrate that fractional imputation can be an alternative approach that combines the strength of both methods.