Semiparametric Methods in the Proportional Odds Model for Ordinal Response Data with Missing Covariates

Abstract

We consider the estimation problem of a proportional odds model with missing covariates. Based on the validation and nonvalidation data sets, we propose a joint conditional method that is an extension of Wang et al. (2002, Statistica Sinica 12, 555-574). The proposed method is semiparametric since it requires neither an additional model for the missingness mechanism, nor the specification of the conditional distribution of missing covariates given observed variables. Under the assumption that the observed covariates and the surrogate variable are categorical, we derived the large sample property. The simulation studies show that in various situations, the joint conditional method is more efficient than the conditional estimation method and weighted method. We also use a real data set that came from a survey of cable TV satisfaction to illustrate the approaches.

A Two-stage Multilevel Randomized Response Technique With Proportional Odds Models and Missing Covariates

“…A closely related problem arises when the covariate X is missing and a surrogate variable for X is available. For this problem, several estimation methods have been proposed (see, e.g., Breslow and Cain 1988; Hsieh, Lee, and Shen 2009; Lee et al 2011; Wang et al 1997, 2002). Lee et al (2011) proposed semiparametric methods to estimate the parameters of a POM for ordinal response data with missing covariates.…”

“…For this problem, several estimation methods have been proposed (see, e.g., Breslow and Cain 1988; Hsieh, Lee, and Shen 2009; Lee et al 2011; Wang et al 1997, 2002). Lee et al (2011) proposed semiparametric methods to estimate the parameters of a POM for ordinal response data with missing covariates. These approaches include the conditional estimation method, joint conditional method, and weighted method.…”

“…where H ( u ) = { 1 + exp ( − u ) } − 1 . Following Lee et al (2011), let T i l = I ( Y i ≤ l ) , where I ( ⋅ ) is an indicator function. The above model can then be rewritten as…”

“…Note that nonignorable missingness means the missing data depend on a missing data mechanism such as data not MAR. Under the MAR assumption, Lee, Gee, and Hsieh (2011) proposed semiparametric methods to estimate the parameters of a POM for ordinal response data with missing covariates. These approaches include the conditional estimation method, joint conditional method, and weighted method.…”

Estimation of parameters of logistic regression with covariates missing separately or simultaneously

“…For more details, refer to, e.g., Wang et al (1997Wang et al ( , 2002, Hsieh et al (2010Hsieh et al ( , 2013, and Lee et al (2011Lee et al ( , 2012Lee et al ( , 2020Lee et al ( , 2023.…”