A semiparametric inference to regression analysis with missing covariates in survey data

Abstract

Parameter estimation in parametric regression models with missing covariates is considered under a survey sampling setup. Under missingness at random, a semiparametric maximum likelihood approach is proposed which requires no parametric specification of the marginal covariate distribution. By drawing from the von Mises calculus and V-Statistics theory, we obtain an asymptotic linear representation of the semiparametric maximum likelihood estimator (SMLE) of the regression parameters, which allows for a consistent estimator of asymptotic variance. An EM algorithm for computation is then developed to implement the proposed method using fractional imputation. Simulation results suggest that the SMLE method is robust, whereas the fully parametric method is subject to severe bias under model misspecification. A rangeland study from the National Resources Inventory (NRI) is used to illustrate the practical use of the proposed methodology.

Fractional Imputation in Survey Sampling: A Comparative Review

“…The above example covers a broad range of applications in the missing data literature, such as missing covariate problems, measurement error models, generalized linear mixed models, and so on. Yang and Kim (2014) considered regression analyses with missing covariates in survey data using FI, where in the current notation, f (y 2 | x, y 1 ) is a regression model with y 2 and x fully observed and y 1 subject to missingness. In generalized linear mixed models, f (y 2 | x, y 1 ) is a generalized linear mixed model where y 1 is the latent random effect.…”

Assessing treatment effect heterogeneity in the presence of missing effect modifier data in cluster-randomized trials

“… 27 , 28 However, choosing a compatible imputation model may not be straightforward, especially when the outcome model contains interaction terms. Semiparametric approaches such as fractional imputation 29 , 30 and nonparametric approaches such as imputation from Bayesian additive regression trees (BARTs) 31 , 32 have been proposed to address missing covariates, but such methods have not yet been extended to account for the within-cluster correlations in the covariates and outcomes in the CRT setting. With independent data, Erler et al.…”

New semiparametric regression method with applications in selection‐biased sampling and missing data problems

“…The inverse-probability weighting approach can also be applied to the nonparametric regression, which requires smoothing and is limited to low-dimensional data. Furthermore, nonparametric regression estimators in general have a convergence rate slower than root n. More recently, Yang & Kim (2017) proposed a semiparametric maximum pseudo-likelihood approach for the regression analysis with covariates missing at random in survey data, assuming that 𝑓 (y | x) takes a parametric form and that the sampling weights are known while leaving the marginal distribution of X unspecified.…”