Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model

Abstract

Complete-case analysis Conditional independence Multi-sample analysis in SEM Selection and pattern-mixture models Shared-parameter model a b s t r a c t It is natural to assume that a missing-data mechanism depends on latent variables in the analysis of incomplete data in latent variate modeling because latent variables are error-free and represent key notions investigated by applied researchers. Unfortunately, the missing-data mechanism is then not missing at random (NMAR). In this article, a new estimation method is proposed, which leads to consistent and asymptotically normal estimators for all parameters in a linear latent variate model, where the missing mechanism depends on the latent variables and no concrete functional form for the missing-data mechanism is used in estimation. The method to be proposed is a type of multi-sample analysis with or without mean structures, and hence, it is easy to implement. Completecase analysis is shown to produce consistent estimators for some important parameters in the model.

Radiation effects on atherosclerosis in atomic bomb survivors: a cross‐sectional study using structural equation modeling

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Why Ordinal Variables Can (Almost) Always Be Treated as Continuous Variables: Clarifying Assumptions of Robust Continuous and Ordinal Factor Analysis Estimation Methods

“…The use of sufficiently complex imputation models, such as the Gaussian copula model (Hollenbach et al, 2018), mixture models (Murray and Reiter, 2016), or latent class models (Vermunt et al, 2008;Si and Reiter, 2013) are advantageous to minimize possible distributional misspecifications for MAR data. Appropriate imputation models can also treat specific deviations from MAR (missing not at random; MNAR; Harel and Schafer, 2009;Jung et al, 2011;Kano and Takai, 2011;Zhang and Reiser, 2015;Bartolucci et al, 2018;Kuha et al, 2018;Pohl and Becker, 2020).…”

Full information maximum likelihood estimation in factor analysis with a large number of missing values

“…Although the FIML procedure performed well even when the true missing data were NMAR based on the logistic function, various other NMAR cases were not explored (e.g., Yuan 2009;Kano and Takai 2011). As a future research topic, it would be interesting to explore the performance of FIML estimation and to determine algorithms that would be efficient for various NMAR cases.…”