A LATENT VARIABLE MODEL WITH NON-IGNORABLE MISSING DATA

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概要

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• A latent variable model is proposed that specifies not only the relationship between latent variables, but also the missing mechanism in which the value of the latent variables influences the frequency of missing patterns. We propose an estimation method for our model that adopts the Monte Carlo EM algorithm. Unlike previous methods, our method can be applied when the missing data assumption "Missing at random" does not hold. Moreover, our method can comprehensively explain the missing mechanism using latent variables, and the proposed estimation does not include multiple group estimation, so we can avoid the limitation present in previous studies of the number of subjects in each missing pattern. The proposed model and method are generalized for several kinds of use, such as monotone missingness. We show how to test that the missing mechanism is MAR/MCAR in this model. We also show the validity of the estimation method in simulation studies of two kinds of missingness (non-ignorable missingness and MAR);we compared the proposed method with ML estimation under the MAR assmuption and found it superior. A read data illustration shows that the proposed method provides a feasible explanation that personality affects the missingness of some questions. 1. Introduction In behavioral sciences, data can often be missing on several variables. Missingness implies a reduction in the information contained in the data set, but the missingness often contains some information on the population or the parameters of interest (Little & Rubin (1987) called this pattern of missingness "non-ignorable missing"). However, there are few estimation methods for modeling latent variables with nonignorable missingness. Here, we model a situation in which the missingness of a variable is influenced by the value of the latent variables, using factor analysis and logistic regression models. Previous studies in this area are based on Rubin's assumption that the data are "missing at random (MAR)".

• 日本行動計量学会の論文

著者

• Hoshino Takahiro

  Department Of Interdisciplinary Statistics Institute Of Statistical Mathematics

• Hoshino Takahiro

  Department Of Cognitive And Behavioral Science The University Of Tokyo

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• A LATENT VARIABLE MODEL WITH NON-IGNORABLE MISSING DATA

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