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 assumption 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.
2005 by The Behaviormetric Society of Japan