A latent class selection model for nonignorably missing data

A Latent-Class Selection Model for Nonignorably Missing Data Most missing-data procedures assume that the missing values are ignorably missing or missing at random (MAR), which means that the probabilities of response do not depend on unseen quantities. Although this assumption is convenient, it is sometimes questionable. For example, questionnaire items pertaining to sensitive information (e.g., substance use, delinquency, etc) may show high rates of missingness. Participants who fail to respond may do so for a variety of reasons, some of which could be strongly related to the underlying true values. Data are said to be nonignorably missing if the probabilities of missingness depend on unobserved quantities. Traditional selection models for nonignorable nonresponse are outcome-based, tying these probabilities to partially observed values directly (e.g., by a logistics regression). These methods are inherently unstable, because the relationship between a partially observed variable and its missingness indicator is understandably difficult to estimate. Moreover, with multivariate or longitudinal responses, the number of distinct missingness patterns becomes quite large, making traditional selection modeling even more unattractive. Information in the missing-data indicators is sometimes well summarized by a simple latent-class structure, suggesting that a large number of missing-data patterns may be reduced to just a few prototypes.