Sequential imputation for models with latent variables assuming latent ignorability
Corresponding Author
Lauren J. Beesley
Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI, 48109 USA
Author to whom correspondence should be addressed.Search for more papers by this authorJeremy M. G. Taylor
Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI, 48109 USA
Search for more papers by this authorRoderick J. A. Little
Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI, 48109 USA
Search for more papers by this authorCorresponding Author
Lauren J. Beesley
Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI, 48109 USA
Author to whom correspondence should be addressed.Search for more papers by this authorJeremy M. G. Taylor
Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI, 48109 USA
Search for more papers by this authorRoderick J. A. Little
Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI, 48109 USA
Search for more papers by this authorSummary
Models that involve an outcome variable, covariates, and latent variables are frequently the target for estimation and inference. The presence of missing covariate or outcome data presents a challenge, particularly when missingness depends on the latent variables. This missingness mechanism is called latent ignorable or latent missing at random and is a generalisation of missing at random. Several authors have previously proposed approaches for handling latent ignorable missingness, but these methods rely on prior specification of the joint distribution for the complete data. In practice, specifying the joint distribution can be difficult and/or restrictive. We develop a novel sequential imputation procedure for imputing covariate and outcome data for models with latent variables under latent ignorable missingness. The proposed method does not require a joint model; rather, we use results under a joint model to inform imputation with less restrictive modelling assumptions. We discuss identifiability and convergence-related issues, and simulation results are presented in several modelling settings. The method is motivated and illustrated by a study of head and neck cancer recurrence. Imputing missing data for models with latent variables under latent-dependent missingness without specifying a full joint model.
Supporting Information
| Filename | Description |
|---|---|
| anzs12264-sup-0001-Supinfo.pdfPDF document, 4.4 MB |
Appendix S1. Ignorability under a joint model (properties 1–5). Appendix S2. Motivating the algorithm and performing parameter draws. Appendix S3. Bias of complete case analysis under LMAR. Appendix S4. Simulation study. Appendix S5. Example 1: identifiability for joint normal models. Appendix S6. Example 2: identifiability under LMAR for a mixture of GLMs. Appendix S7. Implementation of the SMC imputation algorithm. |
Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.
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