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Missing data are ubiquitous in many domain such as healthcare. When these data entries are not missing completely at random, the (conditional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process.Consequently, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. In this paper, we aim at developing a causal discovery method to recover the underlying causal structure from observed data that are missing under different mechanisms, including missing completely at random (MCAR),missing at random (MAR), and missing not at random (MNAR). With missingness mechanisms represented by missingness graphs (m-graphs),we analyze conditions under which additional correction is needed to derive conditional independence/dependence relations in the complete data. Based on our analysis, we propose Miss-ing Value PC (MVPC), which extends the PC algorithm to incorporate additional corrections.Our proposed MVPC is shown in theory to give asymptotically correct results even on data that are MAR or MNAR. Experimental results on both synthetic data and real healthcare applications illustrate that the proposed algorithm is able to find correct causal relations even in the general case of MNAR.
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Fitting Ordinal Factor Analysis Models With Missing Data: A Comparison Between Pairwise Deletion and Multiple Imputation
This study compares two missing data procedures in the context of ordinal factor analysis models: pairwise deletion (PD; the default setting in Mplus) and multiple imputation (MI). We examine which procedure demonstrates parameter estimates and model fit indices closer to those of complete data. The performance of PD and MI are compared under a wide range of conditions, including number of response categories, sample size, percent of missingness, and degree of model misfit. Results indicate that both PD and MI yield parameter estimates similar to those from analysis of complete data under conditions where the data are missing completely at random (MCAR). When the data are missing at random (MAR), PD parameter estimates are shown to be severely biased across parameter combinations in the study. When the percentage of missingness is less than 50%, MI yields parameter estimates that are similar to results from complete data. However, the fit indices (i.e., χ2, RMSEA, and WRMR) yield estimates that suggested a worse fit than results observed in complete data. We recommend that applied researchers use MI when fitting ordinal factor models with missing data. We further recommend interpreting model fit based on the TLI and CFI incremental fit indices.
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- Award ID(s):
- 1659936
- PAR ID:
- 10547535
- Publisher / Repository:
- SAGE Publications
- Date Published:
- Journal Name:
- Educational and Psychological Measurement
- Volume:
- 80
- Issue:
- 1
- ISSN:
- 0013-1644
- Format(s):
- Medium: X Size: p. 41-66
- Size(s):
- p. 41-66
- Sponsoring Org:
- National Science Foundation
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