Multiple Imputation When Variables Exceed Observations: An Overview of Challenges and Solutions
Bibliographic record
Abstract
Missing data are a prevalent problem in psychological research that can reduce statistical power and bias parameter estimates. These problems can be mostly resolved with multiple imputation, a modern missing data treatment that is increasingly used. Imputation, however, requires the number of variables to be smaller than the number of observations (i.e., non-missing values), and this number is often exceeded due to, e.g., large assessments, high missing data rates, the inclusion of variables predictive of missing values, and the inclusion of non-linear transformations. Even when the ratio of variables to observations meets the minimum requirement, convergence failure can occur in large, complex models. Specialized techniques have been developed to overcome the challenges related to having too many variables in an imputation model, but they are still relatively unknown by researchers in psychology. Accordingly, this paper presents an overview of four imputation techniques that can be used to reduce the number of predictors in an imputation model: item aggregation with scales and parcels, passive imputation, principal component analysis (PcAux) and two-fold fully conditional specification. The purpose, advantages, limitations, and applications of each method are discussed, along with recommendations and illustrative examples, with the aims of (1) understanding different imputation methods and (2) identifying methods that could be useful for one’s imputation problem.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.048 | 0.092 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.004 |
| Bibliometrics | 0.006 | 0.010 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.007 | 0.009 |
| Open science | 0.006 | 0.005 |
| Research integrity | 0.006 | 0.011 |
| Insufficient payload (model declined to judge) | 0.004 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".