Dealing with multivariate missing data in principal component analyses and subsequent model estimation: a two-step worked example using data from the Canadian Longitudinal Study of Aging
Bibliographic record
Abstract
Missing data can be a significant problem for statistical inference in many disciplines when information is not missing completely at random. In the worst case, it can lead to biased results when participants or subjects with certain characteristics contribute more data than other participants. Multiple imputation methods can be used to alleviate the loss of sample size and correct for this potential bias. Multiple imputation entails filling in the missing data using information from the same and other participants on the variables of interest and potentially other available data that correlate with the variables of interest. The missing data estimates and uncertainty associated with their estimation may then be taken into account in statistical inference from those variables. A complication may arise when using compound variables, such as principal component loadings (PC), which draw on a number of raw variables that themselves have non-overlapping missing data. Here, we propose a sequential multiple imputation approach to facilitate the use of all available data in the raw variables contained in compound variables in a way that conforms to the specifications of the multiple imputation framework. We first use multiple imputation to impute missing data for the subset of raw variables used in a principal component analysis (PCA) and perform the PCA with the imputed data; then, use the factor loadings to calculate PC scores for each individual with complete raw data. Finally, we include these PC scores as part of a global multiple imputation approach to estimate a final statistical model. We demonstrate (including annotated Stata code) the use of this approach by examining which sensory, health, social and cognitive factors explain self-reported sensory difficulties in the Canadian Longitudinal Study of Aging (CLSA) Comprehensive Cohort. The proposed sequential multiple imputation approach allows us to deal with the issue of having large cumulative amount of data that is missing (not completely at random) among a large number of variables, including composite cognitive scores derived from a battery of cognitive tests. We examine the resulting parameter estimates using a range of recommended diagnostic tools to highlight the potential and consequences of the approach to the statistical results.
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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 | 0.045 | 0.116 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.009 |
| Science and technology studies | 0.004 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".