Variable selection in multivariate regression models with measurement error in covariates
Bibliographic record
Abstract
Multivariate regression models have been broadly used in analyzing data having multi-dimensional response variables. The use of such models is, however, impeded by the presence of measurement error and spurious variables. While data with such features are common in applications, there has been little work available concerning these features jointly. In this article, we consider variable selection under multivariate regression models with covariates subject to measurement error. To gain flexibility, we allow the dimensions of the covariate and response variables to be either fixed or diverging as the sample size increases. A new regularized method is proposed to handle both variable selection and measurement error effects for error-contaminated data. Our proposed penalized bias-corrected least squares method offers flexibility in selecting the penalty function from a class of functions with different features. Importantly, our method does not require full distributional assumptions for the associated variables, thereby broadening its applicability. We rigorously establish theoretical results and describe a computationally efficient procedure for the proposed method. Numerical studies confirm the satisfactory performance of the proposed method under finite settings, and also demonstrate deleterious effects of ignoring measurement error in inferential procedures.
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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 | 0.142 | 0.271 |
| Meta-epidemiology (narrow) | 0.003 | 0.003 |
| Meta-epidemiology (broad) | 0.005 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.004 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
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".