POSTER: The Impact of Group Imbalance on Logistic Regression Analyses with Assessment Data
Bibliographic record
Abstract
Introduction Logistic regression (LogReg) is widely used in analyzing educational assessment data, a special case of which is LogReg for differential item functioning (DIF). The model of interest in this paper is a LogReg akin to an analysis of covariance analysis with a dichotomous outcome variable and three predictors: a continuous covariate, a (skewed) dichotomous grouping variable and the interaction. The skewed grouping variable reflects an imbalance in sample sizes of the two groups. Little to no research has been done to examine the effects of skewed predictors on parameter estimates in logistic regression. Objectives The present simulation study investigates the impact of unbalanced group membership on the Type I error rate and statistical power of the Wald tests in this model. Methods To examine Type I error of the Wald tests: a 4A—4A—10 completely crossed factorial design, varying three factors: sample size (from 200 to 5000), skewness of the dichotomous predictor (from 50:50 to 1:99), skewness of the dependent variable (from 50:50 to 1:99). To examine power, a 4A—4A—10A—2 completely crossed factorial design, varying four factors: the same three as studied for Type I error, and effect size of dichotomous predictor and interaction (odds ratios of 2 and 4). Results and Conclusions The Type I error and power findings are a complicated interaction of the skewness of the dependent variable, the imbalance of the group sizes (i.e., skewness of the grouping predictor variable), and sample size. As a general statement, the Type I error rate and power are negatively affected by severe imbalance in group sizes. In cases wherein the Type I error rate of the Wald test of the grouping variable is effected, it is consistently deflated and close to zero. The complicated findings will be interpreted focusing on providing advice for data analysts and practitioners.
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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 | 0.060 | 0.258 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.089 | 0.021 |
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".