Estimating Explained Variation of a Latent Scale Dependent Variable Underlying a Binary Indicator of Event Occurrence
Bibliographic record
Abstract
The coecient of determinant, also known as the R2 statistic, is widely used as a measure of theproportion of explained variation in the context of a linear regression model. In many real lifeevents, interests may lie on measuring the proportion of explained variation, rho^2, of a latent scaledependent variable U which follows a multiple regression model. But in practice, U may not beobservable and is represented by its binary proxy. In such situations, use of logistic regressionanalysis is a popular choice. Many analogues to R2 type statistics have been proposed to measureexplained variation in the context of logistic regression. McFadden's R2 measure stands out fromothers because of its intuitive interpretation and its independence on the proportion of successin the sample. It, however, severely underestimates the proportion of explained variation of theunderlying linear model. In this research we present a method for estimating the explained variationfor the underlying linear model using the McFadden's R2 statistics. When used in a real lifedataset, our method estimated rho^2 of the underlying model within an acceptable margin of error.
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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 | 0.015 | 0.048 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".