Graphical assessment of internal and external calibration of logistic regression models by using loess smoothers
Bibliographic record
Abstract
Predicting the probability of the occurrence of a binary outcome or condition is important in biomedical research. While assessing discrimination is an essential issue in developing and validating binary prediction models, less attention has been paid to methods for assessing model calibration. Calibration refers to the degree of agreement between observed and predicted probabilities and is often assessed by testing for lack-of-fit. The objective of our study was to examine the ability of graphical methods to assess the calibration of logistic regression models. We examined lack of internal calibration, which was related to misspecification of the logistic regression model, and external calibration, which was related to an overfit model or to shrinkage of the linear predictor. We conducted an extensive set of Monte Carlo simulations with a locally weighted least squares regression smoother (i.e., the loess algorithm) to examine the ability of graphical methods to assess model calibration. We found that loess-based methods were able to provide evidence of moderate departures from linearity and indicate omission of a moderately strong interaction. Misspecification of the link function was harder to detect. Visual patterns were clearer with higher sample sizes, higher incidence of the outcome, or higher discrimination. Loess-based methods were also able to identify the lack of calibration in external validation samples when an overfit regression model had been used. In conclusion, loess-based smoothing methods are adequate tools to graphically assess calibration and merit wider application.
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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 | 0.079 | 0.341 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".