A statistical comparison of three goodness-of-fit criteria used inmodelling distances
Bibliographic record
Abstract
Distance predicting functions may be used in a variety of applications for estimating travel distances between points. To evaluate the accuracy of a distance predicting function and to determine its parameters, a goodness-of-fit criteria is employed. AD (Absolute Deviations), SD (Squared Deviations) and NAD (Normalized Absolute Deviations) are the three criteria that are mostly employed in practice. In the literature some assumptions have been made about the properties of each criterion. In this paper, we present statistical analyses performed to compare the three criteria from different perspectives. For this purpose, we employ the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\ell_{kp\theta}$"><mml:mrow><mml:msub><mml:mi>ℓ</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mi>p</mml:mi><mml:mi>θ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-norm as the distance predicting function, and statistically compare the three criteria by using normalized absolute prediction error distributions in seventeen geographical regions. We find that there exist no significant differences between the criteria. However, since the criterion SD has desirable properties in terms of distance modelling procedures, we suggest its use in practice.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".