Effects of Sample Size on Goodness-of-Fit Statistic and Confidence Intervals of Crash Prediction Models Subjected to Low Sample Mean Values
Bibliographic record
Abstract
The statistical relationship between motor vehicle crashes and covariates can generally be modeled via generalized linear models (GLMs) with logarithmic links with errors distributed in a Poisson or Poisson-gamma manner. The scaled deviance and Pearson's χ 2 have been proposed to test the statistical fit of GLMs. Recent studies have shown that these two estimators are not adequate for testing the goodness of fit (GOF) of GLMs when they are developed from data characterized by low sample mean values. To circumvent this problem, a testing method has been proposed to evaluate the GOF of such GLMs. Because this method can be time-consuming to implement, there is a need to determine whether it is sensitive to different sample sizes. The primary objective of this paper is to investigate the effects of decreasing sample sizes on the GOF testing technique. A secondary objective is to estimate how the reducing of sample size influences the confidence intervals of GLMs. To accomplish the objectives, GLMs were fit with the use of two data sets subjected to average and low sample means collected in Toronto, Ontario, Canada. Several models were estimated for different sample sizes. The results of the study show that the testing technique is more effective for smaller than for larger samples when data are subjected to low sample mean values. The results also show that the width of the confidence intervals increases, as expected, as the sample size decreases and can be extremely large for small sample sizes. Hence, statistical models characterized by low sample mean values should be developed on the basis of a large number of observations. Data sets containing at least 100 observations (e.g., intersections, segments) are recommended in the development of models. The paper concludes with recommendations for future studies involving such data sets.
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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 | 0.131 | 0.551 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".