Response to Discretising and validating Keyfitz' entropy for any demographic classification
Bibliographic record
Abstract
Abstract In recent years, demographers have parsed variation in survivorship into two distinct components: the shape and the pace of ageing. The pace of ageing is defined by measures of longevity such as mean life expectancy or maximum longevity, whereas measures of the shape of ageing attempt to classify different shapes of the survivorship curve. We recently published a paper pointing out that a commonly used discretization of a shape measure, Keyfitz' entropy, does not correctly classify survivorship curves into negatively and positively senescing curves (de Vries et al., 2023). In that paper, we also suggested an alternative, accurate discrete‐time version of Keyfitz' entropy. de Vries et al. (2023) ended with two open questions, both of which have been answered by Giaimo (2024) now: (1) Can a discrete‐time entropy measure of survivorship be generalized beyond age‐based population models? Giaimo (2024) introduce a new formula that achieves this. (2) Will a discretization of Keyfitz' derivation of his measure as the elasticity of lifespan to a uniform change in mortality lead to the same formula as a discretization of Keyfitz' result? Giaimo (2024) answers: no. Here, we briefly discuss the implications of the results obtained by Giaimo (2024), and the implementation of his new formula into the Rpackage Rage, which is widely used for comparative demographic studies. We showcase the strength of the new method by reanalysing a comparison of Keyfitz' entropy to another shape measure. We find that the comparison is significantly altered by using Giaimo's new Keyfitz' formula. This example strengthens Giaimo's (2004) words of warning in approaching discretizations with attentiveness.
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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 | 0.048 | 0.344 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.005 | 0.010 |
| Insufficient payload (model declined to judge) | 0.006 | 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".