Identification of parameters in normal error component logit‐mixture (NECLM) models
Bibliographic record
Abstract
Abstract Although the basic structure of logit‐mixture models is well understood, important identification and normalization issues often get overlooked. This paper addresses issues related to the identification of parameters in logit‐mixture models containing normally distributed error components associated with alternatives or nests of alternatives ( normal error component logit mixture , or NECLM, models). NECLM models include special cases such as unrestricted, fixed covariance matrices; alternative‐specific variances; nesting and cross‐nesting structures; and some applications to panel data. A general framework is presented for determining which parameters are identified as well as what normalization to impose when specifying NECLM models. It is generally necessary to specify and estimate NECLM models at the levels, or structural, form. This precludes working with utility differences, which would otherwise greatly simplify the identification and normalization process. Our results show that identification is not always intuitive; for example, normalization issues present in logit‐mixture models are not present in analogous probit models. To identify and properly normalize the NECLM, we introduce the ‘equality condition’, an addition to the standard order and rank conditions. The identifying conditions are worked through for a number of special cases, and our findings are demonstrated with empirical examples using both synthetic and real data. Copyright © 2007 John Wiley & Sons, Ltd.
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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 | 0.012 | 0.075 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".