Estimation of regression and dynamic dependence paremeters for non‐stationary multinomial time series
Bibliographic record
Abstract
In a time‐series regression setup, multinomial responses along with time dependent observable covariates are usually modelled by certain suitable dynamic multinomial logistic probabilities. Frequently, the time‐dependent covariates are treated as a realization of an exogenous random process and one is interested in the estimation of both the regression and the dynamic dependence parameters conditional on this realization of the covariate process. There exists a partial likelihood estimation approach able to deal with the general dependence structures arising from the influence of both past covariates and past multinomial responses on the covariates at a given time by sequentially conditioning on the history of the joint process (response and covariates), but it provides standard errors for the estimators based on the observed information matrix, because such a matrix happens to be the Fisher information matrix obtained by conditioning on the whole history of the joint process. This limitation of the partial likelihood approach holds even if the covariate history is not influeced by lagged response outcomes. In this article, a general formulation of the auto‐covariance structure of a multinomial time series is presented and used to derive an explicit expression for the Fisher information matrix conditional on the covariate history, providing the possibility of computing the variance of the maximum likelihood estimators given a realization of the covariate process for the multinomial‐logistic model. The difference between the standard errors of the parameter estimators under these two conditioning schemes (covariates Vs. joint history) is illustrated through an intensive simulation study based on the premise of an exogenous covariate process.
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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 | 0.011 | 0.064 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".