Nonstationary longitudinal autoregressive mixed model for count data with measurement error in covariates: Estimation and asymptotics
Why this work is in the frame
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Bibliographic record
Abstract
Several methods have been proposed in the literature for computing unbiased and efficient estimates of the parameters of generalized linear models when the covariates are measured with error. However, to our knowledge, no documented research on computational techniques for parameter estimation currently exist in the literature when the data is a longitudinal count data influenced by an unobservable latent variable and observable covariates that are measured with error. In this paper, we propose a nonstationary conditionally Poisson mixed model for such data and develop unbiased estimating equations with iterative methods for computing estimates of the effect of the covariates, variance of the latent variable, and the correlation index parameter. The performance of the iterative methods is examined through extensive simulation studies. The results show that the methods performed well when the magnitude of the measurement error is not so large as to dominate or mask the effect of the true covariates. Using observed longitudinal count data on the number of patents awarded to 168 firms in the United States from 1974 to 1979 along with associated covariate information on the type of firm, log of the book value of capital in 1972 and research and development (R & D) expenditures we have demonstrated how the methods proposed in this paper can be applied to a real data. In addition, we derive the influence function of the estimator of the covariate effect and discuss the asymptotic properties of the estimator. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 151-180.
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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 | 0.004 | 0.002 |
| 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 | 0.000 | 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 it