Bibliographic record
Abstract
Advancements in statistics are normally geared to addressing topics that will either address an existing gap in the field or to render analysis results more accurate/reliable.This work aims to add to existing research by extending from binary Generalized Linear Model (GLM) and Generalized Linear Mixed Model (GLMM) to a multinomial logit, multivariate GLM (MGLM) and multivariate GLMM (MGLMM), subject to ordered equality and inequality constraints.We extended the maximum likelihood estimate (MLE) and likelihood ratio hypothesis testing (LRT) methods for the binary and multinomial GLM and GLMM subject to linear equality and inequality constraints on the parameters of interest.These methods will build on existing literature to allow for more options in hypothesis testing and the construction of confidence intervals.The innovative procedures take advantage of the gradient projection (GP) technique for the MLE, and chi-bar-square statistics for constrained LRTs.The model presented in this thesis yields accurate results since parameter orderings or constraints often occur naturally; and when this occurs, we optimize the efficiency of a statistical method by incorporating the parameter constraints into the MLE and hypothesis testing.More specifically, we use ordered constrained inference for multinomial data whereby including equality and inequality constraints adds value to our predictions.Using real-world data from the Canadian Community Health Survey (C-CHS), the methodology of using constraints showed significant improvement on methodology that does not, which substantiates the added value of the work presented here.This work contributes to the field by dealing with inequality constraints in MGLMM, specifically multinomial data, which is the most challenging problem in constrained inference.This helps improve results for researchers in both scientific and non-scientific fields.
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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 | 0.057 | 0.307 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.004 | 0.007 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.006 | 0.005 |
| Research integrity | 0.003 | 0.009 |
| Insufficient payload (model declined to judge) | 0.010 | 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".