Functional Principal Component Analysis of Density Families with Categorical and Continuous Data on Canadian Entrant Manufacturing Firms
Bibliographic record
Abstract
This paper investigates the evolution of firm distributions for entrant manufacturing firms in Canada using functional principal components analysis. This methodology describes the dynamics of firms by examining production variables, size and labour productivity, and a financial variable, leverage (debt-to-asset ratio). We adapt the original method proposed in Kneip and Utikal (2001, JASA) to allow for the inclusion of qualitative information in the form of discrete variables, industry and region, to capture market structure differences, which it is shown to change the dynamics of firm size and labour productivity distributions only. We also perform various tests with the null hypothesis that the distributions are equal across time. When accounting for industry and regional categories, there is a substantial fall in the number of rejections of the null hypothesis of equality for size and labour productivity, which is not the case for leverage. These results show the importance of including qualitative information to account for potential heterogeneity when applying functional principal component analysis to firm level data. Finally, the methodology finds a correlation between the evolution of variable distributions and macroeconomic factors.
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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 | 0.005 | 0.034 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".