A Parametric Test to Discriminate Between a Linear Regression Model and a Linear Latent Growth Model
Bibliographic record
Abstract
In longitudinal studies with subjects measured repeatedly across time, an important problem is how to select a model generating data by choosing between a linear regression model and a linear latent growth model. Approaches based both on information criteria and asymptotic hypothesis tests of the variances of ''random'' components are widely used but not completely satisfactory. We propose a test statistic based on the trace of the product of an estimate of a variance covariance matrix defined when data come from a linear regression model and a sample variance covariance matrix. We studied the sampling distribution of the test statistic giving a representation in terms of an infinite series of generalized F-distributions. Knowledge about this distribution allows us to make inference within a classical hypothesis testing ramework. The test statistic can be used by itself to discriminate between the two models and/or, if duly modified, it can be used to test randomness on single components. Moreover, in conjunction with some model selection criteria, it gives additional information which can help in choosing the model.
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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 | 0.036 | 0.209 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.005 | 0.004 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".