Graphical analysis of residuals in multivariate growth curve models and applications in the analysis of longitudinal data
Why this work is in the frame
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Bibliographic record
Abstract
Statistical models often rely on several assumptions including distributional assumptions on outcome variables as well as relational assumptions representing the relationship between outcomes and independent variables. Model diagnostics is, therefore, a crucial component of any model fitting problem. Residuals play important roles in model diagnostics and checking assumptions. In multivariate models, residuals are not commonly used in practice, although approaches have been proposed to check multivariate normality and other model assumptions. When done, ordinary residuals are often used. Nevertheless, it has been shown that ordinary residuals in the analysis of longitudinal data are correlated and are not normally distributed. Under sufficiently large sample size, a transformation of residuals were previously proposed to check the normality assumption. The transformation solely focuses on removing the correlation. In this paper, we show that the ordinary residuals in the analysis of longitudinal data are not normally distributed and should not be used for checking the normality assumption. Via extensive simulations, we also show that the transformed (de-correlated) residuals fail to provide accurate model validation, in particular in the presence of model misspecification. We consider decomposed residuals from the multivariate growth curve model, provide practical interpretations, examine their property analytically as well as via simulations, and show how the different components can be used to examine model misspecification and distributional assumptions. Extensive simulations are performed to evaluate and compare performances for normal and non-normal data. Analysis of real data sets are presented as illustrations.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| 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