Strategies for handling normality assumptions in multi-level modeling: a case study estimating trajectories of Health Utilities Index Mark 3 scores.
Bibliographic record
Abstract
BACKGROUND: With longitudinal data, lifetime health statusŏ dynamics can be estimated by modeling trajectories. Health status trajectories measured by the Health Utilities Index Mark 3 (HUI3) modeled as a function of age alone and also of age and socio-economic covariates revealed non-normal residuals and variance estimation problems. The possibility of transforming the HUI3 distribution to obtain residuals that approximate a normal distribution was investigated. DATA AND METHODS: The analysis is based on longitudinal data from the first six cycles of the National Population Health Survey (NPHS). The data pertain to 7,784 individuals, who, in 1994/1995, were aged 40 to 99, were living in private households, and had complete information on HUI3. A multilevel growth model was used to examine the hierarchical structure of NPHS data (repeated measurements nesting within respondents). The transformation of arcsine [2 x (HUI + 0.36) / (1 + 0.36)-1] was used to improve the distribution of the residuals at both levels and limit the conditional mean to the -0.36 to 1.00 interval. A model was estimated using socio-economic determinants. Analyses were performed with SAS and MLwiN. RESULTS: After the transformation of HUI3, the model was satisfactory and allowed for inclusion of new socio-demographic and health variables in order to estimate their impact on the health-related quality of life of aging populations. Because of the complex transformation of the arcsine model, the regression coefficients were not interpreted. Instead, the estimation results were summarized graphically.
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How this classification was reachedexpand
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 | 0.005 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".