Stepwise Regression in Mixed Quantitative Linear Models with Autocorrelated Errors
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Bibliographic record
Abstract
ABSTRACT In the stepwise procedure of selection of a fixed or a random explanatory variable in a mixed quantitative linear model with errors following a Gaussian stationary autocorrelated process, we have studied the efficiency of five estimators relative to Generalized Least Squares (GLS): Ordinary Least Squares (OLS), Maximum Likelihood (ML), Restricted Maximum Likelihood (REML), First Differences (FD), and First-Difference Ratios (FDR). We have also studied the validity and power of seven derived testing procedures, to assess the significance of the slope of the candidate explanatory variable x 2 to enter the model in which there is already one regressor x 1. In addition to five testing procedures of the literature, we considered the FDR t-test with n − 3 df and the modified t-test with nˆ − 3 df for partial correlations, where nˆ is Dutilleul's effective sample size. Efficiency, validity, and power were analyzed by Monte Carlo simulations, as functions of the nature, fixed vs. random (purely random or autocorrelated), of x 1 and x 2, the sample size and the autocorrelation of random terms in the regression model. We report extensive results for the autocorrelation structure of first-order autoregressive [AR(1)] type, and discuss results we obtained for other autocorrelation structures, such as spherical semivariogram, first-order moving average [MA(1)] and ARMA(1,1), but we could not present because of space constraints. Overall, we found that: the efficiency of slope estimators and the validity of testing procedures depend primarily on the nature of x 2, but not on that of x 1; FDR is the most inefficient slope estimator, regardless of the nature of x 1 and x 2; REML is the most efficient of the slope estimators compared relative to GLS, provided the specified autocorrelation structure is correct and the sample size is large enough to ensure the convergence of its optimization algorithm; the FDR t-test, the modified t-test and the REML t-test are the most valid of the testing procedures compared, despite the inefficiency of the FDR and OLS slope estimators for the former two; the FDR t-test, however, suffers from a lack of power that varies with the nature of x 1 and x 2; and the modified t-test for partial correlations, which does not require the specification of an autocorrelation structure, can be recommended when x 1 is fixed or random and x 2 is random, whether purely random or autocorrelated. Our results are illustrated by the environmental data that motivated our work.
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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 | 0.000 | 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 | 0.000 | 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