A Comparison of Two General Approaches to Mixed Model Longitudinal Analyses Under Small Sample Size Conditions
Bibliographic record
Abstract
There is no general exact analysis for the class of generalized mixed models, and asymptotic procedures are widely used. Importantly, under small sample conditions equivalent asymptotic procedures can yield conflicting inference when applied to the same data set [Aubin, E. C. Q., Cordeiro, G. M. (2000). Bartlett-corrected tests for normal linear models when the covariance matrix is nonscalar. Commun. Statist.—Theory Methods 29:2405–2426]. For the classical likelihood ratio test (LRT), Bartlett’s [Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proc. R. Soc. London. Ser. A, Math. Phys. Sci. 160(901):268–282] correction may be used to yield improved small sample performance. Zucker et al. [Zucker, D. M., Lieberman, O., Manor, O. (2000). Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. J. R. Statist. Soc., Ser. B 62:827–838] proposed and investigated methods for improved small sample inference in the mixed linear model using refined LRTs. The refinements included the use of a Bartlett correction and the Cox–Reid adjusted likelihood [Cox, D. R., Reid, N. (1987). Approximations to noncentral distributions. Can. J. Statist. 15(2):105–114], which using simulation studies (under a random-line model, and a two-period, four-treatment crossover design) were shown to yield Type I error rates very close to the nominal level. An alternative approach which has also been shown [Kowalchuk, R., Keselman, H. (2001). The analysis of repeated measurements with mixed-model Kenward Roger's adjusted F-tests. Paper presented at the Annual Meeting of the American Educational Research Association, Seattle, Washington] to have improved performance characteristics is a procedure involving t and F statistics for tests of fixed effects with modified degrees of freedom calculations detailed by Kenward and Roger [Kenward, M. G., Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics 53:983–997]. However, to date there has been no direct comparison of the Bartlett modified likelihood ratio and Kenward Roger procedures. This paper provides the results from a Monte Carlo simulation study examining the Type I error control and power profiles of modified likelihood ratio procedures including those described in Zucker et al. and proposed by Kenward and Roger for tests of fixed effect parameters in mixed linear models with data simulated from small sample unbalanced repeated measures designs, followed by results from a real data example.
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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 | 0.130 | 0.292 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.005 |
| Bibliometrics | 0.006 | 0.005 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.007 | 0.008 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.007 | 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".