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The use of score tests for inference on variance components
Geert Verbeke1, Geert Molenberghs
1Biostatistical Centre, Catholic University of Leuven, U.Z. St.-Rafaël, Kapucijnenvoer 35, B-3000 Leuven, Belgium. geert.verbeke@med.kuleuven.ac.be
Biometrics
|August 21, 2003
Summary
The choice between one-sided and two-sided tests for variance components is critical. This study clarifies score test statistics for one-sided inference, demonstrating that classical two-sided versions are inappropriate.
Area of Science:
- Statistics
- Biostatistics
Background:
- Inference for variance components necessitates choosing between one-sided and two-sided tests.
- This choice often depends on whether negative variance components are permissible.
- Classical inferential procedures exist for two-sided tests (likelihood ratio, score, Wald statistics).
Purpose of the Study:
- To address confusion surrounding one-sided score tests for variance components.
- To demonstrate the inadequacy of classical two-sided score test statistics in this context.
- To propose and validate suitable one-sided score test statistics.
Main Methods:
- Development of one-sided score test statistics and derivation of their null distributions.
- Comparison with likelihood ratio tests for one-sided inference.
- Application to continuous longitudinal data analyzed with linear mixed models.
Main Results:
- Classical two-sided score test statistics are inappropriate for one-sided inference of variance components.
- Well-chosen one-sided score test statistics can be effectively used.
- The relationship between one-sided score tests and likelihood ratio tests is established.
Conclusions:
- The study clarifies the correct application of score tests for one-sided variance component inference.
- It highlights the limitations of commonly used two-sided statistics.
- The findings are validated through practical analysis of longitudinal data.
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