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Checking linearity of non-parametric component in partially linear models with an application in systemic
1Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, NY 14642, USA.
Statistical Methods in Medical Research
|June 14, 2006
Summary
Two new statistical tests assess linearity in partially linear models. The Crámer-von Mises test demonstrates superior power for detecting deviations from linearity compared to a penalized spline approach.
Area of Science:
- Statistics
- Econometrics
- Biostatistics
Background:
- Partially linear models are widely used in various fields.
- Assessing the linearity of the nonparametric component is crucial for model validity.
- Existing methods may lack sufficient power or have limitations in certain scenarios.
Purpose of the Study:
- To propose two novel statistical tests for checking the linearity of the nonparametric function in partially linear models.
- To evaluate the performance of these tests through simulation experiments.
- To provide practical tools for model diagnostics in applied research.
Main Methods:
- Development of a Crámer-von Mises type test statistic.
- Utilizing a bootstrap resampling technique for critical value calculation.
- Construction of a likelihood ratio test within a penalized spline and linear mixed-effects (LME) modeling framework.
Main Results:
- Both proposed tests exhibit good level properties, maintaining the nominal significance level.
- The Crámer-von Mises test demonstrates substantially superior power compared to the penalized spline-based test across various simulation settings.
- The tests were successfully applied to a real-world dataset, demonstrating their practical utility.
Conclusions:
- The Crámer-von Mises test offers a powerful and reliable method for assessing linearity in partially linear models.
- The penalized spline approach provides an alternative, though generally less powerful, method.
- These tests enhance the diagnostic capabilities for users of partially linear models.
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