Bartlett corrections for zero-adjusted generalized linear models

Tiago M. Magalhães (), Gustavo H. A. Pereira, Denise A. Botter and Mônica C. Sandoval
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Tiago M. Magalhães: Federal University of Juiz de Fora
Gustavo H. A. Pereira: Federal University of São Carlos
Denise A. Botter: University of São Paulo
Mônica C. Sandoval: University of São Paulo

Statistical Papers, 2024, vol. 65, issue 4, No 11, 2209 pages

Abstract: Abstract Zero-adjusted generalized linear models (ZAGLMs) are used in many areas to fit variables that are discrete at zero and continuous on the positive real numbers. As in other classes of regression models, hypothesis testing inference in the class of ZAGLMs is usually performed using the likelihood ratio statistic. However, the LR test is substantially size distorted when the sample size is small. In this work, we derive an analytical Bartlett correction of the LR statistic. We also consider two different adjustments for the LR statistic based on bootstrap. Monte Carlo simulation studies show that the improved LR tests have null rejection rates close to the nominal levels in small sample sizes and similar power. An application illustrates the usefulness of the improved statistics.

Keywords: Bartlett corrections; Chi-squared distribution; Maximum likelihood estimates; 62Fxx; 62F05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01477-2

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