The simultaneous assessment of normality and homoscedasticity in linear fixed effects models

ABSTRACT

This article investigates the problem of simultaneously testing the normality and homoscedasticity assumptions in a linear fixed effects model when we have grouped data. This has been facilitated by the assumption of a smooth alternative to the normal distribution. The smooth alternative is specified using Legendre polynomials, and the score statistic is derived under two scenarios: a common smooth alternative across the different groups, or different smooth alternatives across the different groups. A data-driven approach available in the literature is used for determining the order of the polynomials. For the null distribution of the score statistic, the accuracy of the asymptotic chi-squared distribution is numerically investigated under a one-way fixed effects model with balanced and unbalanced data. The results are illustrated with an example.

KEYWORDS:

• Balanced data
• Legendre polynomials
• one-way fixed effects model
• score test
• smooth alternative
• unbalanced data

AMS SUBJECT CLASSIFCATION:

• 62F03
• 62j20

Acknowledgments

We thank Dr. M. Bogdan for providing us with a copy of the preprint of her work, Bogdan (1996). We are grateful to two reviewers for several helpful suggestions, which resulted in improved presentation of the results.

Funding

The facility is supported by the U.S. National Science Foundation through the MRI program (grants CNS-0821258 and CNS-1228778) and the SCREMS program (grant DMS-0821311), with additional substantial support from the University of Maryland, Baltimore County (UMBC). See www.umbc.edu/hpcf for more information on HPCF and the projects using its resources. The hardware used in the computational studies is part of the UMBC High Performance Computing Facility (HPCF).

Additional information

Funding

The facility is supported by the U.S. National Science Foundation through the MRI program (grants CNS-0821258 and CNS-1228778) and the SCREMS program (grant DMS-0821311), with additional substantial support from the University of Maryland, Baltimore County (UMBC). See www.umbc.edu/hpcf for more information on HPCF and the projects using its resources. The hardware used in the computational studies is part of the UMBC High Performance Computing Facility (HPCF).