Scandinavian Working Papers in Economics
Working Papers in Economics,
University of Gothenburg, Department of Economics
No 102: Maximum Likelihood Ratio based small-sample tests for random coefficients in linear regression
Max Petzold and Robert Jonsson
Additional contact information
Max Petzold: Department of Statistics,, Postal: School of Economics and Commercial Law, Göteborg University, Box 640, SE 405 30 GÖTEBORG
Robert Jonsson: Department of Economics, School of Economics and Commercial Law, Göteborg University, Postal: Göteborg University, Box 640, SE 405 30 GÖTEBORG
Abstract: Two small-sample tests for random coefficients in linear regression are derived from the Maximum Likelihood Ratio. The first test has previously been proposed for testing equality of fixed effects, but is here shown to be suitable also for random coefficients. The second test is based on the multiple coefficient of determination from regressing the observed subject means on the estimated slopes. The properties and relations of the tests are examined in detail, followed by a simulation study of the power functions. The two tests are found to complement each other depending on the study design: The first test is preferred for a large number of observations from a small number of subjects, and the second test is preferred for the opposite situation. Finally, the robustness of the tests to violations of the distributional assumptions is examined.
Keywords: Exact test; Hypothesis test; Maximum Likelihood; Pre-test; Random coefficient regression
21 pages, August 25, 2003
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