Test to Check the Equality of Regression Models and a Medical Application
Sérgio Ricardo Silva Magalhães *
Universidade Vale do Rio Verde, Av. Amazonas, 1700 – Belo Horizonte /Minas Gerais, CEP: 30.180-001, Brasil.
*Author to whom correspondence should be addressed.
Abstract
In this study, we considered the Model Identity and the Dummy Variables methods used to compare regression models. The adjustment of h linear regression equations was considered to verify the equality of the regression models by data simulation. Using features from the Interactive Matrix Language (IML) from the SAS® system, appropriate routines were developed for the methodology of regression models comparison. A data simulation with 100,000 experiments was performed considering different sample sizes (10, 50 and 100 observations). The performances of the two methods were essentially equivalent when comparing the different sample sizes. The results from all cases simulated by the methods had low percentages of Type I and Type II error rates. For larger samples, Type I and Type II error rates were always lower when using the approximate F statistics, which must therefore be the method of choice. The Dummy Variables method was the most efficient for all three sample sizes because it exhibited the lowest Type I and Type II error rates.
Keywords: Linear regression models, data simulation, hypothesis tests