Improved Likelihood Ratio Tests for Varying Dispersion Simplex Regression Models

Abstract

Abstract The simplex regression model is tailored to response variables that assume values in the standard unit interval, such as rates and proportions. The estimation of the parameters that index the model is performed by maximum likelihood, and test inferences are commonly reached using the likelihood ratio test. Such a test is based on an asymptotic approximation, and thus the resulting inferences may be misleading when the sample size is not large. In this paper, Bartlett‐corrected likelihood ratio tests are obtained for varying dispersion simplex regressions. Monte Carlo simulations are performed to compare the finite sample behavior of the corrected tests to that of standard likelihood ratio. The numerical results show that one of the corrected tests displays excellent control of the type I error frequency. An empirical application is presented and discussed.