Testing distributional assumption of unit-Lindley regression model

Year 2022, Volume: 51 Issue: 3, 882 - 899, 01.06.2022

Deniz Özonur

https://doi.org/10.15672/hujms.932811

Abstract

This paper proposes smooth goodness of fit test statistic and its components to test the distributional assumption of the unit-Lindley regression model, which is useful for describing data measured between zero and one. Orthonormal polynomials on the unit-Lindley distribution, score functions and Fisher's information matrix are provided for the smooth test. Deviance and Pearson's chi-square tests are also adapted to the unit-Lindley regression model. A parametric bootstrap simulation study is conducted to compare type I errors and powers of the tests under different scenarios. Empirical findings demonstrate that the first smooth component, deviance, and chi-square tests have undesirable behavior for the unit-Lindley regression model. A real data set is analyzed by using the developed tests to show the adequacy of the unit-Lindley regression model. Model selection criteria and residual analysis prove that the unit-Lindley regression model provides a better fit than the Beta and simplex regression models for the real data set.

Keywords

Chi-square test, deviance test, power of test, smooth test, unit-Lindley distribution, parametric bootstrap

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