Detecting Model Misspecification in Inflated Beta Regressions

Abstract

Beta regression models are useful for modeling data that assume values in the standard unit interval (0, 1), such as rates and proportions. These models, however, cannot be used when the data contain observations that equal zero or one (the limits of the unit interval). Ospina and Ferrari (2012) developed the class of inflated beta regressions to handle situations in which the data contain positive mass at zero and/or one. The model is quite general and contains three submodels: for the mean, for the precision, and for the probability that the variate equals zero or one (α). In this article, we propose a misspecification test for inflated beta regressions with fixed and variable dispersion. In particular, we propose two variants of the test. In the first variant, we only add testing variables to the mean submodel. The second variant follows from adding testing variables to all submodels. We perform extensive Monte Carlo simulations in order to assess the finite-sample properties of the tests (size and power), and also to gain insight on which variables should be used as testing variable and on which asymptotic testing procedure delivers the most reliable inferences. We consider a number of different misspecifications, namely: neglected nonlinearities, omitted independent variables, incorrect link functions, neglected spatial correlation, and neglected variable dispersion. Finally, an empirical illustration is presented and discussed.

KEYWORDS:

• Beta distribution
• Beta regression
• Inflated beta regression
• Link function
• Misspecification test
• Nonlinearity
• Spatial correlation

Mathematics Subject Classification:

• Primary 62J02
• Secondary 62J20

Acknowledgments

TLP and FCN gratefully acknowledge financial support from CAPES and CNPq, respectively. The authors also thank three anonymous referees for comments and suggestions.

Notes

For brevity, we do not consider simultaneous inflation at 0 and 1.