Presentation of Degree Project E

  • Date: –12:00
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 74118
  • Lecturer: Max Raner
  • Contact person: Raazesh Saiunudiin
  • Seminarium

Title: Behavior and Performance of Some Inference Tools in Beta Regression

Abstract: 

Finite interval data, such as proportions, concentrations or rates, often exhibits asymmetry and heteroscedasticy in a regression setting, which can cause issues when trying to model such data using common modelling approaches. Ferrari and Cribari-Neto, 2004 proposed a modeling approach similar to a generalized linear model, in which the response is assumed to be beta distributed using an alternative parameterisation in terms of a mean and precision parameter, and then modeled via a link function depending on a linear predictor. The properties of the beta distribution then accommodate for many of the issues inherent with interval data. This model, called beta regression, was later extended in Smithson and Verkuilen, 2006 to further account for heteroscedasticity, and then further and more formally developed in Simas, Barreto-Souza, and Rocha, 2010.

In this thesis, an introduction to the beta regression model is given, and then a potential goodness of fit statistic for the beta regression model, based on non parametric smoothing, is introduced, repurposed from a statistic in logistic regression developed in Cessie and Houwelingen, 1991. Then, through an extensive exploratory simulation study, the behavior and performance of some of the available inference tools for the beta regression model, such as point and interval estimators, is explored. 

Lastly, a simulated comparison study of the performance of the beta regression model and other alternatives is carried out.

It is found that the goodness of fit statistic could have potential use, though it seems to be suffering from low power. In some settings, point estimators of the dispersion parameter can exhibit considerable bias, resulting in confidence intervals of the mean value parameters with below nominal coverage. This can in large part be accounted for by the use of bias corrected estimators, though that in turn can introduce additional, though less relevant problems in terms of coverage for the dispersion parameter. Comparing the beta regression model to other alternatives, it is found to have as good or better performance, in terms of relative efficiency.