Dr Lu Yang

Regression models with noncontinuous (e.g. count, binary, ordinal, and semicontinuous) outcomes have been long and widely used in many domains of science and engineering. Having fit a regression model, judging the adequacy of the model’s fit is a routine and critical task in statistics. However, there is a lack of valid tools for assessment of regression models with noncontinuous outcomes.

The long-term goal of this research is to establish a principled framework for assessing regression models with noncontinuous outcomes. The envisioned framework includes informal graphical assessment tools and formal goodness-of-fit tests. Specifically, this project has two objectives:

• Develop a goodness-of-fit test for regression models with general discrete outcomes in order to assist analysts to obtain p-values and draw conclusions on the adequacy of their models with statistical confidence. The theoretical properties of the proposed goodness-of-fit statistic will be studied using empirical process theory, and extensive simulation studies will be conducted to evaluate its rate of type I and type II errors.
• Develop a graphical assessment tool and a goodness-of-fit test for regression models with semicontinuous outcomes, which are characterized with a point mass of observations at zero and the remaining observations following a positive-valued distribution.