Colloquium - Lu Yang
Institution: University of Minnesota
Title: New Residuals for Regression Models with Noncontinuous Outcomes
Date: April 27, 2023
Location: C405 Wells Hall, Simulcast to Zoom (Click here for meeting details)
Time: 10:20 AM - 11:10 AM Eastern Time
Abstract:
Noncontinuous outcomes are found frequently in a wide variety of fields. For example,
stages of cancer in medical research (ordinal), the number of offspring of organisms
in ecology (count), and rainfall amounts in climate research (semicontinuous with
a probability of zero corresponding to no rain). Given the potential detrimental consequences
of model misspecification, after fitting a regression model, it is of prime importance
to check the adequacy of the model. However, the assessment of regression models with
noncontinuous outcomes is challenging and has many fundamental issues. With noncontinuous
outcomes, standard regression model assessment tools such as Pearson and deviance
residuals do not follow their null distributions under the true model, calling into
question the legitimacy of model assessment based on these tools. To bridge this gap,
we propose a new type of residuals for noncontinuous outcomes that are applicable
to general regression models. The proposed residuals are based on two layers of probability
integral transform. When at least one continuous covariate is available, the proposed
residuals converge to being uniformly distributed under the correctly specified model.
One can construct visualizations such as QQ plots to check the overall fit of a model
straightforwardly, and the shape of QQ plots can further help identify possible causes
of misspecification such as overdispersion. Through simulation, we demonstrate empirically
that the proposed tools outperform commonly used residuals for various model assessment
tasks.