Walter W. Piegorsch
Department of Statistics
University of South Carolina
Extended logistic regression via the Heckman-Willis model, or "When is
a trend a trend"?
Methods are discussed for modeling trends in proportions that exhibit
extra-binomial variability. Motivation is taken from experiments in
developmental toxicology, where correlations among embryos within a litter
lead to the extra-binomial variability. Appeal is made to the well-known
beta-binomial distribution to represent the excess variability. An
exponential function is used to model the dose-response relationship, which
leads to a form of logistic regression for the mean proportion response. The
exponential relation also induces a functional model for the intra-litter
correlation. The model is common in the econometric literature, and is known
there as the Heckman-Willis beta-logistic model. In the biological and
environmental sciences, however, the model is virtually unused. An example
is presented to illustrate how easily the model is applied to developmental
toxicity data. An associated question of how to define an increasing trend
in the mean response under non-constant correlation will be discussed.
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