ABSTRACT

Correlated binary responses occur in a wide variety of areas of
application from genetics to spatial sampling, clinical trials
and a range of social science applications.
Such effects are usually due to random effects that are common
to several units, or random effects that are spatially correlated.
The standard way to accommodate such effects is to incorporate
correlated additive Gaussian variables on the logistic scale.
Although the computation is not easy, such models have been widely
used for the past 20+ years.  I argue that the direct application
of such models to random samples is incorrect and misleading without
a correction for sampling bias.