BinaryEPPM: Mean and Scale-Factor Modeling of Under- And Over-Dispersed
Binary Data
Under- and over-dispersed binary data are modeled using an extended Poisson
process model (EPPM) appropriate for binary data. A feature of the model is that the
under-dispersion relative to the binomial distribution only needs to be greater than
zero, but the over-dispersion is restricted compared to other distributional models
such as the beta and correlated binomials. Because of this, the examples focus on
under-dispersed data and how, in combination with the beta or correlated distributions,
flexible models can be fitted to data displaying both under- and over-dispersion. Using
Generalized Linear Model (GLM) terminology, the functions utilize linear predictors for
the probability of success and scale-factor with various link functions for p, and log
link for scale-factor, to fit a variety of models relevant to areas such as bioassay.
Details of the EPPM are in Faddy and Smith (2012) <doi:10.1002/bimj.201100214> and
Smith and Faddy (2019) <doi:10.18637/jss.v090.i08>.
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