TY - JOUR AU - Smith, David M. AU - Faddy, Malcolm J. PY - 2019/07/31 Y2 - 2024/03/28 TI - Mean and Variance Modeling of Under-Dispersed and Over-Dispersed Grouped Binary Data JF - Journal of Statistical Software JA - J. Stat. Soft. VL - 90 IS - 8 SE - Articles DO - 10.18637/jss.v090.i08 UR - https://www.jstatsoft.org/index.php/jss/article/view/v090i08 SP - 1 - 20 AB - This article describes the R package BinaryEPPM and its use in determining maximum likelihood estimates of the parameters of extended Poisson process models for grouped binary data. These provide a Poisson process family of flexible models that can handle unlimited under-dispersion but limited over-dispersion in such data, with the binomial distribution being a special case. Within BinaryEPPM, models with the mean and variance related to covariates are constructed to match a generalized linear model formulation. Combining such under-dispersed models with standard over-dispersed models such as the beta binomial distribution provides a very general form of residual distribution for modeling grouped binary data. Use of the package is illustrated by application to several data-sets. ER -