TY - CHAP
TI - Dirichlet-Multinomial Regression Models in R
AB - Categorical data are ubiquitous in psychological research and commonly analyzed using, for example, multinomial logistic regression. The latter model, relying on the multinomial distribution, can exhibit serious problems related to over-dispersion. To remedy this, a compound distribution is constructed, where the multinomial distribution's parameters (probabilities in (0, 1) that must sum up to 1) are assumed to be Dirichlet-distributed. Integration over those probabilities yields a compound Dirichlet-multinomial distribution that has one parameter more than the multinomial distribution and acts like a "categorical Version" of the Dirichlet distribution with one parameter (α) per category. This additional parameter allows for a wide variety of possible distributional shapes (e.g., marginally U- or J-shaped, uniform, or unimodal). For dependent categorical variables that include n > 1 trials (at least for some observations), two regression models are described: one that models the alpha parameters directly and one with a reparametrization in means and precision, which can be interpreted similarly to multinomial logistic regression. This implementation extends the framework established in the R-package "DirichletReg".
AF - Psychoco 2013: International Workshop on Psychometric Computing
PP - Zürich
UR - http://eeecon.uibk.ac.at/psychoco/2013/
PY - 2013-04-01
AU - Maier, Marco
ER -