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The Poisson Model with Three Binary Predictors: When are Saturated Designs Optimal?

by Graßhoff, U.; Holling, H.; Schwabe, R. .

Series: 2014-10, Preprints

62K05 Optimal designs
62J12 Generalized linear models
62P15 Applications to psychology

In this paper, Poisson regression models with three binary predictors are considered. These models are applied to rule-based tasks in educational and psychological testing. To efficiently estimate the parameters of these models locally D-optimal designs will be derived. Eight out of all 70 possible saturated designs are proved to be locally D-optimal in the case of active effects. Two further saturated designs which are the classical fractional factorial designs turn out to be locally D-optimal for vanishing effects.

optimal design, saturated designs, count data, Poisson regression, Rasch Poisson count model, binary predictors