Fitting a Quasi-Poisson Case of the GSTUN (General Stochastic Tree UNfolding) Model and Some Extensions

Summary

A new family of probabilistic choice models for representing paired comparisons data from different sources (subjects or homogeneous groups of subjects) is derived and extended from a general class of stochastic tree unfolding models proposed by Carroll, DeSarbo and De Soete (1987, 1988, 1989). In this approach, both the sources and the choice objects are represented by the terminal nodes of an additive tree. The probability that source i prefers object j to object k is defined by

$${p_{i,j,k}}\; = \Phi \;(\frac{{{d_{ik}}\; - \;{d_{ij}}}}{{\beta d_{jk}^\alpha }})\;(0 \leqslant \;\alpha \; \leqslant \;1,\;\beta \; \succ \;0)$$

where d _ij (d _ik ) denotes the additive tree distances between the nodes representing source i and object j (object k), and where d _jk denotes the additive tree distance between the nodes representing objects j and k. A mathematical programming procedure for fitting this model to three-way paired comparisons data is mentioned. The model is applied for illustrative purposes to a well-known data set gathered by Rumelhart and Greeno (1971).

Supported as “Brvoegdverklaard Navorser” of the Belgian N.F.W.O.