MULTIDIMENSIONAL α-NOMINATE Keith T. Poole School of Public and International Affairs University of Georgia Athens, Georgia

NOMINATE Deterministic Utility

Expressed as an Exponential Series

The difference simplifies to:

The Difference Between the Quadratic Deterministic Utilities Simplifies to:

The Vector Geometry of Quadratic Utility

The Vector Geometry Simplifies the Standard Quadratic Utility Difference Model (also called IRT) to:

The Quadratic Utility Model in Two Dimensions is only identified up to “tracks” through the Space.

The Natural Log of the Posterior Distribution

Where The Mixture is Expressed

The Algorithm

The Algorithm (Continued)

The Algorithm (Continued)