Probabilistic Measurement of Attributes: A Logit Analysis by Generalized Least Squares

The Rasch latent trait model is derived from a double exponential error theory similar to that utilized for random utility models in choice theory. This formulation imbues multi-attribute measurements with an important probabilistic interpretation; namely, that the brand measurement is the log odds for the brand being rated above the mid-point on a particular attribute scale. Hence, one may compare brand measurements across attributes and construct multi-attribute configurations such as that illustrated. In addition to this theoretical underpinning for rating scale theory, the present paper establishes a statistical inference for survey rating scales based upon generalized least squares. An important advantage of the present GLS analysis stems from its capability of testing various hypotheses concerning brand configurations in multi-attribute spaces.