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A method of evaluation of ordered categorical responses is presented. The probability of re-sponse in a given category follows a normal integral with an argument dependent on fixed thresholds and random variables sampled from a conceptual distribution with known first and second moments, a priori. The prior distribution and the likelihood function are combined to yield the posterior density from which inferences are made. The mode of the posterior distribution is taken as an estimator of location. Finding this mode entails solving a non-linear system; estimation equations are presented. Relationships of the procedure to" generalized linear models" and" normal scores are discussed. A numerical example involving sire evaluation for calving ease is used to illustrate the method.