New statistical procedures for analysis of ordered categorical data were investigated. In using the standardized threshold model, scores are transformed to estimate unknown boundary points and fixed and random effects on an underlying scale of continuous response. The model for calving ease included sex of calf, parity of dam, and the unknown boundary points as fixed effects; herd-year-seasons and sires were random. Data were 5029 dystocia scores on a scale of 1 to 5 collected from June 1982 to January 1984 through the Mid-States Dairy Records Processing Center. The predicted probability of a difficult birth by an average sire indicated that twice as many males as females are born with difficulty. Difficult births declined between first and second parity by a factor of 5. Herd-year-seasons accounted for 13.3% of the variance and sires 3.2%. Heritability on the underlying scale was higher (.147) than on the observed scale (.061). Rank correlations among the threshold model sire solutions and best linear unbiased predictions were .94 when herd-year-seasons were fixed, .98 with random herd-year-seasons, and .99 with normalized scores. Predicted percentage of difficult births for all sires in the analysis ranged from 6 to 18%.