Milk yield records (305d, 2X, actual milk yield) of 123,639 registered first lactation Holstein cows were used to compare linear regression (y = β0 + β1X + e) ,quadratic regression, (y = β0 + β1X + β2X2 + e) cubic regression (y = β0 + β1X + β2X2 + β3X3 + e) and fixed factor models, with cubic-spline interpolation models, for estimating the effects of inbreeding on milk yield. Ten animal models, all with herd-year-season of calving as fixed effect, were compared using the Akaike corrected-Information Criterion (AICc). The cubic-spline interpolation model with seven knots had the lowest AICc, whereas for all those labeled as "traditional", AICc was higher than the best model. Results from fitting inbreeding using a cubic-spline with seven knots were compared to results from fitting inbreeding as a linear covariate or as a fixed factor with seven levels. Estimates of inbreeding effects were not significantly different between the cubic-spline model and the fixed factor model, but were significantly different from the linear regression model. Milk yield decreased significantly at inbreeding levels greater than 9%. Variance component estimates were similar for the three models. Ranking of the top 100 sires with daughter records remained unaffected by the model used.