A single-trait random regression (RR) model was used for a data set of 151,413 test day milk yields of 22,068 cows calving for the first time from 1992 through 1994. The fixed regressions were considered within 32 subclasses of genetic group (defined according to the proportion of HF genes) by age group by season of calving. Two different submodels were used for fixed and random regressions: regression model (RM) and Wilmink model (WM) as well as HYS or HTD fixed effects were incorporated, giving eight different models for comparison. Differences in estimated breeding values (BVs) calculated on the basis of solutions from each of eight RR models indicated that the change of HYS to HTD effect had no significant influence on BVs. Residual variances were reduced by up to 23% when models with HTD effects were used, showing that they accounted for factors specific to each test day much better than did models with HYS. Correlations between BVs from test day models and the national 305d BVs were 0.71-0.79 for sires and were higher for models with HYS effect. Comparison of the correlations between BVs from different test day models indicated that the choice of covariates for random regressions was important. The use of the Wilmink function for those regressions is justified because it is accurate enough and computationally more efficient.