This thesis is an investigation of the effect of using 305-day or random regression test day models to estimate breeding values for milk yield, on the accuracy of estimated breeding values. Test day milk yields were simulated to an existing data structure and used to obtain simulated 305-day milk yields. Simulated milk yields were analyzed using 305-day models and five random regression test day models based on different mathematical functions to describe daily milk yields. Estimated breeding values from each of these models were compared to simulated breeding values. This sequence was replicated ten times. Parameters needed for simulation and estimation of breeding values were estimated from actual Jersey test day yields. Random regression test day models resulted in estimated breeding values for 305-day milk yield which were more accurate than breeding values from 305-day models. Using random regression test day models based on mathematical functions with five instead of three parameters did not improve accuracy of estimated breeding values for 305-day yields. If the only aim is to improve accuracy of breeding values for 305-day yields, then random regression models using functions with three parameters are sufficient. Random regression test day models resulted in breeding values for daily yields and persistency which were accurate enough to be used for selection. Using random regression test day models based on mathematical functions with four or five instead of three parameters improved accuracy of estimated breeding values for daily yields and persistency. If daily or persistency breeding values are of interest, then a random regression model with five (or more) parameters should be used. Ignoring environmental covariances when estimating parameters for test day models resulted in overestimated genetic variances. Environmental covariances should be properly modeled in test day models to remove this bias. Environmental covariances caused a small reduction in the accuracy of estimated breeding values when these covariances were not properly modelled.