In this research, Fixed Regression Test-Day Model (FRM) and Random Regression Test-Day Model (RRM) were studied for genetic evaluation of milk yield of Iranian Holsteins dairy cattle. Breeding values and genetic parameters of milk yield from two models were compared. A total of 164,391 monthly test day milk records obtained from 19,217 first lactation Holstein cows (three times milking a day) calving between 1991 to 2008 were analyzed. The records were distributed among 179 herds and were used to estimate genetic parameters and to predict breeding values. The contemporary groups of herd- year- month- of production were fitted as fixed effects in the models. Also linear and quadratic forms of age at calving and Holstein gene percentage were fitted as covariates. The random effects of the models were additive genetic and permanent environmental effects. In the random regression model, orthogonal Legendre polynomial up to order 4 (cubic) were implemented to take account of genetic and environmental aspects of milk production over the course of lactation. The heritability estimated from the FRM was found to be 0.15. From the RRM, the average estimated heritability of monthly test day milk production was higher for the second half of the lactation than that of the first half of the lactation period. The lowest and the highest heritabilities were found for the first (0.102) and the sixth (0.235) month of lactation, respectively. Genetic, permanent environmental and phenotypic correlations decreased as the interval between consecutive test days increased. Breeding value of animals predicted from FRM and RRM were also compared. The results showed similar ranking of animals based on their breeding values from both models.

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