Milk and fat yield records of the first 4 lactations from 58 herds of Holstein cows recorded from 1999 to 2015 were analyzed. Genetic parameters were estimated by using univariate, repeatability and multivariate animal models. The fixed effects of herd-year-season as contemporary group and age at calving as covariate were fitted in the model of analyses. Heritability estimates under univariate model for lactations 1 to 4 were 0.28, 0.20, 0.19 and 0.13 for milk yield and for fat yield were 0.15, 0.12, 0.12 and 0.05, respectively. The repeatability and heritability values under the repeatability model for milk and fat yield were 0.48 and 0.24, and 0.38 and 0.17, respectively. Estimated heritabilities using a bivariate model for lactations 1 to 4 were 0.29, 0.20, 0.20 and 0.15 for milk yield and 0.12, 0.11, 0.13 and 0.05 for fat yield, respectively. Heritability estimates for lactations 1 to 4 by multivariate model were 0.30, 0.23, 0.22 and 0.19 for milk yield, and 0.17, 0.16, 0.17 and 0.12 for fat yield, respectively. Genetic, phenotypic and environmental correlations of milk yield were 0.91, 0.50 and 0.36 for first and second lactation; and 0.87, 0.45 and 0.31 for first and third lactation; and 0.79, 0.39 and 0.26 for first and fourth lactation; and 0.97, 0.53 and 0.41 for second and third lactation; and 0.91, 0.50 and 0.39 for second and fourth lactation; and 0.96, 0.56 and 0.46 for third and fourth lactation, respectively. These parameters for fat yield were 0.87, 0.35, 0.25 and 0.91, 0.29, 0.16 and 0.83, 0.26, 0.17 and 0.96, 0.45, 0.35 and 0.90, 0.40, 0.32 and 0.98, 0.47, 0.38, respectively. Results from this study confirm that multivariate analysis is recommended for estimating the genetic parameter of milk and fat yield, because it considers the effects of selection bias of the first lactation.
