Application of test-day models for the genetic evaluation of dairy populations requires the solution of large mixed model equations. The size of the (co)variance matrices required with such models can be reduced through the use of its first eigenvectors. Here, the first two eigenvectors of (co)variance matrices estimated for dairy traits in first lactation were used as covariables to jointly estimate genetic parameters of the first three lactations. These eigenvectors appear to be similar across traits and have a biological interpretation, one being related to the level of production and the other to persistency. Furthermore, they explain more than 95% of the total genetic variation. Variances and heritabilities obtained with this model were consistent with previous studies. High correlations were found among production levels in different lactations. Persistency measures were less correlated. Genetic correlations between second and third lactations were close to one, indicating that these can be considered as the same trait. Genetic correlations within lactation were high except between extreme parts of the lactation. This study shows that the use of eigenvectors can reduce the rank of (co)variance matrices for the test-day model and can provide consistent genetic parameters.