ESTIMATION OF THE PARAMETERS INVOLVED IN A 1ST-ORDER AUTOREGRESSIVE PROCESS FOR CONTEMPORARY GROUPS

A methodology was developed for estimating the parameters involved in a first-order autoregressive process; these parameters comprise a variance component associated with the random effect, a correlation coefficient, rho, and a residual variance. These parameters were estimated using REML with an expectation-maximization algorithm. For two single-trait analyses (milk and fat production being the dependent variable), the example chosen for the analyses was year-month-treated as random and following a first-order autoregressive process-within fixed herd. Initially, estimates failed to converge, possibly because of a time trend in the data, which was not accounted for by the model. After the random effect that follows the first-order autoregressive process was redefined as month within fixed herd-year, the parameters converged, and rho was estimated as .8 for milk and fat yield. Results suggest that the estimation procedures may be useful for situations when a first-order autoregressive process seems appropriate.