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Journal of Dairy Science Vol. 76 No. 10 3033-3040
© 1993 by American Dairy Science Association ®
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Estimation of the Parameters Involved in a First-Order Autoregressive Process for Contemporary Groups

K. M. Wade 1, R. L. Quaas 1, and L. D. Van Vleck 1

1 Department of Animal Science, Cornell University, Ithaca, NY 14853

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.

Key Words: parameter estimation • autoregressive process • contemporary groups

Submitted on August 17, 1992
Accepted on June 7, 1993




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