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Journal of Dairy Science Vol. 76 No. 10 3026-3032
© 1993 by American Dairy Science Association ®
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Solutions to a System of Equations Involving a First-Order Autoregressive Process

K. M. Wade 1 and R. L. Quaas 1

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

A first-order autoregressive process is proposed for modeling certain random effects in instances for which a more general model would involve too many (co)variance components. This process requires only two parameters, and its inverse—needed for its inclusion in mixed model methodology—is tridiagonal and easy to obtain. The (co)variance matrix for effects that follow a first-order autoregressive structure is introduced, and the rules for obtaining its inverse are derived and outlined in an algorithm (an example is also given). Incorporation of such a structure into the mixed model equations is also discussed, and an iterative procedure for obtaining solutions to this potentially large system of equations is outlined.

Key Words: autoregressive process • mixed model equations • solutions

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




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