SOLUTIONS TO A SYSTEM OF EQUATIONS INVOLVING A 1ST-ORDER AUTOREGRESSIVE PROCESS

A first-order autoregressive process is proposed for modeling certain random effects in instances for which a more general model would invol ve too many (co)variance components. This process requires only two pa rameters, and its inverse-needed for its inclusion in mixed model meth odology-is tridiagonal and easy to obtain. The (co)variance matrix for effects that follow a first-order autoregressive structure is introdu ced, and the rules for obtaining its inverse are derived and outlined in an algorithm (an example is also given). Incorporation of such a st ructure into the mixed model equations is also discussed, and an itera tive procedure for obtaining solutions to this potentially large syste m of equations is outlined.