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2 Some theory 11(V ) models and are discussed in detail in Chapter 7. Some correlation modelsinclude• autoregressive (order 1 or 2)• moving average (order 1 or 2)• ARMA(1,1)• uniform• banded• general correlation.Some of the covariance models include• diagonal (that is, independent with heterogeneous variances)• antedependence• unstructured• factor analytic.There is the facility within ASReml to allow for a nonzero covariance between thesubvectors of u, for example in random regression models. In this setting theintercept and say the slope for each unit are assumed to be correlated and it ismore natural to consider the two component terms as a single term, which givesrise to a single G structure. This concept is discussed later.2.2 EstimationEstimation involves two processes that are closely linked. They are performedwithin the ‘engine’ of ASReml. One process involves estimation of τ and predictionof u (although the latter may not always be of interest) for given θ, φ and γ.The other process involves estimation of these variance parameters. Note that inthe following sections we have set θ = 1 to simplify the presentation of results.Estimation of the variance parametersEstimation of the variance parameters is carried out using residual or restrictedmaximum likelihood (REML), developed by Patterson and Thompson (1971). Anhistorical development of the theory can be found in Searle et al. (1992). Notefirstly thaty ∼ N(Xτ , H). (2.3)