Two-Stage Analysis Based on a Mixed Model: Large-Sample Asymptotic Theory and Small-Sample Simulation Results

A two-stage analysis for the mixed model in which variance components due to the random effects are estimated and used to compute generalized least squares estimates of fixed effects is developed, using large-sample theory to establish asymptotic properties.

Abstract

SUMMARY A two-stage analysis for the mixed model in which variance components due to the random effects are estimated and used to compute generalized least squares estimates of fixed effects is developed. Large-sample theory is used to establish asymptotic properties. An approximate t test that can be used to test linear contrasts among fixed effects is discussed. Two modest simulations, based on a model for a grazing trial (Burns, Harvey, and Giesbrecht, 1981, Proceedings of 14th International Grassland Conference, J. A. Smith and V. W. Hays (eds), 497-500, Boulder, Colorado: Westview Press; Burns et al., 1983, Agronomy Journal 75, 865-871) are used to show that the asymptotic results are reasonable for small samples.