Question: For the balanced random-intercept linear mixed model (9.8) based on conditional independence given the random effect (Section 9.2.1), show that ???? = ( XTV1X )1

For the balanced random-intercept linear mixed model (9.8) based on conditional independence given the random effect (Section 9.2.1), show that

????̃ = (

XTV−1X

)−1 XTV−1y simplifies to the ordinary least squares estimator, (

XTX

)−1 XTy; i.e., with compound symmetry, observations do not need weights. (Diggle et al. (2002, p. 63) showed that ordinary least squares can have poor efficiency; however, when a model instead has autoregressive error structure with a time-varying explanatory variable.)

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