Centre for Statistical & Survey Methodology Working Paper Series

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This paper considers the problem of estimating fixed effects, random effects and variance components for the multi-variate random effects model with complete and incomplete data. It also considers making inference about the fixed and random effects, a problem which requires careful consideration of the choice of degrees of freedom to use in confidence intervals. This paper uses the EM algorithm to maximise the hierachical likelihood (HL). The HL estimates are often the same as the REML and Bayesian-justified estimates in Shah, Laird, and Schoenfeld (1997). A key benefit of the h-likelihood approach is its simplicity- it doesn’t require integrating over the random effects or use of priors for its justification. Another benefit is that all inference can be made within a single framework. Extensive simulations show: that the h-likelihood approach is significantly more accurate than the well-known ANOVA approach; the h-likelihood approach often recovers a lot of the information lost through missing data; the h-likelihood approach has good coverage properties for fixed and random effects that are estimated using small samples.