#### Title

IMPACT OF VARIANCE COMPONENT ESTIMATES ON FIXED EFFECT INFERENCE IN UNBALANCED LINEAR MIXED MODELS

#### Abstract

Inference on fixed effects in mixed models depends on standard errors or test statistics which in turn depend on estimates of variance and covariance components. For unbalanced mixed models, even relatively simple models such as two-way cross-classification models with interaction where one factor is fixed and the other is random, dilemmas arise that have received inadequate attention to date. For example, if one uses SAS PROC MIXED, one can estimate variance components using expected means squares from Type I, II, or III sums of squares, or one can use likelihood-based algorithms such as the default restricted maximum likelihood. If there is a negative variance component estimate, one can set the estimate to zero and proceed with fixed effects inference, or one can allow the variance estimate to remain negative. These decisions affect inference on fixed effects in ways that are not generally well-understood. The purposes of this presentation are to 1) clarify what the main issues are and 2) present some guidelines data analysts can use.

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IMPACT OF VARIANCE COMPONENT ESTIMATES ON FIXED EFFECT INFERENCE IN UNBALANCED LINEAR MIXED MODELS

Inference on fixed effects in mixed models depends on standard errors or test statistics which in turn depend on estimates of variance and covariance components. For unbalanced mixed models, even relatively simple models such as two-way cross-classification models with interaction where one factor is fixed and the other is random, dilemmas arise that have received inadequate attention to date. For example, if one uses SAS PROC MIXED, one can estimate variance components using expected means squares from Type I, II, or III sums of squares, or one can use likelihood-based algorithms such as the default restricted maximum likelihood. If there is a negative variance component estimate, one can set the estimate to zero and proceed with fixed effects inference, or one can allow the variance estimate to remain negative. These decisions affect inference on fixed effects in ways that are not generally well-understood. The purposes of this presentation are to 1) clarify what the main issues are and 2) present some guidelines data analysts can use.