Parametric Bootstrap Interval Approach to Inference for Fixed Effects in the Mixed Linear Model

Abstract

In mixed models, empirical best linear unbiased estimators of fixed effects generally have mean square errors (MSEs) that cannot be written in closed form. Standard methods of inference depend upon approximation of the estimator MSE, as well as upon approximation of the test statistic distribution by some known distribution, and may not perform well under small samples. The parametric bootstrap interval is presented as an alternative to standard methods of inference. Several parametric bootstrap intervals (Efron percentile, bias-corrected [BC], Hall percentile, and bootstrap-t) were compared using simulated data, along with analytic intervals based on the naïve MSE approximation and the Kenward-Roger method. Among the bootstrap methods, the bootstrap-t seems especially promising.