Empirical Standard Errors for Longitudinal Data Mixed Linear Models

In longitudinal data analysis, as with cross-sectional regression, correction for heteroscedasticity is important for accurate hypothesis tests and confidence intervals. Using empirical standard errors to adjust for heteroscedasticity is common practice. In this article, we investigate alternative empirical standard errors that have better finite sample properties than those commonly used. We review the properties of an estimator that is based on the deletion, or jackknife, principle. We also consider an estimator based on standardized residuals that is unbiased in many circumstances. Our Monte Carlo simulations show that both alternatives have better small-sample properties than the usual empirical standard errors, regardless as to whether heteroscedasticity is present. Both alternatives behave well in terms of size and power even when the covariance matrix is completely misspecified. We recommend the use of the alternative empirical standard errors whenever there is a reason to suspect that heteroscedasticity is present.