The sensitivity of hierarchical linear models to outliers
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The hierarchical linear model (HLM) has become popular in behavioral research, and has been widely used in various educational studies in recent years. Violations of model assumptions can have a non-ignorable impact on the model. One issue in this regard is the sensitivity of HLM to outliers. The purpose of this study is to evaluate the sensitivity of two-level HLM to the outliers by exploring the influence of outliers on parameter estimates of HLM under normality assumptions at both levels. A simulation study is performed to examine the biases of parameter estimates with different numbers and types of outliers (3 SD and 5 SD) given different sample sizes. Results indicated that the biases of parameter estimates increased with the growing of standard deviation and the number of outliers. The estimates have very small biases with a few outliers. A robust method Huber sandwich estimator corrects the standard errors efficiently when there is a large proportion of outliers.