A Monte Carlo Simulation Comparing Parameter Estimates from Multiple Linear Regression and Hierarchical Linear Modeling

Abstract

In this simulation study, the parameter estimates obtained from hierarchical linear modeling (HLM) and multiple linear regression (MLR) were examined for differences under different values of the intraclass correlation. 15,000 data sets were generated for each of ten different ranges of intraclass correlations. The resulting vectors of parameter estimates from both HLM and MLR were subtracted, averaged across 50 data sets and compared to a null vector of zeros using Hotelling’s T^2 statistic. Little difference was found between the vectors of parameter estimates in any of the intraclass correlation ranges.