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

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 T2 statistic. Little difference was found between the vectors of parameter estimates in any of the intraclass correlation ranges. ultiple Linear Regression (MLR) and Hierarchical Linear Modeling (HLM) are two statistical procedures that can be used to model the relationship between a numerical dependent (i.e., response) variable and two or more numerical independent (i.e., predictor) variables. For an algebraic description and comparison of the HLM and MLR models see Mundfrom & Schultz (2001). Although similar in many ways, these two procedures are not identical in how they analyze the data and consequently may not produce the same results on any specific set of data. Raudenbush & Bryk (1986) and Goldstein (1987) have suggested that HLM is useful for data-analytic situations that may not be adequately handled using the general linear model, of which MLR is a specific case. Specifically, HLM is believed to be, and in fact was designed to be, more accurate in situations involving multi-leve