The Influence of Misspecification of the Heteroscedasticity on Multilevel Regression Parameter and Standard Error Estimates
Abstract
Like in ordinary regression models, in multilevel analysis, homoscedasticity of the residual variances is an assumption that is mostly unchecked. However, in experimental research, the residual variance component at level two may differ in the experimental and the control condition, leading to heteroscedastic second level variances. Using a simulation study, the consequences of ignoring second level heteroscedasticity on the estimation of the fixed and random parameters and their standard errors was investigated. It was found that the standard error of the second level variance is underestimated, but that the estimated fixed parameters of the independent variables, the first level variance and their standard errors are mostly unbiased.
References
2002). Short-term effects of a randomized computer-based out-of-school smoking prevention trial aimed at elementary schoolchildren. Preventive Medicine, 34, 581–589.
(1992). Hierarchical linear models. London: Sage.
(1988). Statistical power analysis for the behavioral sciences. London: Erlbaum.
(1995). Multilevel statistical models. London: Arnold.
(1993). Random coefficient models. Oxford, UK: Oxford University Press.
(2003). The influence of violation of assumptions on multilevel parameter estimates and their standard errors. Computational Statistics and Data Analysis, 46, 427–440.
(2005). Sufficient sample sizes for multilevel modeling. Methodology, 1, 86–92.
(2004). A users guide to MLwiN version 2.0. London: Multilevel Models Project, University of London.
(1997). Statistical analysis and optimal design for cluster-randomized trials. Psychological Methods, 2, 173–185.
(2005). Design and analysis of clinical trials with clustering effects due to treatment. Clinical Trials, 2, 152–162.
(2000). Using heteroscedasticity consistent standard errors in the linear regression model. The American Statistician, 54, 217–224.
(1999). Multilevel analysis: An introduction to basic and advanced multilevel modeling. London: Sage.
(1986). Impact of vitamin A supplementation on childhood mortality. A randomized control Community trial. The Lancet, 8491, 1169–1173.
(2001). Using multivariate statistics. Boston: Allyn and Bacon.
(