Authors
Oliver Lüdtke, Herbert W Marsh, Alexander Robitzsch, Ulrich Trautwein, Tihomir Asparouhov, Bengt Muthén
Publication date
2008
Journal
Psychological Methods
Volume
13
Issue
3
Pages
203-229
Publisher
American Psychological Association
Description
In multilevel modeling (MLM), group-level (L2) characteristics are often measured by aggregating individual-level (L1) characteristics within each group so as to assess contextual effects (eg, group-average effects of socioeconomic status, achievement, climate). Most previous applications have used a multilevel manifest covariate (MMC) approach, in which the observed (manifest) group mean is assumed to be perfectly reliable. This article demonstrates mathematically and with simulation results that this MMC approach can result in substantially biased estimates of contextual effects and can substantially underestimate the associated standard errors, depending on the number of L1 individuals per group, the number of groups, the intraclass correlation, the sampling ratio (the percentage of cases within each group sampled), and the nature of the data. To address this pervasive problem, the authors introduce a new …
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