The multilevel latent covariate model: a new, more reliable approach to group-level effects in contextual studies.
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 (e.g., 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 multilevel latent covariate (MLC) approach that corrects for unreliability at L2 and results in unbiased estimates of L2 constructs under appropriate conditions. However, under some circumstances when the sampling ratio approaches 100%, the MMC approach provides more accurate estimates. Based on 3 simulations and 2 real-data applications, the authors evaluate the MMC and MLC approaches and suggest when researchers should most appropriately use one, the other, or a combination of both approaches.
Lüdtke
Oliver
O
Center for Educational Research, Max Planck Institute for Human Development, Berlin, Germany. luedtke@mpib-berlin.mpg.de
Marsh
Herbert W
HW
Robitzsch
Alexander
A
Trautwein
Ulrich
U
Asparouhov
Tihomir
T
Muthén
Bengt
B
D006801:Humans; D008960:Models, Psychological; D011584:Psychology / Q000379:methods* / Q000706:statistics & numerical data*; D015203:Reproducibility of Results