Predicting group-level outcome variables from variables measured at the individual level: A latent variable multilevel model.

Abstract

In multilevel modeling, one often distinguishes between macro-micro and micro-macro situations. In a macro-micro multilevel situation, a dependent variable measured at the lower level is predicted or explained by variables measured at that lower or a higher level. In a micro-macro multilevel situation, a dependent variable defined at the higher group level is predicted or explained on the basis of independent variables measured at the lower individual level. Up until now, multilevel methodology has mainly focused on macro-micro multilevel situations. In this article, a latent variable model is proposed for analyzing data from micro-macro situations. It is shown that regression analyses carried out at the aggregated level result in biased parameter estimates. A method that uses the best linear unbiased predictors of the group means is shown to yield unbiased estimates of the parameters.

The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies.

“…Thus, reflective aggregations are analogous to the typical latent variable approach based on classical measurement theory and the domain sampling model (Kline, 2004;Nunnally & Bernstein, 1994), in which multiple indicators (in this case, multiple persons within each group rather than the multiple items for each construct) are used to infer a latent construct that is corrected for measurement error (based on the number of indicators and the extent of agreement among the multiple indicators) that would otherwise result in biased estimates. Hence, the concept of reflective measurement is consistent with the notion of a generic group-level construct that is measured by individual responses (Cronbach, 1976;Croon & van Veldhoven, 2007). Under these conditions, it is reasonable to use variation within each L2 group (the intraclass correlation, ICC) to estimate L2 measurement error that includes error due to finite sampling and error due to a selection of indicators (i.e., a specific constellation of individuals used to measure a group-level construct).…”

“…Recently, Croon and van Veldhoven (2007) proposed a two-stage latent variable approach. The unobserved group mean for each L2 unit is calculated using weights obtained from applying basic ANOVA formulas.…”

“…The numbers of L2 groups were set to K = 50, 100, 200, or 500 (Croon & van Veldhoven, 2007, considered two levels: 50 and 100). A sample of 50 groups is common in educational and organizational research (e.g., Maas & Hox, 2005), although many MLM studies are conducted with fewer than 50 L2 groups.…”

A general multilevel SEM framework for assessing multilevel mediation.

“…Effects characterized by a Level-1 variable predicting a Level-2 outcome are known as bottom-up effects (Bliese, 2000;, micro-macro or emergent effects (Croon & van Veldhoven, 2007;Snijders & Bosker, 1999), or (cross-level) upward influence (Griffin, 1997). Bottom-up effects are commonly encountered in practice.…”

“…He illustrated the procedure by predicting group-level cohesion using group-level empirical Bayes estimated residuals drawn from the individual-level prediction of affect by concurrent and previous group cohesion. Conversely, Croon and van Veldhoven (2007) applied linear regression analysis predicting a Level-2 outcome from group means of a Level-1 predictor adjusted for the bias that results from using observed means as proxies for latent means. Applying Griffin's (1997) or Croon and van Veldhoven's (2007) methods in the context of mediation analysis would involve multiplying the estimate thus obtained for the 1-2 portion of the design by another coefficient to compute an indirect effect.…”