The Multilevel Latent Covariate Model: a New, More Reliable Approach to Group-level Effects in Contextual Studies the Multilevel Latent Covariate Model: a New, More Reliable Approach to Group-level Effects in Contextual Studies Reflective and Formative L2 Constructs

In multilevel modeling (MLM), group level (L2) characteristics are often measured by aggregating individual level (L1) characteristics within each group as a means of assessing contextual effects (e.g., group-average effects of SES, achievement, climate). Most previous applications have used a multilevel manifest covariate (MMC) approach, in which the observed (manifest) group mean is assumed to have no measurement error. This paper shows 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 in each of the groups, 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, we 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, our simulation results also suggest that the contextual effects estimated in typical research situations (e.g., fewer than 100 groups) may be highly unreliable. Furthermore, under some circumstances when the sampling ratio approaches 100%, the MMC approach provides more accurate estimates. Based on three simulations and two real-data applications, we critically evaluate the MMC and MLC approaches and offer suggestions as to when researchers should most appropriately use one, the other, or a combination of both approaches. In the last two decades multilevel modeling (MLM) has became one of the central research methods for applied researchers in the social sciences. A major advantage of MLMs over single level regression analysis lies in the possibility of exploring relationships among variables located at different levels simultaneously Different types of group-level variables can be distinguished. The first type can be measured directly (e.g., class size, school budget, neighborhood population). These variables that cannot be broken down to the individual level are often referred to as " global " or " integral " variables (Blakely & Woodward, 2000). The second type is generated by aggregating variables from a lower level. For example, ratings of school climate by individual students may be aggregated at the school level, and the resulting mean used as an indicator for the school's collective climate. Variables that are obtained through the aggregation of scores at the lower level are known as " contextual " or " analytical " variables. For instance, Anderman (2002), using a …