Models to Examine the Validity of Cluster-Level Factor Structure Using Individual-Level Data. Issue 3 (September 2019) - Stapleton, Laura M.; Johnson, Tessa L.
When researchers model multilevel data, often a shared construct of interest is measured by individual-level observations, for example, students' responses regarding how engaging their instructor's teaching style is. In such cases, the construct of interest, "engaging teaching, " is shared at the cluster level across individuals, yet rarely are these shared constructs modeled as such. To address this gap, we discuss multilevel confirmatory factor analysis models that have been applied to item-level data obtained from multiple raters within given clusters, focusing particularly on measuring a characteristic at the cluster level. After discussing the parameters in each potential model, we make recommendations as to the appropriate modeling approach and the steps to be taken for model assessment given a set of data and hypothesized construct of interest. In particular, we encourage applied researchers not to use a model without constraints across the within-cluster level and the between-cluster level because such models assume that the average amount of the individual-level construct in a cluster does not differ across clusters. To illustrate this issue, we present simulation results and evaluate a series of models using empirical data from the Trends in International Mathematics and Science Study.