ABSTRACT
In practice, data are often hierarchically structured such that their individuallevel cases are grouped within higher-level units. For example, adolescents’ substance use can be measured across different urban areas nested within different provinces. The standardized test scores of students can be collected from different schools. In functional neuroimaging data, neuronal activities of participants, who come from different experimental groups, are recorded repeatedly over time in voxels. For such hierarchical data, generalized structured component analysis estimates parameters by aggregating the data across all individuals, under the assumption that they are independent. This implies that each parameter does not depend on higher-level units, ignoring any nested structure inherent to the data. However, the individual-level measures nested within the same higher-level unit are likely to be more similar than those in different units, thus leading to dependency among individuallevel observations within the same unit. If parameters are estimated under the independence assumption, ignoring such potential dependency, this is likely to lead to inference errors (cf. Bryk and Raudenbush 1992; Snijders and Bosker 1999).
