Factor analysis of multilevel data: Gauging the Muthén model

Abstract

Social data often have a hierarchical structure. A familiar example is educational research data, with their distinct pupil, class and school levels. In the most general case there are variables defined at each level, and the variable set may be different at the different levels. Even if all variables are measured at the lowest level, the clustering in the data leads to problems, because the usual assumptions of independently and identically distributed variables are not met. Muthen has described an approximate model for factor analysis and path analysis with hierarchical data. This chapter presents a model for factor analysis of hierarchical data proposed by Harnqvist and the model proposed by Muthen model. The accuracy of the approximation of the Muthen model is assessed by gauging.