Levels of Aggregation in Higher Level Confirmatory Factor Analysis: Application for Academic Self-Concept

The effects of levels of aggregation on measures of goodness of fit and higher order parameter estimates obtained from confirmatory factor analysis (CFA) were investigated. For a higher order model of academic self-concept, 3 levels of aggregation were considered-disaggregated, partially disaggregated, and partially aggregated. In the disaggregated model, measured variables represented individual items. In the partially disaggregated model, testlets (groups of 4 items) represented measured variables. In the partially aggregated model, subscale scores represented measured variables. Three indexes of fit were employed: the Tucker-Lewis Index (TLI), the Comparative Fit Index (CFI), and chi-square. Solutions for the disaggregated models consistently evidenced poor fit. TLI and CFI values for partially disaggregated and partially aggregated solutions were satisfactory. Standardized parameter estimates were similar across all solutions. Implications of these findings are discussed with consideration of other research on model complexity in CFA.