Effects of Ignoring Hierarchical Data Structure on Factor Analytic Models

Open Access
- Author:
- Nolan, Katherine A
- Graduate Program:
- Educational Psychology
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- March 21, 2014
- Committee Members:
- Pui Wa Lei, Thesis Advisor/Co-Advisor
Hoi Kin Suen, Thesis Advisor/Co-Advisor
Rayne Audrey Sperling, Thesis Advisor/Co-Advisor - Keywords:
- nested
hierarchical
multilevel
factor analysis - Abstract:
- Educational research often involves hierarchical or nested data such as students nested within classrooms. Nested data violates the independence assumption which may lead to incorrect standard error estimates and inflated Type I error rates when traditional analyses are used. The consequences of ignoring hierarchical or multilevel data structure in general linear models have been well examined and documented. However, little is known about the consequences of ignoring multilevel data structure in factor analytic models. Multilevel factor analyses (MFA) produce a within-level and a between-level correlation matrix in addition to the traditional total correlation matrix. Individuals within-cluster are typically the focus in MFA and therefore the within-cluster matrix should be examined rather than the traditional total correlation matrix. This study intends to examine the consequences of ignoring multilevel data structure in factor analytic models by comparing factor solutions from analyzing total and within-cluster correlation matrices using empirical data from several educational and psychological measures. Results demonstrate that although the number of factors retained is often the same for the total and within-cluster matrices, examination of the item content and factor loadings often revealed different interpretations between the factor solutions of the total and within-cluster matrices. The findings suggest that the presence of simple structure, small ICC, and large sample size in relation to number of items result in similar total and within-cluster factor solutions.