A Longitudinal Model for Repeated Cross Sectional Data with Clustering

• Activity Number: 310
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Albert Satorra*+ and Peter M. Bentler
• Companies: Universitat Pompeu Fabra and University of California, Los Angeles
• Keywords: factor analysis ; structural equation models ; two-level data ; clustered data ; factor score estimation ; second-order factor model

Abstract

Cross-sectional data based on independent repeated samples do not obviously lend themselves to longitudinal modeling. We show that when data is clustered (e.g., repeated measures within individuals, patients nested in clinics, students nested in schools, respondents nested in areas) with invariant second-level units, longitudinal modeling at the second level is possible and meaningful. Specifically, we consider a factor analysis model with autoregressive factors whose measurement structure varies by first-level sample size m, being a 1-factor model when m is very large but a 2nd-order factor model otherwise. We consider issues of consistency, bias, alternative estimators, chi-square model tests, and factor score estimation, as well as model misspecification and effects of intraclass correlation. Among other things, we note that Bartlett's factor score estimates require modification for 2nd-order factor models. The models are implemented using standard software, evaluated via simulations, and illustrated with repeated survey data on information and communication technology.