Graphical and Clustering Methods for Exploring Regions of Misfit in Latent Variable Models

• Activity Number: 90
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 9:00 AM to 10:50 AM
• Sponsor: Section on Statistical Graphics
• Author(s): Todd E. Bodner*+ and Daniel Wilson
• Companies: Portland State University and Portland State University
• Keywords: clustering methods ; exploratory data analysis ; factor analysis ; graphical displays ; goodness of fit ; structural equation modeling

Abstract

In practice, latent variable model misfit is assessed with scalar statistics at the level of the overall model (e.g., chi-square statistics or fit indices like RMSEA) or at the level of missing individual paths (e.g., modification indices). The present paper discusses graphical and clustering methods that might be useful for exploring model misfit between these two extremes. These approaches focus on information available in the discrepancy matrix (i.e., the matrix of differences between the observed and model-implied covariances). Looking for patterns of misfit in a discrepancy matrix by inspecting its scalar elements becomes more difficult as the number of indicator variables increases. Using readily available software, we propose creating a 2- or 3-D picture of the discrepancy matrix where colors or bar-lengths represent the direction and magnitude of the discrepancies. Descriptively, one can then see where regions of misfit lie, if anywhere. Permutation of the rows and columns of the discrepancy matrix to cluster large discrepancies can further aid exploration. The efficacy of these approaches are explored and illustrated with real and simulated data.