CFA and Log-Linear Modeling

  • Mark Stemmler
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)


This chapter describes the relationship between log-linear modeling and CFA. Log-linear modeling and CFA may be used as complimentary statistical tools. Log-linear modeling looks for models with an appropriate goodness-of-fit; they can be used to investigate the patterns of association or the structure of dependency among the variables. CFA needs a non-fitting model in order to detect types and/or antitypes. In CFA and log-linear models, the expected frequencies are calculated according to the underlying null model which is specified in the design matrix using the General Linear Model approach (GLM). Following log-linear modeling hierarchical log-linear modeling is presented. Hi-log models are the best way to determine the structure of dependency among the variables or to find out which interactions are significant. Hi-log modeling is a special form of log-linear modeling. The main effects and interactions are structured hierarchically such that if there are significant higher order interactions in the model, all lower order interactions and main effects must be included. In addition to describing the traditional first-order CFA, a zero-order CFA called Configural Cluster Analysis (CCA) is explained. Finally, the statistic Q describing the pregnancy or precision of a cell is introduced. Small data examples are presented and analyzed with the von Eye program as well as with the R-package confreq.


Order Effect Design Matrix Saturated Model Expected Frequency Main Effect Model 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mark Stemmler
    • 1
  1. 1.Institute of PsychologyFriedrich-Alexander University of Erlangen-Nuremberg (FAU)ErlangenGermany

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