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Deciding between competing models: Chi-square ... - UZH

Introduction to Structural Equation Modeling with LISREL Version February Christina Werner and Prof. Dr. Karin Schermelleh-Engel Goethe University, FrankfurtDeciding between competing Models: Chi-square Difference Tests1 Research SituationUsing structural equation modeling to investigate a research question, the simplest strategywould involve constructing just a single model corresponding to the hypotheses, test it againstempirical data, and use a model fit test and other fit criteria to judge the underlying , frequently, it is not particularly satisfactory to analyze a single model, but moreappropriate to analyze severalcompeting modelsandcompare the results, e. g. in the followingsituations: The favorite model fits the data well, but there is a competing model based on different hy-potheses which may explain the observed relationships as well. If possible, this competingmodel should be rejected (it should fit the data worse compared to the favorite model).

decide between them. Descriptive model comparison using criteria suitable for non-nested models, for example AIC (Akaike Information Criterion). This does not allow signi cance testing, though. 3 Procedure To compute a ˜2 di erence test, the di erence of the ˜2 values of the two models in question

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