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Deciding between competing models: Chi-square difference …

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.

˘-variable on an -variable, or an indirect e ect only? A model assuming a relationship between two latent variables compared to a model where these latent variables are presumed to be unrelated: Are the factors ˘ 1 and ˘ 2 independent of each other or not? A model with an additional loading of a manifest variable on a latent variable, compared

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