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Unformatted text preview: STA 4107/5107 Chapter 11: SEM and Confirmatory Factor Analysis April 11, 2007 1 Key Terms As always, please review these terms and learn them as we cover this material. 2 What is Confirmatory Factor Analysis? Confirmatory factor analysis is a technique for testing and developing models where a large number of measured variables are used to represent a smaller number of constructs. We will work through a simple example and see how it is done in SAS. 3 A Simple Example 3.1 The Research Question Rusbult (1980) has developed a model of relationship commitment called the investment model . One possible interpretation of the investment model is that how committed an individual is in his or her romantic relationship is determined by satisfaction , personal investment in the relationship (i.e. time, energy, money), and the attractiveness of alternatives to the relationship (i.e. other potential partners, freedom, etc). Satisfaction in turn is determined by the rewards that come from being in the relationship and the costs of the relationship. For this example the constructs rewards, investment, alternatives, and costs are each measured by 3 manifest variables (answers to questions on a questionnaire) while commitment is measured by 4. 1 Path Diagram of the Theoretical Model to Be Tested 3.2 The Research Method The research method for this example is as follows: we have a 19 item instrument to assess the six constructs in the investment model. All questionnaire items used a 9-point response format. The questionnaire was administered to 240 individuals involved in romantic relationships. Please note that this is a fictitious example developed by Larry Hatcher (1994) for his book on using SAS in SEM. Please see the bibliography. This analysis will follow the two-phase procedure recommended by Anderson and Gerbing (1988). We will begin by developing a measurement model that adequately fits the data (i.e. a full model). In this phase, we will allow each construct, F , to covary with every other construct. This is the confirmatory factor analysis part of structural equation modeling. If the initial measurement model has poor fit, then variables are reassigned or deleted in order to achieve better fit. Once the measurement model is acceptable, we will begin the second phase where the theoretical model is tested. This is done by fixing specific covariances at zero and setting unidirectional causal paths according to the theoretical model. We then proceed to test the theoretical model with goodness-of-fit tests. If the theoretical model survives, then we have evidence in favor of the theory. If it does not survive, then it can be modified to obtain better fit. As you know by now, the path models weve seen can also be expressed as linear equations....
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- Spring '08