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Unformatted text preview: STA 4107/5107 Chapter 12 SEM: Testing a Structural Model April 17, 2007 1 Key Terms As always, please learn these terms. 2 Testing the Fit of the Theoretical Model Now that we have tested and validated the measurement model (confirmatory factor analysis), the next step in structural equation modeling is to test and validate the structural model. We will continue with our example from Chapter 11 and now test the theoretical model from the relationship study. This process is quite similar to that of testing the measurement model, the main difference being that our linear equations are modified to reflect our theoretical model, as well as some subtle differences in the parameters to be estimated. Recall the final measurement model: Path Diagram for the Final Measurement Model 1 In the measurement model there are no unidirectional pathsthat is, we are not testing any causal relationships between any of the latent constructs. Each construct is allowed to covary with every other. Notice also that we have removed variable 4, as indicated by the CFA analysis. Recall also the theoretical model: Path Diagram for the Theoretical Model Here, the pertinent covariances have been replaced by causational paths and some paths have been removed altogether. 2.1 The Rules for Structural Equation Modeling Here we outline the rules for codifying the structural model. Rule 1: In general, only exogenous variables are allowed to have covariances. Rule 2: A residual term must be identified for each endogenous variable. Rule 3: Exogenous variables do not have residual terms. Rule 4: Variances should be estimated for every exogenous variable in the model, including the residuals. Rule 5: In most cases, covariances should be estimated for every possible pair of manifest exoge nous variables. Covariances are not estimated for endogenous variables. Rule 6: For simple recursive models, covariances should not be estimated for residual terms. Rule 7: One equation should be created for each endogenous variable. 2 Rule 8: In SEM, the variances of the exogenous latent constructs are free parameters to be esti mated. In contrast to CFA, where we fixed the variances of the latent constructs at 1. Rule 9: In SEM, one factor loading for each latent construct should be set at 1. 2.2 The Steps for Structural Equation Modeling As in the last chapter we will work through the investment model following a set of steps. Step 1: Preparing the Program Figure. These steps are similar to those we went through for the measurement model. The main difference here is that we need to identify error terms (called disturbances ) for all the en dogenous variables. We denote these with a D to distinguish them from the residuals for manifest variables that we denote with E . Disturbance terms represent causal effects on a de pendent variable due to such factors as random perturbations, misspecifications, and omitted independent variables....
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This note was uploaded on 07/14/2011 for the course STA 4702 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
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