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Dear Linda & Bengt, I am in the fourth week of an SEM class as part of my doctoral training. The class has introduced me to MPlus and we just had an assignment using the software (4.0). The assignment asks us to analyze a structural model (no latent), determine its fit, and if doesn't, how it might be improved to fit the data. Running the model as specified reveals that it does not fit. In analyzing the output, one can see that a direct path of the model is nonsignicant (Est./S.E. = .363). As such, I took this path out of the model, and then reran it. It now fit the data, but just barely (chi square = .06). Examination of the residuals for both the original model and the fitting model does not show any values at the professor identified 'concern' value of >.1. Nonetheless, to improve on the model, I added a direct path that was not specified in the original model, and add it to the model above which fit the data. This added path made the chisquare value more nonsignificant .356 so I was pleased, but in the order of parsimony, is the simplest model the best? I recognize the question is a bit elementary and poorly asked, but please bear with me as I am new at this. 


One always seeks the most parsimonious model that fits the data using theory as a guide. Deleting paths are are coincidentally nonsignificant is not recommended to improve model fit. This may simply capitalize on the chance relationships in the sample data. Instead, you should retain that path and try to determine why the model does not fit. Likewise, paths should not be added simply to improve model fit unless there is a theoretical reason to do so. Finally, you should be using Version 4.1 which is the latest version of Mplus. 


Linda, thanks for the feedback. In examining the residuals for the first (nonfitting)model, none of them approached .1 (absolute); the closest would have been .068 (positive); in this case, since no residuals seem to suggest underfitting or overfitting, is it necessary to go back to the theoretical drawing board without deleting or adding any paths to the model? J 


One issue to think about is whether your variables are valid and reliable measures of the constructs intended. 


Linda, for purposes of this assignment, we are to assume that diagnostics on the data have been performed, and that all measures are reliable and valid. That said, is it feasible to delete the nonsignificant path to obtain model fit, since this would seem to be our only option (or throw the theory all together). 


As stated earlier, I would not delete a nonsignificant path. It sounds like this would be a good question for the class to discuss. 

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