Xu, Man posted on Wednesday, March 11, 2009 - 7:32 pm
Dear Sir or Madam,
I am running into a puzzling situation here. In a SEM model, I specified each predictor variables with only one indicator, with the factor loading to be 1, the residual to be 0. I also set the same model using manifest variable approach, i.e. using the indicator directly in the model as an observed variable rather than specifying a fake latent variable. The fit indeces for the two models turned out not to be the same, especially the CFI and TLI. The CFI and TLI indeces are slightly higher in the first model. Should the fit indeces be exactly the same in the two models? Could you help to see what the cause is for this please? I use Mplus 5.1.
If you make factors equivalent to single indicators that are dependent variables in the model, the results are the same as if you use the observed variables. When you do this for independent variables, you change the way they are treated. As observed variables, they are treated are independent variables and the model is estimated conditioned on them. When they are used in a BY statement, they are treated as dependent variables and they are brought into the model and distributional assumptions are made about them. So the results will not be the same.
Xu, Man posted on Thursday, March 12, 2009 - 6:30 am
I see. Thanks for the clarification! Which way do you recommend then?