young park posted on Tuesday, November 20, 2012 - 4:54 am
I conducted CFA and full SR using complex data. Weight and cluster were applied. Also, MLR as an estimator and complex as a type were applied.
To construct one latent actor, three items were used. From the CFA, we got good factor loadings; they were all over 0.6. However, when the full structural model with others was conducted, standard estimates of three items decreased (0.143, 0.235 and 0.177). We have tried to find some solutions but could not. How do I explain the change (decrease) of standard estimate?
When you put two models together, there are many zero paths in the model that may not be zero. This will cause changes in the results.
young park posted on Tuesday, November 20, 2012 - 1:24 pm
Thanks you so much.
Looking at our model with your suggestion, there were no zero paths in this model. However, we can see several paths, closing to zero (example, 0.022, 0.018..). But the paths are not directly associated with the latent factor, consisting three items that I mentioned. In this case, could it be interpreted by your suggestion?
You said you started with a factor model and then added other model parts to it. The observed variables of the other model parts are related to the factor indicators of your initial factor model only through its factor, not directly to the factor indicators themselves. These are the (implied) zero paths which may be misfitting. Use modindices (all) to see which ones are misfitting.
young park posted on Wednesday, November 21, 2012 - 12:02 pm
Thank you so much for your response. We will take a look at the modification indices as you suggested. I have a couple of follow up questions:
(1) I am wondering about how the reduced factor loading would impact the path coefficient in the structural part of the model. In our model, the factor with reduced loading had moderate (¥ã = .57) to strong relations (¥ã = .86) to other latent variables.
(2) Do you have any suggested readings for this issue of changes in factor loadings?
When parameter values change considerably when going from analyzing only a part of a model to analyzing the full model, this is generally a sign that the model specification/fit can be improved. I would investigate it via MIs.
young park posted on Tuesday, November 27, 2012 - 10:31 am
Thanks again for your suggestion. When we tried reasonable changes based on the modification indices, no change was observed in the factor loadings. Our concern is mostly about the impact of the low loadings on the path coefficients in the structual model. As noted earlier, the path coefficients are moderate to strong. Would they change if the factor loadings are higher?
Yes, most likely. For a well-fitting model the estimates for a part of the model should not change dramatically when expanding the model. And I assume that you have taken into account possible differences in metrics of the two models by inspecting their standardized solutions.