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 Fabian Wolff posted on Thursday, November 17, 2016 - 5:27 am
I ran a latent path model in which two criteria should represent the same construct that has been measured with different scales. Now I would like to compare the beta weights from my predictors to the corresponding criteria (and expect the corresponding path coefficients to be similar).
How can I test if the beta weights differ signifiantly from one another?
I just checked if the confidential intervals of the beta weights in the standardized solution overlaped. If they did not, I concluded that the beta weights differed. But possibly this way of analysis might not be indicated? Is there a test to compare beta weights for significant differences?
Thank you!
 Bengt O. Muthen posted on Thursday, November 17, 2016 - 2:41 pm
I think you want to test equality of unstandardized (raw) coefficients because standardized coefficients may be different even when raw are not; this is due to difference variances. You can do any such testing in Model Constraint by expressing the difference in terms of model parameters.
 Fabian Wolff posted on Friday, November 18, 2016 - 1:48 am
Thanks for your reply!
Probably you are right and I want to test the unstandardized coefficients. I thought that I had to compare the standardized coefficients since my criteria are scaled differently. One criterium has been assessed by self-assessment on a 5-point-Likert scale. The other criterium has been rated by external asssessment on a 3-point-Likert scale. But I am quite new to SEM and did not know that standardized coefficients may be different even when raw are not. With respect to the conficence intervals, I have similar solutions for my standardized and unstandardized model.
However, unfortunately I do not understand how to express the difference between beta coefficients in the model constraints. Could you please give me an example or is there anything in the Mplus handbook that I did not find?
By the way, I hoped that there would have been something like Fisher's z transformation for beta weights. E.g., if I want to compare Pearson coefficients r_12 and r_13 (derived from the same sample) for a significant difference, I can just use r_12, r_13, r_23 and N for a significance test. But there is no analogon for path analyses so that I can compare beta_12 and beta_13 when I have information about r_23 and N?
Thanks a lot for your help!
 Bengt O. Muthen posted on Friday, November 18, 2016 - 2:10 pm
The easiest way to handle this is to set the metric of the two factors by fixing their variances at 1 instead of the default fixing of their first loading to 1.

See UG ex 5.20 for how to work with Model Constraint.

One problem is, however, that you can't be sure you measure the same construct when you don't have the same indicators.

Your other questions should be directed to a general discussion list like SEMNET.
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