I am working on a SEM model using Mplus. The model includes 2 latent factors each with about 4 dichotomous indicators. The latent factors are regressed onto 5 exogenous predictors (also dichotomous). A dichotomous outcome is, in turn, regressed onto the 2 latent factors. I used WLSMV to estimate the model, which is recommended when the latent factor indicators are dichotomous.
The model fits well but my understanding is that Mplus uses probit regression for the DV and latent factors. And I am not very familiar with how to interpret probit results. So I do not know how to interpret the parameter estimates (the indicator coefficients for each latent factor; the exogenous coefficients for those variables after regressing the latent factor on them; and the coefficients for the DV regressed onto the latent risk factors).
Can anyone point me towards reference material that might walk me through how to interpret (and write-up) the results of this modeling?
Thanks for any help.
James
Dr. Swartz,
I haven't used WLSMV estimator before, but out of my curiosity I found some information in the book below: in Page 69 under the subtitle 'CFA model with binary indicators' and in page 77 under the subtitle 'CFA model with ordered categorical indicators' you can find examples using WLSMV estimator with their Mplus commands:
Wang, J., & Wang, X. (2012). Structural equation modeling: Applications using Mplus. John Wiley & Sons.
Also, in page 70 of this book: "With binary indicators, the relationships between the observed response variables and their underlying latent construct variable/factor are nonlinear. With a weighted least square estimator (e.g., WLSMV), Mplus uses PROBIT function to link the observed binary indicators to their underlying latent variables/factors...As each binary indicator has only two categories (i.e., 0 vs. 1), one threshold (t) is estimated for each indicator. The negative value of the threshold (t) is equivalent to the intercept of regressing the item on its underlying factor (Appendix 2.D). The factor loading of each item here is the PROBIT slope coefficient of regressing the item on its underlying factor. In the PROBIT models the residual variances of the binary indicators are not identified and not estimated."
Hope it helps!
Thanks Orhan,
I have that book and am familiar with the passage you cite. What I am looking for is a source where they have written up the results of a similar model. I can interpret and odds ratio or even a log odds, but I have no idea what.a probit-based coefficient means or how to write about it. Annotated Mplus output interpreting the probit-based coefficients or a paper that reports on such a model is what I am looking for.
Thanks,
James
James A Swartz . I recommend you consult the following resources:
http://www.statmodel.com/discussion/messages/11/25070.html?1516837472
http://www.statmodel.com/discussion/messages/11/657.html?1342887417
Dr. Swartz, in the following link (an article in medical research), in page 6, they converted probit coefficients into logit ones, and then they exponantiated the logit coefficients and obtained odds ratios using the formulas that are suggested by Muthen & Muthen (2009, the second link below). I guess that is what you needed.
https://www.mdpi.com/1660-4601/19/6/3265
In the following link, starting from Page 22 they explain the interpretation of logit and probit coefficients and their relationships.
https://www.statmodel.com/download/Topic%202.pdf
Many thanks Eulogio and Orhan. I will have a look at the provided references.
You can ask here :
https://stats4edu.com/services/structural-equation-modeling/
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