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Mplus Discussion > Structural Equation Modeling >
 Sun Kim posted on Saturday, April 07, 2012 - 7:42 pm
Dear Dr. Muthen,

The output using MODEL IND in Mplus does not give the same results as hand-calculated sobel test-- I thought they should be similar. My N = 1,006 (fairly large), and my predictors and mediators are categorical (overall use of WLSMV estimator) but my outcomes continuous.

Which test should I go with, and do you have any suggestions?
Thank you.
 Bengt O. Muthen posted on Saturday, April 07, 2012 - 8:13 pm
The more general method is the delta method used in Mplus,which can always be applied. In some settings it is the same as the Sobel test. We have a FAQ on our web site on this, saying

The MacKinnon (2008) book describes the Sobel method and the delta method for the
indirect effect a*b in Section 4.14. See especially page 92. The delta method uses
formula (4.27) with an added covariance term between the a and b estimates (see second line below 4.27). For some models, such as the mediation model for continuous observed variables, the covariance term is zero so that the delta method simplifies to the formula of (4.27). I believe (4.27) is what is referred to as the Sobel method. Mplus uses the delta method in Model Indirect and also in Model Constraint. Note that the zero covariance term is exactly zero when the ML estimator is used, but only approximately zero when MLF or MLR are used.
 Sun Kim posted on Saturday, April 07, 2012 - 9:33 pm
Dear Dr. Muthen,

Thank you so much for your kind response.

Yes, I noticed that sometimes, the Model Indirect gave the same results as the sobel test and sometimes not.

It seems though in reading published articles (I am in the field of psychology), it is rare to use the delta method (usually, sobel test is simply calculated and reported in published mediation model papers, with according citations).

So (1) which method would you think is superior, and (2) do you have any examples of published articles that cite the delta method?

Thank you so much for your time.
 Bengt O. Muthen posted on Saturday, April 07, 2012 - 10:01 pm
As the quote from the FAQ says, Delta=Sobel in most cases - that's why you see it in your literature. So in those cases, when you are using Sobel, you are in fact also using Delta. When they differ Delta should be used. In this way, you can never go wrong with Delta. You can cite the MacKinnon book pages that I gave for the Delta method.
 Sun Kim posted on Sunday, April 08, 2012 - 12:06 am
Dear Dr. Muthen,

Thank you so much for your response.
It is so helpful and informative.
I will do exactly that.

- Sun
 Joseph posted on Monday, October 21, 2013 - 4:06 pm
Dear Drs Muthen,

I am running SEM to explore mediation. I am calculating the 95%CIs using the Delta method. When I compare the CIs calculated using the delta method to those obtained specifying the bootstrap option, the results are essentially equivalent. I suspect this may be due to my large sample size (approx. 5000 respondents).

A reviewer has asked me to cite a reference which also confirms the two approaches can produce equivalent results, could you recommend one please?

Many thanks
 Linda K. Muthen posted on Monday, October 21, 2013 - 8:58 pm
This sounds like a good question for a general discussion forum like SEMNET.
 RuoShui posted on Sunday, April 06, 2014 - 5:02 am
Dear Drs. Muthen,

1) Regarding your above comments about the FAQ, is it correct that if the mediation is for continuous latent variables then the method used is delta instead of sobel?

2) when comparing mediation models and direct models, usually the chi square favours the mediated model but incremental fit indices favours the parsimonious direct model. I am wondering if test of mediation using "model indirect" is significant, will that give more confidence to confirm the mediation model is a better model?

Thank you so much for your input.
 Linda K. Muthen posted on Sunday, April 06, 2014 - 11:49 pm
1. Mplus always uses the Delta method.

2. Please send the outputs that illustrate your issue and your license number to
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