Mediation with Integration Algorithm
Message/Author
 Charles Green posted on Tuesday, May 02, 2006 - 4:14 pm
I am currently examining a mediational model that requires the integration algorithm. Since the "model indirect" statement with bootstrapped standard errors is not available with this algorithm, would you have any recommendations for methods of calculating estimates of the indirect effect and possibly even standard errors (e.g. one of the product or difference methods)?
 Linda K. Muthen posted on Wednesday, May 03, 2006 - 8:17 am
You can use the Delta method to calculate standard errors. One place you can find this is in Bollen's SEM book.
 Charles Green posted on Thursday, May 04, 2006 - 9:40 am
To clarify: 1) I can use the product coefficient approach with the deta method for standard errors? 2) Is there any way to test the assumption of a normally distributed sampling distribution for the indirect effect?
 Bengt O. Muthen posted on Thursday, May 04, 2006 - 11:16 am
You get the delta method standard error if you use assign labels to the 2 slopes that are multiplied (say a and b) and use those labels in Model constraint and the NEW option:

Model constraint:
New(ab);

ab = a*b;

This gives you a delta method SE for the indirect effect a*b.

Regarding your last question - I don't know. Check with Dave McKinnon at ASU who works with this. I wouldn't worry too much about non-normality unless the sample is rather small.
 Antonio A. Morgan-Lopez posted on Thursday, May 04, 2006 - 5:42 pm
Hi Charles,
One thing you could do is formulate an empirical distribution of the product based on your raw parms and se's - Dave MacKinnon has a new program that does this for the Asymmetric Confidence Interval test for mediation (in SPSS, SAS and R - and I imagine Mplus in the not-too-distant future ). Here's the link:

http://www.public.asu.edu/%7Edavidpm/ripl/Prodclin/

If you use this, one rough (but pretty good) clue that I would look see is if the distribution approaches normality in the output are in the critical values of the 2.5th and 97.5th percentiles of the empirical distribution of your product - if they deviate from |1.96|, it's not normal. From what I remember, as the sizes of the ratio of the parms/se's (i.e., the Z-statistics) for the individual paths get larger, the product tends toward normality. If you have big effects and/or big sample (as Bengt alludes to), you'll be more likely to see it approach normality. You could also edit Dave's code to a) output the distribution and b) do formal tests for normality on your empirical distribution (i.e., the normality test that comes with SAS Proc Univariate). The ref for the program is here:

MacKinnon, D. P., Fritz, M. S., Williams, J., & Lockwood, C. M. (in press)
Distribution of the product confidence limits for the indirect effect program PRODCLIN. Behavior Research Methods.

His 2002 Psych Methods paper and/or his 2004 MBR paper talk about conditions when the distribution should approach normality. Hopefully, other mediation folks can weigh in if I have erred anywhere in this post......
 Mark Prince posted on Thursday, August 09, 2012 - 6:26 pm
I see here that the last post was in 2006. Is there currently an Mplus equivalent of PRODCLIN?

thank you.
 Linda K. Muthen posted on Friday, August 10, 2012 - 10:26 am
What is PRODCLIN?
 Mark Prince posted on Friday, August 10, 2012 - 1:22 pm
PRODCLIN is Dave MacKinnon's program that computes the Asymmetric Confidence Interval test for mediation.
 Linda K. Muthen posted on Friday, August 10, 2012 - 1:56 pm
Mplus does have those. See the CINTERVAL option of the OUTPUT command.
 Mark Prince posted on Friday, August 10, 2012 - 7:55 pm
Thank you! That is what I was looking for.
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