Mediation with bootstraped CI

[olivier pahud]

Hey all,

If I do a multiple mediation model in lavaan I get the estimate, std.err, p-values, and so on, for the specified regressions as well as the specified indirect effects.
The test for the indirect effects is based on the Sobel test?

I prefer to bootstrap the CI of the indirect effect since the Sobel-test has flaws like the assumption of normality for the product terms of the indirect effects. I do have some unceratinties about bootstrapping and the interpretation of the results...

1) Do I use bootstrapping ONLY to check the CI of the indirect effect or do I also report the CI of the regression coefficients?
2) If I bootstrap, are the following sem-definitions specificed correct or do I miss something? (I don't have to specific test = "bootstrap" or test = "bollen.stine", since I already specified se = "boot")?

fit.modelx <- sem(MODELX,
                     data      = DATAX,     
                     estimator = "ML", 
                     mimic     = "Mplus",
                     se = "boot",
                     bootstrap = 5000)

Thanks for your help in advance!

PS: are there any good and detailed tutorials on bootstrapped mediation in lavaan?  

[olivier pahud]

additional question: how do I decide which boot.ci.type = "" I'll use for my analysis?

[Terrence Jorgensen]

The test for the indirect effects is based on the Sobel test?

Yes, the delta method is used to derive SEs for user-defined parameters

1) Do I use bootstrapping ONLY to check the CI of the indirect effect or do I also report the CI of the regression coefficients?

You can, but bootstrapping has Monte Carlo error, so it won't perform as well as the normal-theory CIs for parameters whose sampling distributions are approximately normal.  (I think that even includes the indirect effect, if you have a large enough sample size for the product term to be approximately normal).

2) If I bootstrap, are the following sem-definitions specificed correct or do I miss something? (I don't have to specific test = "bootstrap" or test = "bollen.stine", since I already specified se = "boot")?

If you also want to use the Bollen-Stine bootstrap to test the null hypothesis of perfect fit, then you should add that option (otherwise you will only see the central chi-squared distribution p value in the summary() output); alternatively, you could just send your model to the bootstrapLRT function.  You can use the "ci = TRUE" argument to get regular percentile bootstrap CIs in the summary() output, or you can request the bias-corrected percentiles from the parameterEstimates() function.

PS: are there any good and detailed tutorials on bootstrapped mediation in lavaan?  

This page has some slides Yves put together for mediation software, including a lot of information about lavaan.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[olivier pahud]

Thanks for your fast response.
your asnwers really helped!