Re: st: SEM with bootstrapping for mediation - goodness of fit and statistical inferences

[John Antonakis <John.Antonakis@unil.ch>]

Hi Neeraj:

Two things:

1.  is your mediator exogenous? If not so, you model is misspecified. 
You can test for the endogeneity of MV by estimating:

 sem (mv <- iv cv1 cv2) (dv <- mv cv1 cv2), cov(e.mv*e.cv)

If the covariance of the disturbances is significant (this is the 
Hausman test) then this means that mv is endogenous with respect to dv. 
If mv is endogenous then including iv next to it as a predict of dv will 
make the estimates of iv inconsistent.

This is all explained in detail here:

Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On 
making causal claims: A review and recommendations. The Leadership 
Quarterly, 21(6). 1086-1120. 
http://www.hec.unil.ch/jantonakis/Causal_Claims.pdf

For quick intuitive explanations too about the problem of endogeneity 
and mediation watch this video (the 16min 30 secs are a basic intro to 
endogeneity--thereafter I talk about mediation):

http://www.youtube.com/watch?v=dLuTjoYmfXs

2. your model, or the one above I have shown you are just identified; 
you are estimating as many parameters as there are elements in the 
variance-covariance matrix. Thus the DF = 0 and there is nothing to test 
and the model will perfectly reproduce the variance-covariance matrix.

3. Bootstrap the indirect effect does not really do much. You might as 
well just you a robust estimate of the variance:

sem (mv <- iv cv1 cv2) (dv <- mv cv1 cv2), cov(e.mv*e.cv), vce(robust)
estat teffects

I suspect you are doing the bootstrap to follow the Preacher and Hayes 
(Preacher, K. J. & Hayes, A. F. 2004. SPSS and SAS procedures for 
estimating indirect effects in simple mediation models. Behavior 
Research Methods, Instruments, & Computers, 36(4): 717-731.
recommendations. However, they recommend to use the bootstrapped 
coefficient along with the boostrapped SE, which is not what you are 
doing, and which is a very bad idea. See p. 198 of the Stata manual 
entry on the bootstrap (for version 13 of Stata)--I am talking about the 
citation by Efron.

HTH,
J.

__________________________________________

John Antonakis
Professor of Organizational Behavior
Director, Ph.D. Program in Management

Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland
Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305
http://www.hec.unil.ch/people/jantonakis

Associate Editor:
The Leadership Quarterly
Organizational Research Methods (incoming)
__________________________________________

On 05.08.2013 19:22, Neeraj Iyer wrote:
> Hello STATA Listers,
>
> I am running a path analytic model for analysis of mediation.  A
> sample program I am running for each mediation model is below.  I also
> generated bootstrapped standard errors and confidence intervals.  Of
> the 12 models I ran, there were two models for which the
> bias-corrected bootstrapped confidence intervals for indirect effect
> did not contain a zero, indicating that the indirect effect is
> significant. I observed a couple issues:
>
> The  "estat gof, stats(all)" command shows that:
>
> 1) The LR chi-square test for model vs. saturated each of the 12
> models has a value:
>      chi2_ms(0) = 0.000 and p > chi2  = '.' (i.e. blank)
>
> 2) The LR chi-square test for baseline vs. saturated each of the 12
> models has a value:
>      p > chi2  = '.' (i.e. blank)
>
> 3) The RMSEA of each model has a value of : 0.000
> 4) Every Comparative Fit Index has a value of : 1.000
> 5) Every Tucker-Lewis index has a value of: 1:000
>
> I am uncertain whether I can conclude that my models show acceptable
> fit criteria.  Are there there goodness-of-fit criteria that I must
> use?  As I observe significant indirect effects (or mediation) from
> two of my models, can I conclude such a finding given the prevailing
> fit statistics?
>
> Could someone point me to any published examples that have used this
> procedure?  I am trying to get some guidance on how to report and
> interpret the results.  Thank you for any leads.
>
> Regards,
> Neeraj
>
>
> SAMPLE PROGRAM:
>
> program indireff, rclass
>   sem (MV <- IV CV1 CV2 ) (DV <- MV IV CV1 CV2)
>   estat gof, stats(all)
>   estat teffects
>   mat bi = r(indirect)
>   mat bd = r(direct)
>   mat bt = r(total)
>   return scalar indir  = el(bi,1,5)
>   return scalar direct = el(bd,1,5)
>   return scalar total  = el(bt,1,5)
> end
>
> sem (MV <- IV CV1 CV2) (DV <- MV IV CV1 CV2)
> quietly estat teffects
>
> matrix list r(indirect)
> matrix list r(direct)
> matrix list r(total)
>
> set seed 358395
>
> bootstrap r(indir) r(direct) r(total), reps(200): indireff
> estat bootstrap, percentile bc
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