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Re: st: SEM with bootstrapping for mediation - goodness of fit and statistical inferences
From
Neeraj Iyer <[email protected]>
To
statalist <[email protected]>, John Antonakis <[email protected]>
Subject
Re: st: SEM with bootstrapping for mediation - goodness of fit and statistical inferences
Date
Mon, 19 Aug 2013 02:37:34 -0400
Dr. Antonakis, STATAlisters
Thank you Sir for the video and the paper. They were both excellent and
comprehensive commentaries on endogeneity and helped me think
critically about the proposed structural model of my study as well as
raise informed questions regarding the associations I have observed.
Below are a few related queries I seek further guidance on:
A brief description of the sample might be of assistance.
The study sample consists of individuals with a disease
condition and who belong to either one of two groups. The sample 53%
from one group and 47% from the other group. My IV is a binary
variable that distinguishes between the two groups.
1) I was unable to run the stata codes you suggested. Instead of
cov(e.mv*e.cv) did you mean to cov(e.mv*e.dv)?
2) I ran the following codes to check for endogeneity for 12 models:
sem (mv <- iv cv1 cv2) (dv <- mv iv cv1 cv2), cov(e.mv*e.dv),
vce(robust)
4 out of 12 models did not converge. For 6 out of 8 models that converged,
the Hausman test or the covariances of the disturbances were not
significant (p-value of 1.00).
For 2 of 8 models that converged, there were no standard errors or p-values.
Hence, I concluded that there was no endogeneity from an omitted
variable for 6 sem models.
However, I wanted to be certain that I was coding for the correct
covariance parameter.
3) Is there any technique to achieve over-identified models in sem?
Must any parameter be constrained to a value of 1, such that there
might be something to test for determining model fit?
3) I was able to understand endogeneity and its impact on causal
associations, but how the use of instrumental variables might aid in
testing for mediation was not clear. Could you point out any paper or
annotated output that might clarify my doubts?
4) As an exploration, I ran the 2SLS models (12 models): ivreg2 dv cv1
cv2 (mv=iv), robust first, exploring the following relationship:
x--->y1----->y2. My assumption is that the 2SLS model is testing for
the mediated effect of x on y2 through y1. A de-identified output is
below. I was unable to understand how to interpret mediation from the
output. I was hoping to receive any guidance on interpreting "ivreg2"
or "ivregress" outputs.
. ivreg2 DV CV1 CV2(MV=IV), robust first
First-stage regressions
-----------------------
First-stage regression of MV:
OLS regression with robust standard errors
------------------------------------------
Number of obs = 236
F( 3, 232) = 4.64
Prob > F = 0.0036
Total (centered) SS = 2205.949153 Centered R2 = 0.0547
Total (uncentered) SS = 7888 Uncentered R2 = 0.7356
Residual SS = 2085.36415 Root MSE
= 3
----------------------------------------------------------------------------------------------------
| Robust
MV | Coef. Std. Err. t P>|t| [95%
Conf. Interval]
-----------------+--------------------------------------------------------------------------------------------
CV1 | -.6266182 .2429967 -2.58 0.011 -1.105381 -.1478559
CV2 | .0716003 .063195 1.13 0.258 -.052909
.1961097
IV | -.879425 .3907967 -2.25 0.025
-1.649389 -.109461
_cons | 6.898368 .9004722 7.66 0.000 5.12422 8.672517
---------------------------------------------------------------------------------------------------------------
Partial R-squared of excluded instruments: 0.0212
Test of excluded instruments:
F( 1, 232) = 5.06
Prob > F = 0.0254
Summary results for first-stage regressions:
Shea
Variable Partial R2 Partial R2 F( 1, 232) P-value
MV 0.0212 0.0212 5.06 0.0254
NB: first-stage F-stat heteroskedasticity-robust
IV (2SLS) regression with robust standard errors
-------------------------------------------------------------------------------------------------------------
Number of obs = 236
F( 3, 232) = 7.41
Prob > F = 0.0001
Total (centered) SS = 1084.059322 Centered R2 = -0.1091
Total (uncentered) SS = 7961.5 Uncentered R2 = 0.8490
Residual SS = 1202.30931 Root MSE = 2.3
-------------------------------------------------------------------------------------------------------------
| Robust
DV | Coef. Std. Err. z P>|z|
[95% Conf. Interval]
-----------------+--------------------------------------------------------------------------------------------
MV | .3332928 .3360621 0.99 0.321 -.3253767 .9919624
CV1 | 1.039985 .2890172 3.60 0.000 .4735217 1.606448
CV2 | .0731464 .0549584 1.33 0.183 -.0345701 .180863
_cons | 1.09525 2.001215 0.55 0.584 -2.82706 5.017559
-----------------------------------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
----------------------------------------------------------------------------------------------------------
Instrumented: MV
Instruments: IV CV1 CV2
--------------------------------------------------------------------------------------------------------------
On Mon, Aug 5, 2013 at 5:02 PM, John Antonakis <[email protected]> wrote:
> 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
>> *
>> * For searches and help try:
>> * http://www.stata.com/help.cgi?search
>> * http://www.stata.com/support/faqs/resources/statalist-faq/
>> * http://www.ats.ucla.edu/stat/stata/
>
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/faqs/resources/statalist-faq/
> * http://www.ats.ucla.edu/stat/stata/
--
Neeraj
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/faqs/resources/statalist-faq/
* http://www.ats.ucla.edu/stat/stata/