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From |
"Ariel Linden. DrPH" <ariel.linden@gmail.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
re: Re: st: Interpreting mediation model sobel goodman test |

Date |
Wed, 19 Oct 2011 11:34:12 -0400 |

John gives an excellent tutorial here on a problem with the standard (Baron and Kenny) mediation approach. I spent the last few days reading through the Stata v12 manual on -sem- and example 7 provides an example of how mediation can be modeled. Also the UCLA website has an example of mediation using sem with multiple mediators (see problem 4 and 5) http://www.ats.ucla.edu/stat/stata/seminars/stata12/ One question that I have about using sem for mediation is if the model can handle different types of variables (ie., continuous, binary or ordinal mediator coupled with continuous, binary or ordinal outcome)? The manual does not explicitly discuss this issue (for mediation or any other framework). Perhaps the 'standardization' option comes into play here? This is one of the biggest limitations of the Baron-Kenny approach because they treat all mediators and outcomes as continuous variables. Ariel Date: Wed, 19 Oct 2011 08:24:53 +0200 From: John Antonakis <John.Antonakis@unil.ch> Subject: Re: st: Interpreting mediation model sobel goodman test Hi Meredith: To answer the first question, 2SLS is the default estimator when estimating mediation models in econometrics. It is almost unheard of in some other social sciences (e.g., management research, psychology), see: 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 Foster, E. M., & McLanahan, S. (1996). An Illustration of the Use of Instrumental Variables: Do neighborhood conditions affect a young person's change of finishing high school? Psychological Methods, 1(3), 249-260. Gennetian, L. A., Magnuson, K., & Morris, P. A. (2008). From statistical associations to causation: What developmentalists can learn from instrumental variables techniques coupled with experimental data. Developmental Psychology, 44(2), 381-394. That this estimator is not used is not because there is something wrong with the estimator; it is probably because the fields that don't use it ignore the problem that 2SLS can address (i.e,. the problem of endogeneity). You really need to look at the difference between how OLS and instrumental-variable estimators estimate systems of equations. If you run the code I showed you below, the OLS method does not recover the correct estimates when the mediator is endogenous. For some types of models, SUR estimators, unless iterated (i.e., using maximum likelihood) will not produce the correct estimates either. See the latter part of my podcast too, when I show with simulated data (and using ballantines) why an instrumental-variable estimator is required with endogenous mediators. We show with really nice examples how estimates can change in the chapter I cited below. If you have multiple mediators you should have multiple exogenous variables (1 for each mediator) at the least, to have an identified system of equations, at least when using least-squares estimators (2SLS, 3SLS; these are "safe bet" estimators because they are limited information estimators; if there is a mispecification in one part of this model the bias will not be spread in other parts--for more complex models, that is). You're better off being overidentified (more instruments than mediators) so that you can test the veracity of the constraints in the model. We explain all this in the chapter. Best, J. __________________________________________ Prof. John Antonakis Faculty of Business and Economics Department of Organizational Behavior 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 __________________________________________ On 18.10.2011 23:24, Meredith T. Niles wrote: > Hi John, Thank you so much for your response this is very helpful. > > I was wondering whether two stage least squares is common in > estimating mediation models? Most of what I found in code for stata > was all sgmediation (which I did in fact use). > > I am also beginning to run multiple mediation models (with the sureg > command). Would it be wise to run multiple mediation models with a > different code as well? > > Best, Meredith > > -----Original Message----- From: > owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John > Antonakis Sent: Tuesday, October 18, 2011 12:11 PM To: > statalist@hsphsun2.harvard.edu Subject: Re: st: Interpreting > mediation model sobel goodman test > > Hi Meredith: > > I assume you used the -sgmediation- package; I would not use this > routine UNLESS your mediator is exogenous (and you are sure of this). > If > > it is endogenous sgmedation will give you inconsistent estimates (it > estimates the system of equations with OLS, and uses the dated > Baron-Kenny methods); you do not tackle the endogeneity problem with > sgmediation. You need to estimate your system of equations with an > instrumental-variable estimator (e.g., 2SLS). > > Take a look at this podcast, where I discuss this problem in detail: > > Endogeneity: An inconvenient truth (full version) (about 32 minutes > in length) http://www.youtube.com/watch?v=dLuTjoYmfXs > > If you just want the nitty gritty see: > > Endogeneity: An inconvenient truth (for researchers) (Excludes the > "gentle introduction" content and discusses the two-stage least > squares estimator straight away; about 16 minutes in length) > http://www.youtube.com/watch?v=yi_5M7oUceE > > See also: > > Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (submitted). > Causality and endogeneity: Problems and solutions. In D.V. Day > (Ed.), The Oxford Handbook of Leadership and Organizations. > http://www.hec.unil.ch/jantonakis/Causality_and_endogeneity_final.pdf > > > To understand exactly the nature of the problem run the following code, > where x is endogenous with respect to y: > > clear set seed 123 set obs 1000 gen x = rnormal() gen e = rnormal() > gen m = e + .5*x + rnormal() gen y = .5*m - e + rnormal() reg3 (y = > m) (m = x), 2sls nlcom [m]x*[y]m sgmediation y, mv(m) iv(x) > > From the above model, we have an instrument x, an endogenous > regressor m, and omitted cause e, and a dependent variable y. We know > that the indirect effect of x on y is .5*.5=.25. 2SLS recovers this > parameter well (.24, p>.001). However, the sgmediation program gives > .03 (and p = .04). > > > Now, let's rerun this to see when you'd get the same results with > sgmediation (if x is exogenous with respect to y): > > clear set seed 123 set obs 1000 gen x = rnormal() gen e = rnormal() > gen m = .5*x + rnormal() gen y = .5*m + rnormal() reg3 (y = m) (m = > x), 2sls nlcom [m]x*[y]m reg3 (y = m) (m = x), ols nlcom [m]x*[y]m > sgmediation y, mv(m) iv(x) > > Notice that the 2SLS model is still consistent (but less efficient). > The > > OLS estimator and sgmediation pretty much give the same estimates and > standard errors. > > HTH, John. > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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