RE: st: Question on multiple equation regression with different types of DVs and NLCOM

[Cameron McIntosh <cnm100@hotmail.com>]

Hi Narasimhan,

Yes, it's possible that you could just proceed as planned w.r.t. your expression below, as I'm not entirely sure either. Mainly I was going by previous work by MacKinnon and colleagues on the need to standardize coefficients in the logit and probit contexts...it may not end up being applicable to what you are doing, but perhaps worth a look as well:

MacKinnon, D. P., & Dwyer, J. H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17, 144-158.

MacKinnon, D.P., Lockwood, C.M., Brown, C.H., Wang, W., & Hoffman, J.M. (2007). The intermediate endpoint effect in logistic and probit regression. Clinical Trials, 4(5), 499-513.http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2857773/pdf/nihms-173365.pdf ;

Cheers,

Cam

----------------------------------------
> Date: Mon, 2 Jan 2012 11:20:50 -0500
> Subject: Re: st: Question on multiple equation regression with different types of DVs and NLCOM
> From: narasimhan.sowmyanarayanan@gmail.com
> To: statalist@hsphsun2.harvard.edu
>
> Hi Cameron:
>
> Thanks for the message. These citations are a very useful. I have
> considered the idea of linear + logit. But when we look at the
> expression it appears that it is simply the marginal of one continuous
> on another continuous variable. Only the "I" in the middle cancels
> out in the final expression. I could be wrong though. I will carefully
> look at these citations for any tips or discussions on this issue.
>
> Really appreciate you taking the time to send these cites.
>
> Best,
>
> N.
>
> On Mon, Jan 2, 2012 at 11:04 AM, Cameron McIntosh  wrote:
> > Will the total effect be meaningful without some kind of standardization of the constituent effect coefficients (linear + logit)?
> >
> > Anyway, you might want to track down the paper that goes with this abstract (one of the authors might be able to help you further):
> >
> > Coxe, S., & MacKinnon, D.P. (2010). Abstract: Mediation Analysis of Poisson Distributed Count Outcomes. Multivariate Behavioral Research, 45(6), 1022.
> >
> > And in the event of an intractable analytical approach for getting the SEs, I might also suggest bootstrapping to get an empirical sampling distribution and compute SEs for the total and other effects:
> > Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40(3), 879-891.http://www.comm.ohio-state.edu/ahayes/indirect2.pdfhttp://www.comm.ohio-state.edu/ahayes/SPSS%20programs/indirect.htm
> >
> > MacKinnon, D. P., Lockwood C. M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39, 99–128.
> >
> > Fitrianto, A., & Midi, H. (2010). Estimating Bias and RMSE of Indirect Effects using Rescaled Residual Bootstrap in Mediation Analysis.  WSEAS Transactions on Mathematics 6(9), 397-406.http://www.wseas.us/e-library/transactions/mathematics/2010/89-645.pdf
> >
> > Mallinckrodt, B., Abraham, W.T., Wei, M. & Russell, D.W. (2006). Advances in Testing the Statistical Significance of Mediation Effects. Journal of Counseling Psychology, 53(3), 372–378. http://www.psychology.iastate.edu/~wei/manuscript/mediation.pdf
> >
> > Cam
> >> Date: Mon, 2 Jan 2012 10:16:59 -0500
> >> Subject: st: Question on multiple equation regression with different types of DVs and NLCOM
> >> From: narasimhan.sowmyanarayanan@gmail.com
> >> To: statalist@hsphsun2.harvard.edu
> >>
> >> charecteristic
> >>
> >> I = exp (α+β_1 P+β_2 V+β_2 V*P) (1)
> >>
> >> Perf= δ+δ_1 *I + δ_2 P + δ_3 P*I + δ_4*V + δ_5*V*P (2)
> >>
> >>
> >> I would like to get the total effect of "P" on perf (direct effect +
> >> effect through I) and its standard error. Equation 1 is a count data
> >> variable with poisson regression and equation 2 is a continuous
> >> metric.
> >>
> >> I know the mean marginal for the total effect is:
> >>
> >> TEffect = (∂Perf(.))/∂P+(∂I(.))/∂P* (∂Perf(.))/∂I
> >>
> >>
> >> I was wondering if there is any way to store these estimates and use
> >> nlcom to get the standard errors through the built in delta method
> >> routines in stata. Comments would be highly appreciated.
> >>
> >> Best.
> >>
> >> N
> >>
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