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RE: st: Categorical mediators and ordinal outcome: using Jackknife to compute the variance of the difference between coefficients


From   Cameron McIntosh <cnm100@hotmail.com>
To   STATA LIST <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Categorical mediators and ordinal outcome: using Jackknife to compute the variance of the difference between coefficients
Date   Mon, 2 Apr 2012 19:31:15 -0400

Fernanda,

I think you need to back up a bit. You will need to take into account the fact that the variance of the outcome is not constant across the logit equations, in order to get unbiased estimates of c - c'. Actually, I think it might be a better idea to do a path analysis with  -cmp- (i.e., test your full model simultaneously) and try to get specific indirect effects for your two mediators from that model, rather than estimating a global reduction in the direct effect, which isn't very informative about where the mediational actions are taking place. Anyway, I think you have some more homework to do before you proceed with this analysis. See the following:
Karlson, A.F.B., Holm, A., & Breen, R. (December 23, 2010). Total, Direct, and Indirect Effects in Logit Models. CSER Working Paper Series, No. 0005. Aarhus, Denmark: Centre for Strategic Educational Research DPU, Aarhus University.http://www.cser.dk/fileadmin/www.cser.dk/wp_005rbkkahfin_01.pdf

Buis, M.L. (2010). Direct and indirect effects in a logit model. The Stata Journal, 10(1), 11–29.https://teamsite.smu.edu.sg/wiki/stats/Shared%20Documents/Stata%20Journals/2010/sj10-1.pdf

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

Li, Y, Schneider, J.A., & Bennett, D.A. (2007). Estimation of the mediation effect with a binary mediator. Statistics in Medicine,  26(18), 3398-3414.

Jasti, S., Dudley, W.N., & Goldwater, E. (2008). SAS macros for testing statistical mediation in data with binary mediators or outcomes. Nursing Research, 57(2), 118-122.

Huang, B., Sivaganesan, S., Succop, P., & Goodman, E. (2004). Statistical assessment of mediational effects for logistic mediational models. Statistics in Medicine, 23(17), 2713–2728.  

Kuha, J., & Goldthorpe, J.H. (2010). Path analysis for discrete variables: the role of education in social mobility. Journal of the Royal Statistical Society: Series A (Statistics in Society), 173(2), 351–369.

Eshima, N., Tabata, M., & Zhi, G. (2001). Path analysis with logistic regression models: effect analysis of fully recursive causal systems of categorical variables. Journal of the Japanese Statistical Society, 31(1), 1-14. http://www.scipress.org/journals/jjss/pdf/3101/31010001.pdf

Roodman, D. (2011). Fitting fully observed recursive mixed-process models with cmp. The Stata Journal, 11(2), 159-206.http://www.stata-journal.com/article.html?article=st0224http://ideas.repec.org/c/boc/bocode/s456882.html

Cam

> Date: Mon, 2 Apr 2012 16:33:02 -0400> Subject: st: Categorical mediators and ordinal outcome: using Jackknife to compute the variance of the difference between coefficients
> From: nandaqueiros@gmail.com
> To: statalist@hsphsun2.harvard.edu
> 
> Dear list participants,
> 
> First of all, I am a PhD student with limited statistical knowledge
> compared to what I’ve seen here at the list. Also, English is not my
> first language; so, forgive me if any part of the message is not
> crystal clear.
> 
> I am trying to estimate the mediation effect for an ordinal outcome
> with 10 levels (ladderw4). The two mediators I’m interested are
> categorical. My main independent variable (IV) is categorical (four
> levels), as well as all my co-variates. I am using complex survey
> data, with 132 PSU’s and 4 strata. I saw here at the list some
> suggestions applying econometrics methods to a question about testing
> mediation with categorical mediators, which is beyond my knowledge.
> 
> Thus, I am trying to compute the difference of my main IV’s
> coefficients (from the models with and without the mediator) to
> measure the change and, therefore, mediation effect. I am thinking
> about using the jackknife procedure to estimate the variance of my
> coefficients. However, the problem I am facing is that I don’t know
> how to compute the variance of the difference…
> 
> That is how I am establishing the survey design using Jackknife (Stata 11.2):
> 
> . svyset psuscid [pweight=gswgt4_2], strata(region) vce(jackknife)
> 
> I am, then, using svy: ologit to run my models: (1) without the
> mediator and (2) with it:
> 
> (1) xi: svy,subpop(subpop2): ologit ladderw4 i.type_disability age_w4
> bio_sex_ i.racew1_r i.parented i.famst3
> 
> (2) xi: svy,subpop(subpop2): ologit ladderw4 i.type_disability age_w4
> bio_sex_ i.racew1_r i.parented i.famst3 deprew1_dic
> 
> The output gives me the “final” coefficients and Jackknife SE’s for my
> IV’s. My question is:
> 
> - Is there a way to get the coefficients/SE’s for each one of the 132
> replications Stata is running in this case? I think that with this
> information it would be possible to compute the variance of the
> difference between the two coefficients of my main IV...
> 
>  - Also, does any one have experience on testing mediation with
> similar types of variables (using complex survey data) and would
> suggest me a different approach from what I am trying to do?
> 
> Looking forward to hearing your ideas/suggestions!
> 
> Many thanks,
> 
> Fernanda
> 
> 
> 
> --
> Fernanda Queirós
> Me., Fonoaudióloga / M.S., Brazilian Speech-Language Pathologist
> Doutoranda - Bolsista CAPES/Fulbright / Ph.D. Candidate -
> CAPES/Fulbright grantee
> University of North Carolina at Chapel Hill
> Gillings School of Global Public Health
> Department of Maternal and Child Health
> 
> 
> Para ser grande, sê inteiro: nada teu exagera ou exclui. Sê todo em
> cada coisa. Põe quanto és
> no mínimo que fazes....
> (Fernando Pessoa)
> 
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