RE: st: MANOVA to verify difference (Away)

["Seyi Soremekun" <Seyi.Soremekun@lshtm.ac.uk>]

I am away from the 21st September until the 12th October. Please direct any urgent enquiries to Linda Vesel (linda.vesel@lshtm.ac.uk).
Seyi

>>> Cameron McIntosh <cnm100@hotmail.com> 09/22/11 02:49 >>>

Hi Damiano,
Thanks for the clarification. It sounds like you have a mediational model (four salience mediators) with 11 dichotomous outcomes, and a number of covariates. You may want to treat your firm and/or role variable as a series of dummies rather than doing a multi-group analysis... and these would predict the salience mediators I assume. And on that note, see this submitted work:
Hayes, A. F., & Preacher, K. J. (2011).  Indirect and direct effects of a multicategorical causal agent in statistical mediation analysis.  Manuscript submitted for publication.http://www.afhayes.com/public/hp2011.pdf
Probably -cmp- would probably be a good choice for elegantly executing the analysis, but you may have a prohibitively small sample size (57)... I don't know if -cmp- or other modules in Stata or elsewhere offer exact tests.
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 Rao, P.V., Li, H., & Roth, J. (2008). Recursive Path Models when Both Predictor and Response Variables are Categorical. Journal of Statistical Theory and Practice, 2(4), 663-676.http://mch.peds.ufl.edu/recent_pubs/Rao.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., 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
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.
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
You may need to collect a lot more data before you can examine such a model. Maybe some preliminary comparisons of proportions (the objectives) across role/firm and different levels of salience, or looking at role/firm and salience as predictors of objectives using logistic regression (where you could test for mediation without doing a path analysis), may be a reasonable start with the data you have... and you could use exact methods instead of asymptotic approximations:
Oster, R.A. (2002). An Examination of Statistical Software Packages for Categorical Data Analysis Using Exact Methods. The American Statistician, 56(3), 235-246.
Oster, R.A. (2003). An Examination of Statistical Software Packages for Categorical Data Analysis Using Exact Methods—Part II. The American Statistician, 57(3), 201-213. 
Oster, R.A., & Hilbe, J.M. (2008). An Examination of Statistical Software Packages for Parametric and Nonparametric Data Analyses Using Exact Methods. The American Statistician, 62(1), 74-84.
Sawilowsky, S.S. (2011). Statistical Reanalysis of Jewish Priests’ and Non-Priests’ Haplotypes Using Exact Methods. SAGE Open, 1-3.http://sgo.sagepub.com/content/early/2011/06/10/2158244011413475.full.pdf
Hirji, K.F. (2006). Exact analysis of discrete data. Boca Raton, FL: Chapman & Hall/CRC.
Cytel Software Corporation. (2010). StatXact Version 9. Cambridge, MA: Cytel Software Corporation
Cytel Software Corporation (2002). LogXact 5 user manual. Cambridge, MA: Cytel Software Corporation.  
Zamar, D., McNeney, B., & Graham, J. (2007). elrm: Software Implementing Exact-like Inference for Logistic Regression Models. Journal of Statistical Software, 21(3). http://www.jstatsoft.org/http://cran.r-project.org/web/packages/elrm/vignettes/v21i03.pdf
Zamar, D., Graham, J., & McNeney, B. (May 1, 2010). Exact Logistic Regression via MCMC: Package ‘elrm’, Version 1.2.1.http://cran.r-project.org/web/packages/elrm/elrm.pdfhttp://cran.r-project.org/web/packages/elrm/index.html
Flanders, W.D., & Dash, C. (2009). Exact logistic regression: an extension of Barnard’s approach for continuous covariates. International Journal of Statistics and Management System, 4(1–2), 82–95.http://www.math.binghamton.edu/arcones/ijsms/abstract-4-5.pdf
Derr, R.E. (Revised 2009). Performing Exact Logistic Regression with the SAS System. Cary, NC: SAS Institute Inc. http://support.sas.com/rnd/app/papers/exactlogistic2009.pdf
Venkataraman, G., & Ananthanarayanan, V. (2008). Demystifying “exact” logistic regression for pathologists. Journal of Clinical Pathology, 61(2), 237-238.
Cam



> Date: Thu, 22 Sep 2011 01:00:13 +0200
> Subject: Re: st: MANOVA to verify difference
> From: damiano.bordogna@gmail.com
> To: statalist@hsphsun2.harvard.edu
> 
> Dear Cameron,
> 
> here are my answers to your questions:
> 1) The groups of stakeholders are from different firms ( in ex. i've 2
> CEO from the firm A, 1 CEO from B, 2 from C, 1 External Manager from
> A, 3 from E etc...)
> 2) Yes, if the stakeholder chose the objective, its value is 1
> 3) Both: i mean differences in the counts/percentage of people holding
> the objective across groups, but i would also like to see if the
> chosen objectives are related to differences on some other variable
> (the "salience" variable)
> 4) Stakeholder salience underlines the importance of the stakeholder
> in the firm decisional process. For example, a simple employee has a
> low level of salience, while a manager has an high level. Salience is
> influenced by experience, ownage of the firm, prestige, structural
> power etc..
> 5) No: i'm building theory from case study (surveys). So i'm trying to
> analize my data searching for something interesting. My hypotesis is
> that the choose of an objective instead of another one is influenced
> by the interviewee's role as well as his salience (which is influenced
> by the role).
> 
> Role --------------------> Objectives
>   |__ Salience________|
> 
> Thank you again Cameron!
> Have a nice day
> 
> Damiano
> 
> 2011/9/21 Cameron McIntosh <cnm100@hotmail.com>:
> > Damiano,
> > From what you say, I'm not sure that MANOVA is the optimal approach, but I think there still isn't enough information to give the best advice. So, let's be more precise:
> > 1. Are the six groups stakeholders from six different firms, or from one firm but divided along some other qualitative aspect? Either way, your sample size is going to be on low side.2. As for the 11 dummies, are these just 0=holds the objective; 1=doesn't hold the objective?3. When you say, "differences according to chosen objectives", do you just mean differences in the counts/percentage of people holding the objective across groups, or are the chosen objectives supposedly related to differences on some other variable?4. What do you mean by "stakeholder salience"? What role are these variables supposed to play?5. Similar to question 4: Do you have some kind of guiding theory and specific hypotheses? If so, What are they?
> > Thanks,
> > Cam
> >
> > ----------------------------------------
> >> Date: Wed, 21 Sep 2011 18:18:13 +0200
> >> Subject: Re: st: MANOVA to verify difference
> >> From: damiano.bordogna@gmail.com
> >> To: statalist@hsphsun2.harvard.edu
> >>
> >> Thank you Ronan,
> >>
> >> i'll try to introduce you my problem!
> >>
> >> My database is made of
> >> - 57 observation (divided into 6 groups of respondant), representing
> >> firm's stakeholders (iROWS)
> >> - 11 binary variables, representing stakeholders' objectives (COL)
> >> - 4 normal (not descrete) variables, representing stakeholders' salience (COL)
> >>
> >> I want to verify if there are differences between the different groups
> >> according to the choosed objectives (VERY IMPORTANT: as said before,
> >> objectives are dummy variables, 0-1).
> >>
> >> Thank you again Ronan!
> >>
> >> 2011/9/21 Ronan Conroy <rconroy@rcsi.ie>:
> >> > On 2011 MFómh 21, at 14:36, Damiano Bordogna wrote:
> >> >
> >> >> Is it possible, with MANOVA, to verify if there's some kind of
> >> >> difference between different goups of observation?
> >> >
> >> > That is the kind of question that doesn't get you very far. Can you explain what you are trying to do?
> >> >
> >> > Many statistical procedures examine difference of some kind between groups of observations. And no statistical procedure can verify that there is a difference. All you can do is see how well the observed differences are explained by chance, and, more important, see if the observed effect sizes are of any real life importance.
> >> >
> >> > Tell us a little more about your problem, then!
> >> >
> >> >
> >> > Ronán Conroy
> >> > rconroy@rcsi.ie
> >> > Associate Professor
> >> > Division of Population Health Sciences
> >> > Royal College of Surgeons in Ireland
> >> > Beaux Lane House
> >> > Dublin 2
> >> >
> >> >
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