[R-sig-ME] 4 binary DVs, subjects nested within schools

[John Maindonald]

NB also R's mlogit package, which has an accompanying vignette that includes
a number of worked examples, with R code.
Cheers
John Maindonald.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

On 23/11/2011, at 11:21 AM, Chris Howden wrote:

> You've just described a classic market research problem and method.
> It's called choice modes.
> 
> They used to be modelled using aggregate multinomial logit models.
> 
> But these days they are more commonly modelled using Bayesian
> multinomial logit, this can allow us to get individual level
> parameters and since a lot of the variance is at the individual level
> we model it that way.
> 
> Sawtooth software are experts on this. You'll find all types of good
> reference material on their web site. Plus they have a Bayesian
> software for multinomial logit.
> 
> Chris Howden
> Founding Partner
> Tricky Solutions
> Tricky Solutions 4 Tricky Problems
> Evidence Based Strategic Development, IP Commercialisation and
> Innovation, Data Analysis, Modelling and Training
> 
> (mobile) 0410 689 945
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> On 23/11/2011, at 4:25, Paul Johnson <pauljohn32 at gmail.com> wrote:
> 
>> Greetings
>> 
>> I'm trying to get my footing under a researcher's request for
>> statistical support. I need your advice.
>> 
>> The gist of this is that there are 4 dichotomous outputs that can be
>> modeled separately with logistic or probit models, and lme4 works fine
>> treating each one separately.  There is a random effect at the school
>> level.
>> 
>> However, a reviewer says a multivariate model is needed to fully model
>> this problem.
>> 
>> The data is like selections from a menu, where all of the above is
>> possible.  This actual project is about student behaviors in the class
>> room, but it seems more understandable to me to think of it as a
>> person's taste for ice cream. Respondents are asked "do you like
>> chocolate ice cream" or "do you like vanilla ice cream" or "strawberry
>> ice cream".  So the dependent variable is multivariate like this (yes,
>> no, yes, no).
>> 
>> Where can I learn more about the multivariate approach to this?
>> 
>> And why are multivariate approaches not making the same mistake that
>> is described in this literature on comparison of coefficients across
>> logit models fitted for separate groups. I mean, if the variance
>> parameter is not identified, how can I meaningfully put together 4
>> logit models?
>> 
>> Allison, Paul. 1999. “Comparing Logit and Probit Coefficients Across
>> Groups.” Sociological Methods and Research 28(2): 186-208
>> 
>> Richard Williams, 2008, "Using Heterogeneous Choice Models To Compare
>> Logit and Probit Coefficients Across Groups"
>> http://nd.edu/~rwilliam/oglm/RW_Hetero_Choice.pdf
>> 
>> Mood, C. (2010). Logistic Regression: Why We Cannot Do What We Think
>> We Can Do, and What We Can Do About It. European Sociological Review,
>> 26(1), 67 -82. doi:10.1093/esr/jcp006
>> 
>> Well, anyway, this looks like a project to me.  I (probably) first
>> need to understand how to fit this model without any distractions due
>> to nested effects or sampling weights, and then I need to take into
>> account the fact that students are nested in classrooms.
>> 
>> I've been digging about for models of more-than-one dichotomy.  VGAM
>> has bivariate logit and probit.   The brand new package mvProbit has
>> "experimental" support for several dichotomous DVs.   But I don't
>> think it is going to help with the classroom random effect.
>> 
>> I'm trying to find the simplest way to write all this down as a model
>> so I can see where the correlations come in across questions and
>> across units. For each outcome,  yj, j=1,2,3,4, there is a coefficient
>> vector Bj and an error term ej and the model states:
>> 
>> y1 = 1 if XB1 + e1 > 0; 0 otherwise
>> y2 = 1 if XB2 + e2 > 0; 0 otherwise
>> y3 = 1 if XB3 + e3 > 0; 0 otherwise
>> y4 = 1 if XB4 + e4 > 0; 0 otherwise
>> 
>> Suppose (e1,e2,e3,e4) is multivariate (normal or logistic?).  Because
>> of the "you can't compare logistic regressions across groups" problem,
>> it appears problematic to assert that the variances of ej = 1.
>> 
>> Pj
>> 
>> 
>> 
>> --
>> Paul E. Johnson
>> Professor, Political Science
>> 1541 Lilac Lane, Room 504
>> University of Kansas
>> 
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