[R] Analysing ordinal/nominal data

[Prof Brian Ripley]

As I suggested before, a binomial logistic model is appropriate here, not 
a Poisson log-linear one.  (They are equivalent, but the binomial version 
is easier to interpret and less wasteful to fit.)

You have still not defined v' and w', nor the scores (are they estimated 
or not).  But the model I suggested is such a model with scores 1,2,...

On Fri, 17 Jun 2005, Piotr Majdak wrote:

> Prof Brian Ripley wrote:
>
>> On Thu, 16 Jun 2005, Piotr Majdak wrote:
>> 
>>> I'm looking for a solution to analyse data, which consists of
>>> dichotomous  responses (yes/no) for 2 multinomial ordinal variables.
>> 
>> 
>> Please explain how you get a binary response for a `multinomial ordinal 
>> variables'?  If you intend these variables to be explanatory variables, in 
>> what sense are they `multinomial'?
>
> My data are results from a pychoacoustical experiment:
> - Response: 2 levels, frequencies for "yes"/"no"
> - PR: factor, independent variable, 4 levels, ordinal
> - ENV: factor, independent variable, 3 levels, ordinal
>
> The hypothesis is that:
> - PR is independent of ENV, given Response
> - Response and ENV are conditionally dependent, given PR
> - Response and PR are conditionally dependent, given ENV
>
> The model:
>
> fit=glm(count ~ PR+ENV+Response + PR:Response + ENV:Response, data=table, 
> family=poisson)
>
> fits with p=0.04 only. My explanations are:
> - I have a three-way interaction
> - I must consider the ordinal information of PR and ENV
>
>> One normally fits a logistic regression to a binary response.
>> Probably no `trick' is required, but we need to start from a complete and 
>> accurate description of the model you want to fit.
>
> I don't know how to include the interaction to the logit model.
> I think the log-linear row effects model for the 3-dim. nominal-ordinal table 
> (Agresti 1984, p.89) would be the right one, but please correct me if I'm on 
> a wrong way:
>
> log mijk = intercept + lambda^X_i + lambda^Y_j + lambda^Z_k +
>           tau^XY_i*(v_j-v') + tau^XZ_i*(w_k-w') +
> 	   beta^YZ*(v_j-v')*(w_k-w')
>
> mijk: expected frequencies for cell with indicies i,j,k
> v_j: scores of Y with {v_1 < v_2 < .. < v_j}
> w_k: scores of Z with {w_1 < w_2 < .. < w_k}
> lambda^X_i, lambda^Y_j, lambda^Z_k: estimated parameters for X, Y and Z
> tau^XY_i, tau^XZ_j: association parameters for XY and XZ
> beta^YZ: association parameter for ordinal factors Y and Z
>
> In my case, X==Response, Y==PR and Z==ENV. I presume no interaction between Y 
> and Z and would like to test beta. My idea is: if beta is significant, this 
> model won't hold, the saturated model fits only and I must calculate odds 
> ratios and beta's from partial tables. But: how can I tell glm() to use 
> something like beta*PR*ENVm in the formula? And, am I on the right way?
>
> Thanks a lot for your response.
>
> Piotr Majdak
>
>
> Agresti 1984: "Analysis of ordinal categorical data". John Wiley & Sons Inc.
>
>
> -- 
>
> Piotr Majdak
> Acoustics Research Institute
> Austrian Academy of Sciences
> Reichsratsstr. 17
> A-1010 Vienna
> AUSTRIA
> phone: +43-1-4277-29511
> fax: +43-1-4277-9296
> email: piotr at majdak.com
> WWW: http://www.kfs.oeaw.ac.at
>
>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595