# Re: [R] Analysing ordinal/nominal data

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Fri 17 Jun 2005 - 19:55:50 EST

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
> Reichsratsstr. 17
> A-1010 Vienna
> AUSTRIA
> phone: +43-1-4277-29511
> fax: +43-1-4277-9296
> email: piotr@majdak.com
> WWW: http://www.kfs.oeaw.ac.at
>
>

```--
Brian D. Ripley,                  ripley@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

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