# Re: [R] Analysing ordinal/nominal data

From: Piotr Majdak <piotr_at_majdak.com>
Date: Fri 17 Jun 2005 - 19:41:51 EST

```>> 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

______________________________________________
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help