# Re: [R] How to intepret a factor response model?

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Wed 04 May 2005 - 18:37:54 EST

On Wed, 4 May 2005, Maciej [iso-8859-2] BliziDski wrote:

What you have done here is to fit a logistic regression. The interpretation of that is covered in many good books: for example there are plots of the predicted values in MASS4.

I do wonder if that is what you intended, though. You have fitted a model of 'two or three' vs 'one'. You may have intended a multinomial logistic model: again MASS4 has details of such models.

>> mydata <- data.frame(factor_var = as.factor(c(rep('one', 100), rep('two', 100), rep('three', 100))), real_var = c(rnorm(150), rnorm(150) + 5))
>> summary(mydata)
> factor_var real_var
> one :100 Min. :-2.742877
> three:100 1st Qu.:-0.009493
> two :100 Median : 2.361669
> Mean : 2.490411
> 3rd Qu.: 4.822394
> Max. : 6.924588
>> mymodel = glm(factor_var ~ real_var, family = 'binomial', data = mydata)
>> summary(mymodel)
>
> Call:
> glm(formula = factor_var ~ real_var, family = "binomial", data = mydata)
>
> Deviance Residuals:
> Min 1Q Median 3Q Max
> -1.7442 -0.6774 0.1849 0.3133 2.1187
>
> Coefficients:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) -0.6798 0.1882 -3.613 0.000303 ***
> real_var 0.8971 0.1066 8.417 < 2e-16 ***
> ---
> Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
>
> (Dispersion parameter for binomial family taken to be 1)
>
> Null deviance: 381.91 on 299 degrees of freedom
> Residual deviance: 213.31 on 298 degrees of freedom
> AIC: 217.31
>
> Number of Fisher Scoring iterations: 6
>
> ---------------------------------------------------------------------
>
> For models with real-type response variable it's easy to figure out,
> what's the equation for the response variable (in the model). But here
> - how do I interpret the model?

```--
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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