Re: [R] How to find the significant differences among interactions in logit model?

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Fri 24 Jun 2005 - 18:22:33 EST

Use an analysis of deviance test for the term color:width. Probably most clearly by (untested)

crabs.glm2 <- update(crabs.glm, . ~ . - color:width) anova(crabs.glm2, crabs.glm, test="Chisq")

This is covered with several examples in MASS.

On Fri, 24 Jun 2005, Wuming Gong wrote:

> I have a question about interpret the results from logistic regression
> model.

Not really: this is about comparing two such models.

> I used a dataset from the book Categorical Data Analysis (2nd
> Edition) by Alan Agresti.
>
>> summary(crabs)
> color spine width satell weight psat
> 2:12 1: 37 Min. :21.0 Min. : 0.000 Min. :1200 Mode :logical
> 3:95 2: 15 1st Qu.:24.9 1st Qu.: 0.000 1st Qu.:2000 FALSE:62
> 4:44 3:121 Median :26.1 Median : 2.000 Median :2350 TRUE :111
> 5:22 Mean :26.3 Mean : 2.919 Mean :2437
> 3rd Qu.:27.7 3rd Qu.: 5.000 3rd Qu.:2850
> Max. :33.5 Max. :15.000 Max. :5200
>
>> crabs.glm <- glm(psat ~ color*width, family=binomial(), data=crabs)
>> summary(crabs.glm)
>
> Call:
> glm(formula = psat ~ color * width, family = binomial(), data = crabs)
>
> Deviance Residuals:
> Min 1Q Median 3Q Max
> -2.0546 -0.9129 0.5285 0.8140 1.9657
>
> Coefficients:
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) -1.75261 11.46409 -0.153 0.878
> color3 -8.28735 12.00363 -0.690 0.490
> color4 -19.76545 13.34251 -1.481 0.139
> color5 -4.10122 13.27532 -0.309 0.757
> width 0.10600 0.42656 0.248 0.804
> color3:width 0.31287 0.44794 0.698 0.485
> color4:width 0.75237 0.50435 1.492 0.136
> color5:width 0.09443 0.50042 0.189 0.850
>
> (Dispersion parameter for binomial family taken to be 1)
>
> Null deviance: 225.76 on 172 degrees of freedom
> Residual deviance: 183.08 on 165 degrees of freedom
> AIC: 199.08
>
> Number of Fisher Scoring iterations: 5
>
> Note the predictors are mixture of continuous data and categorical
> data. Here, I wonder whether there is *significant difference* among
> the four interactions of color and width (say, to get a p-value). In a
> two-way ANOVA, we may do a F-test. But is there an "equivalent" method
> for logit 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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Received on Fri Jun 24 18:28:08 2005

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