R help - Jun 2005 - How to find the significant differences among interactions in logit model?

Hi, 

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

Thanks,

Wuming

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 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