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

[Wuming Gong]

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