The data are from Bishop, Fienberg & Holland (1975), Discrete Multivariate Analysis, MIT Press, page 103.
Note that there is one case with n = 0 (row 31 in cancer.logit); in GLMStat this row has to be deleted from the data, in Splus it can be removed with the subset command. (The Subset command in GLMStat should do the same thing but doesn't suppress the "n = 0" error.)
Note the rather odd way you give the Binomial n to Splus: the dependent variable is created with cbind() as a matrix with columns survive and n-survive.
You should be able to duplicate these results exactly in GLMStat.
> fitc1 <- glm(cbind(survive, n - survive) ~ city * age, data = cancer.logit,
subset = n > 0, family = binomial(link = logit))
Call:
glm(formula = cbind(survive, n - survive) ~ city * age, family = binomial(
link = logit), data = cancer.logit, subset = n > 0)
Coefficients:
(Intercept) city1 city2 age1 age2 city1age1 city2age1
0.8829087 -0.2455197 -0.05302903 0.01288113 -0.1247131 0.2337226 0.1101006
city1age2 city2age2
0.01946304 0.05995766
Degrees of Freedom: 35 Total; 26 Residual
Residual Deviance: 34.19691
> anova(fitc1,test="Chisq")
Analysis of Deviance Table
Binomial model
Response: cbind(survive, n - survive)
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(Chi)
NULL 34 57.58802
city 2 11.26979 32 46.31823 0.0035711
age 2 3.52566 30 42.79258 0.1715588
city:age 4 8.59567 26 34.19691 0.0720398
>
What is the "best" model for these data? In Splus, try the model: city * age * hist - city:age:hist, or, equivalently, city + age + hist + city:age + age:hist + city:hist, that is, all main effects and two-way interactions, then apply step() to reduce the model. Here is what I ended up with. What does it mean?
Analysis of Deviance Table
Binomial model
Response: cbind(survive, n - survive)
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(Chi)
NULL 34 57.58802
city 2 11.26979 32 46.31823 0.00357105
hist 3 9.79477 29 36.52346 0.02039370
You can also duplicate the logistic results with the loglinear data structure: in this case, survive is a factor, so city:age in the logistic analysis will be the same as survive:city:age in the loglinear analysis, city in the logistic analysis will be the same as survive:city in the loglinear analysis, etc.
> fitc2 <- glm(count ~ survive * city * age, family = poisson(link = log), data
= cancer.loglin)
Call:
glm(formula = count ~ survive * city * age, family = poisson(link = log), data
= cancer.loglin)
Coefficients:
(Intercept) survive city1 city2 age1 age2 survivecity1
2.098911 0.4414557 0.1240612 -0.01666544 0.1663998 -0.2912447 -0.1227575
survivecity2 surviveage1 surviveage2 city1age1 city2age1 city1age2
-0.02651606 0.006440126 -0.06235573 0.180255 0.002370039 0.2886847
city2age2 survivecity1age1 survivecity2age1 survivecity1age2
0.01979807 0.1168608 0.05505104 0.009732593
survivecity2age2
0.02997881
Degrees of Freedom: 72 Total; 54 Residual
Residual Deviance: 484.1559
> anova(fitc2,test="Chisq")
Analysis of Deviance Table
Poisson model
Response: count
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(Chi)
NULL 71 860.0076
survive 1 160.6009 70 699.4066 0.00000000
city 2 9.3619 68 690.0447 0.00927008
age 2 105.5350 66 584.5097 0.00000000
survive:city 2 11.2698 64 573.2400 0.00357105
survive:age 2 7.1529 62 566.0871 0.02797536
city:age 4 73.3356 58 492.7515 0.00000000
survive:city:age 4 8.5957 54 484.1559 0.07203980
>
> cancer.logit inflam benign hist city age survive n 1 1 1 1 1 1 26 35 2 1 1 1 1 2 20 29 3 1 1 1 1 3 1 3 4 1 1 1 2 1 11 17 5 1 1 1 2 2 18 26 6 1 1 1 2 3 15 24 7 1 1 1 3 1 16 32 8 1 1 1 3 2 27 41 9 1 1 1 3 3 12 15 10 1 2 2 1 1 68 75 11 1 2 2 1 2 46 55 12 1 2 2 1 3 6 9 13 1 2 2 2 1 24 31 14 1 2 2 2 2 58 78 15 1 2 2 2 3 26 44 16 1 2 2 3 1 20 27 17 1 2 2 3 2 39 51 18 1 2 2 3 3 11 18 19 2 1 3 1 1 25 29 20 2 1 3 1 2 18 29 21 2 1 3 1 3 5 6 22 2 1 3 2 1 4 10 23 2 1 3 2 2 10 13 24 2 1 3 2 3 1 4 25 2 1 3 3 1 8 11 26 2 1 3 3 2 10 13 27 2 1 3 3 3 4 7 28 2 2 4 1 1 9 12 29 2 2 4 1 2 5 7 30 2 2 4 1 3 1 1 31 2 2 4 2 1 0 0 32 2 2 4 2 2 3 5 33 2 2 4 2 3 1 1 34 2 2 4 3 1 1 1 35 2 2 4 3 2 4 4 36 2 2 4 3 3 1 1 > cancer.loglin count inflam benign hist city age survive 1 9 1 1 1 1 1 1 2 26 1 1 1 1 1 2 3 9 1 1 1 1 2 1 4 20 1 1 1 1 2 2 5 2 1 1 1 1 3 1 6 1 1 1 1 1 3 2 7 6 1 1 1 2 1 1 8 11 1 1 1 2 1 2 9 8 1 1 1 2 2 1 10 18 1 1 1 2 2 2 11 9 1 1 1 2 3 1 12 15 1 1 1 2 3 2 13 16 1 1 1 3 1 1 14 16 1 1 1 3 1 2 15 14 1 1 1 3 2 1 16 27 1 1 1 3 2 2 17 3 1 1 1 3 3 1 18 12 1 1 1 3 3 2 19 7 1 2 2 1 1 1 20 68 1 2 2 1 1 2 21 9 1 2 2 1 2 1 22 46 1 2 2 1 2 2 23 3 1 2 2 1 3 1 24 6 1 2 2 1 3 2 25 7 1 2 2 2 1 1 26 24 1 2 2 2 1 2 27 20 1 2 2 2 2 1 28 58 1 2 2 2 2 2 29 18 1 2 2 2 3 1 30 26 1 2 2 2 3 2 31 7 1 2 2 3 1 1 32 20 1 2 2 3 1 2 33 12 1 2 2 3 2 1 34 39 1 2 2 3 2 2 35 7 1 2 2 3 3 1 36 11 1 2 2 3 3 2 37 4 2 1 3 1 1 1 38 25 2 1 3 1 1 2 39 11 2 1 3 1 2 1 40 18 2 1 3 1 2 2 41 1 2 1 3 1 3 1 42 5 2 1 3 1 3 2 43 6 2 1 3 2 1 1 44 4 2 1 3 2 1 2 45 3 2 1 3 2 2 1 46 10 2 1 3 2 2 2 47 3 2 1 3 2 3 1 count inflam benign hist city age survive 48 1 2 1 3 2 3 2 49 3 2 1 3 3 1 1 50 8 2 1 3 3 1 2 51 3 2 1 3 3 2 1 52 10 2 1 3 3 2 2 53 3 2 1 3 3 3 1 54 4 2 1 3 3 3 2 55 3 2 2 4 1 1 1 56 9 2 2 4 1 1 2 57 2 2 2 4 1 2 1 58 5 2 2 4 1 2 2 59 0 2 2 4 1 3 1 60 1 2 2 4 1 3 2 61 0 2 2 4 2 1 1 62 0 2 2 4 2 1 2 63 2 2 2 4 2 2 1 64 3 2 2 4 2 2 2 65 0 2 2 4 2 3 1 66 1 2 2 4 2 3 2 67 0 2 2 4 3 1 1 68 1 2 2 4 3 1 2 69 0 2 2 4 3 2 1 70 4 2 2 4 3 2 2 71 0 2 2 4 3 3 1 72 1 2 2 4 3 3 2 >