[R] Poisson regression in R

From: glmstat <dn2261_at_gmail.com>
Date: Sat, 01 Mar 2008 22:36:03 -0800 (PST)

I have these questions:
(1) Use Poisson regression to estimate the main effects of car, age, and dist (each treated as categorical and modelled using indicator variables) and interaction terms.
(2) It was determined by one study that all the interactions were unimportant and decided that age and car could be treated as though they were continuous variables. Fit a model incorporating these features and compare it with the best model obtained in (1).

n is the number of insurance policies
y is the number of claims
car is the car in an insurance category
age is the age of policy holder
dist is the district where the policy holder lived (1 for London and other major cities, and 0 otherwise)

Data:

car	age	dist	y	n
1	1	0	65	317
1	2	0	65	476
1	3	0	52	486
1	4	0	310	3259
2	1	0	98	486
2	2	0	159	1004
2	3	0	175	1355
2	4	0	877	7660
3	1	0	41	223
3	2	0	117	539
3	3	0	137	697
3	4	0	477	3442
4	1	0	11	40
4	2	0	35	148
4	3	0	39	214
4	4	0	167	1019
1	1	1	2	20
1	2	1	5	33
1	3	1	4	40
1	4	1	36	316
2	1	1	7	31
2	2	1	10	81
2	3	1	22	122
2	4	1	102	724
3	1	1	5	18
3	2	1	7	39
3	3	1	16	68
3	4	1	63	344
4	1	1	0	3
4	2	1	6	16
4	3	1	8	25
4	4	1	33	114


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I need help finding the correct R code to construct models. According to the previous study, the model in (2) "is simpler than (1), fits well (deviance = 53.11, d.f. = 60, p-value = 0.72) and gives coefficients (standard errors): AGE, – 0.177 (0.018); CAR, 0.198 (0.021); DIST, 0.210 (0.059)."

As of the first model, I think that I should use this code, but not sure:

> firstmodel<-glm(y~factor(age)*factor(car)*factor(dist),family=poisson)

As of the second model, I used this code, but it produces results that contradict what the previous study says (and deleting intercept does not help):

> secondmodel<-glm(y~age+car+factor(dist),family=poisson)
> summary(secondmodel)

Call:
glm(formula = y ~ age + car + factor(dist), family = poisson)

Deviance Residuals:

     Min 1Q Median 3Q Max -14.0258 -3.3200 -0.6296 2.0575 18.1442

Coefficients:

              Estimate Std. Error z value Pr(>|z|)

(Intercept)    3.08222    0.08127   37.92   <2e-16 ***
age            0.83664    0.02067   40.48   <2e-16 ***
car           -0.16723    0.01612  -10.37   <2e-16 ***
factor(dist)1 -2.15937    0.05849  -36.92   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 5660.6  on 31  degrees of freedom
Residual deviance: 1154.5  on 28  degrees of freedom
AIC: 1330.8

Number of Fisher Scoring iterations: 5
-- 
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Received on Sun 02 Mar 2008 - 08:00:18 GMT

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