# [R] Poisson regression in R

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

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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