# [R] R and Poisson

Paul Mcgeoghan Mcgeoghan at Cardiff.ac.uk
Mon Aug 18 20:46:41 CEST 2003

```Hi, I wonder if anyone can answer the following or point me in the direction of
how to obtain answers to the questions. Below is Output from R and further down
are the questions raised and explanation of the study.

Output from R:
glm(formula = CB95TO00 ~ URB + INC, family = poisson)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.2272  -1.1290   0.2709   0.4272   2.1376

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.30621    0.13499  -2.268   0.0233 *
URB2         0.02253    0.16826   0.134   0.8935
URB3        -0.00936    0.15263  -0.061   0.9511
INC2        -0.14430    0.12342  -1.169   0.2423
INC3        -0.55092    0.31351  -1.757   0.0789 .
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 403.97  on 420  degrees of freedom
Residual deviance: 399.61  on 416  degrees of freedom
AIC: 883.8

Number of Fisher Scoring iterations: 4

Explanation and Questions raised.

The dependent variable is:

Number of children born in last 5 years: (values range from 0 to 3).
Distribution of dependent variable (named CB95TO00)
0  203
1  157
2    59
3     2

Predictors are:
Level of Urbanisation (3 categories 1: Rural; 2:Semi-Urban; 3: Urban)
Income  Level (3 categories: 1: Low; 2:Medium; 3: High)

The questions are (1) how does one interpret the coefficients in the output:
Our interpretation is Urb2 compared to Urb1 gives an estimate of .02253;
Urb3 compared to Urb1 gives a parameter estimate of -.00936 etc. Neither of
these shows significance. How does one interpret this exactly with regards to
the dependent variable which is Number of children?
2) How does one interpret the intercept which shows significance?
3) What does the Null Deviance tell us and the Residual Deviance?
4) What does the AIC tell us?
5) Is it possible to obtain goodness of fit statistics such as Pearson
ChiSquare and Log-Likelihood similar to what SAS statistical software gives?
6) Is it possible to find out if Urbanisation and Income are significant
overall in R?

Thanks in advance for any assistance,
Regards,
Paul

==================
Paul McGeoghan,
Application support specialist (Statistics and Databases),
Information Services,
Cardiff University.
Tel. 02920 (875035).

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