# [R] R and Poisson

Roger Bivand Roger.Bivand at nhh.no
Mon Aug 18 22:20:40 CEST 2003

```On Mon, 18 Aug 2003, Paul Mcgeoghan wrote:

I think that Peter Dalgaard's book "Introductory Statistics with R" will
help, especially for some of the "generic" functions, even though his
chapter 11 is for logistic regression, not specifically the Poisson case.
His book contains further references. I think you may find that
help(anova.glm) will provide some insight too.

> 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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> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>

--
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of