I am not very familiar with Poisson regression, so I think I must have made a mistake in the below analysis:
I am studying the effects of smoking on lung cancer rates. The dataset is provided here. The variable smoking_status
is defined:
smoking status: coded 1 = doesn't smoke, 2 = smokes cigars or pipe only, 3 = smokes cigarrettes and cigar or pipe, and 4 = smokes cigarrettes only,
I modified the data a bit and made two new categorical variables: pipe/cigar smoker and cigarette smoker, to replace smoking_status. So a smoking status 1 maps to (0,0), 2 maps to (1,0), 3 maps to (1,1) etc.
I also added a constant column to my dataset. This is all I did to the data.
I then performed Poisson regression on this dataset, using a exponential link function. My hopes was that the coefficients of the two new variables would be positive, but instead only cigarette_smoker is positive. The confidence intervals do not contain positive points either.
Have I analysed the data incorrectly, or is my data just wrong?
EDIT
The output (it's from a Python library Statsmodels )
Generalized Linear Model Regression Results
Dep. Variable: y No. Observations: 36
Model: GLM Df Residuals: 31
Model Family: Poisson Df Model: 4
Link Function: log Scale: 1.0
Method: IRLS Log-Likelihood: -815.93
Date: Thu, 31 Jan 2013 Deviance: 1391.8
Time: 13:19:32 Pearson chi2: 1.22e+03
No. Iterations: 7
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
x1 0.2596 0.006 44.097 0.000 0.248 0.271
x2 -0.1850 0.024 -7.775 0.000 -0.232 -0.138
x3 0.5327 0.031 17.101 0.000 0.472 0.594
x4 0.0004 7.95e-06 54.637 0.000 0.000 0.000
const 2.9593 0.046 63.903 0.000 2.869 3.050
The variables in order are age, smoke_cigar (0,1), smoke_cigarettes (0,1), population (in hundred of thousands), constant_term.
Some example data:
array([[ 2., 0., 0., 359., 1.], [ 4., 0., 1., 3270., 1.]])
with target deaths [ 22., 514.] respectively.