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I run some Poisson regressions with the following results: (with number of associations an individual belongs to as the dependent variable)

                 Estimate Std. Error z value  
(Intercept)       -0.92      0.11     -8.43   
age(decades)       0.07      0.01      5.64        
female            -0.10      0.04     -2.57      
education(degree)  0.18      0.02     10.55    
income(in 1000     0.09      0.01      8.38     
east              -0.46      0.05     -9.27
TV                -0.08      0.02     -4.98

I'm trying to make a nice hook in my work however I have struggles to capture the following:

I would like to say something about a 25 year west male who holds a particular degree(education=5) earns 1000 .- per month and watches 1 hour TV per day.

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Where are you stuck ? – Claude Leibovici Jul 2 '14 at 9:19
I just not sure how to write it down for one observation and it gets harder to think about 25 year old male rather than a female – HiThere Jul 2 '14 at 9:21
2*0.07+5*0.18+1000*0.09+1*(-0.08) I somehow lost sorry – HiThere Jul 2 '14 at 9:49
This is almost right, except you forgot the intercept (always include that if it is estimated) and multiplying the income coeffficient by 1000 is incorrect since it is in 1000. See my answer below. – Nameless Jul 4 '14 at 14:02
up vote 1 down vote accepted

Ok, so you estimate a Poisson regression, which gives you a probability distribution over all counts $y=0,1,2,\ldots$ given some observables. I am guessing you don't want to give the entire probability distribution, just the expected value (i.e., how many associations will this 25 year old male be expected to belong to).

First, from the Poisson model we know $$\log(\text{E}[y|x])=\alpha+\beta'x.$$ This sum should be $$-0.92+0.07*3+0.18*5+0.09-0.08=0.2,$$ where I am assuming "education" is linear (i.e., $education=5$ is 5 times the coefficient) and "TV" is one hour of TV - please check if that is right.

By the way, with age you would usually include at least a quadratic term to capture nonlinear age effects, or use groups instead of trends (e.g., split your sample in 0-18 years, 19-25, etc. and use dummies for each). I would also rather use groups for education (different group for high school, college etc.).

Consequently, you expect such an individual to belong to $\exp(\log(\text{E}[y|x]))=\exp(0.2)\approx 1.22$ associations. Does that make sense?

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Thx for the nice example – HiThere Jul 7 '14 at 12:52

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