Colleagues,
I hope someone can help me with a question about deviance/DF in a Poisson
regression.
I recently ran a model in which I am trying to predict a dependent variable
which can take on the values 0, 1, . . ., 100. I have a series of independent
variables, but to make this discussion simple, I will describe my results when I
use a single independent variable, age which is a continuous covariate. Please
look at the results of my analysis:
*** Generalized Linear Model ***
Call: glm(formula = attendance ~ age, family = poisson(link = log), data =
complia,
na.action = na.exclude, control = list(epsilon = 0.0001, maxit = 50,
trace = F))
Deviance Residuals:
Min 1Q Median 3Q Max
-10.86184 -5.039905 1.774169 3.639788 4.877516
Coefficients:
Value Std. Error t value
(Intercept) 4.07994684441 0.102159338 39.93709183
age -0.00006456078 0.001524272 -0.04235516
(Dispersion Parameter for Poisson family taken to be 1 )
Null Deviance: 3033.602 on 107 degrees of freedom
Residual Deviance: 3033.6 on 106 degrees of freedom
Number of Fisher Scoring Iterations: 4
You will note that the value of the residual deviance is 3033, with 106 degrees
of freedom. Thus resid dev/DF= approx 29. I looked at a plot of my deviance
residuals by fitted age, and the plot has no clear shape, no single residual is
very much larger than the rest, but many of the residuals are very large, e.g.
-10 to +5. I remember my teachers saying that the resid dev/DF should be
approximately one. I do not think that 29 is "approximately" one. Does anyone
have any suggestions why my resid dev/DF is so large? Is it because the range of
my independent variable is so large i.e. zero to 100? Should I be concerned?
Thanks,
John Sorkin
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