From: Constantinos Antoniou <antoniou_at_central.ntua.gr>

Date: Tue 24 May 2005 - 04:59:11 EST

**POISSON - LOG LINK
**

-3.6900 -1.1901 -0.1847 0.9477 4.3967

*---
*

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

**GAUSSIAN
**

-61.326 -12.012 -1.756 14.204 78.991

*---
*

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue May 24 05:03:32 2005

Date: Tue 24 May 2005 - 04:59:11 EST

Hello,

I am a new R user and I am trying to estimate some generalized linear models (glm). I am trying to compare a model with a gaussian distribution and an identity link function, and a poisson model with a log link function. My problem is that while the gaussian model has significantly lower (i.e. "better") AIC (Akaike Information Criterion) most of the coefficients are not significant. On the other hand, the poisson model has a higher (i.e. "worse") AIC, but almost all the coefficients are extremely significant (expect for one that still has p=0.07).

Summary output of the two models follows... [sorry for the large number of independent variables, but the issue is less pronounced with fewer covariates].

My question is two-fold:

- AIC supposedly can be used to compare non-nested models (although

there are concerns and I have also seen a couple in this list's
archives). Is this a case where AIC is not a good measure to compare
the two models? If so, is there another measure (besides choosing the
model with the significant coefficients)? [These are time-series
data, so I am also looking at acf/pacf of the residuals].

- Could the very high significance of the coefficients in the poisson

model hint at some issue?

+++++++++++++++++++++++

+++++++++++++++++++++++

Call:

glm(formula = TotalDeadInjured[3:48] ~ -1 + Month[3:48] + sin(pi *

Month[3:48]/6) + cos(pi * Month[3:48]/6) + sin(pi * Month[3:48]/ 12) +

cos(pi * Month[3:48]/12) + ThousandCars[3:48] + monthcycle[3:48] + TotalDeadInjured[1:46] + I((TotalDeadInjured[1:46])^2) + I((TotalDeadInjured[1:46])^3), family = poisson(link = log)) Deviance Residuals: Min 1Q Median 3Q Max

-3.6900 -1.1901 -0.1847 0.9477 4.3967

Coefficients:

Estimate Std. Error z value Pr(>|z|) Month[3:48] -7.712e-02 5.530e-03 -13.947 < 2e-16 *** sin(pi * Month[3:48]/6) -1.419e-01 2.759e-02 -5.144 2.68e-07 *** cos(pi * Month[3:48]/6) -8.407e-02 1.799e-02 -4.672 2.99e-06 *** sin(pi * Month[3:48]/12) -2.776e-02 1.558e-02 -1.782 0.074702 . cos(pi * Month[3:48]/12) 5.195e-02 1.608e-02 3.232 0.001231 ** ThousandCars[3:48] 2.733e-02 2.255e-03 12.118 < 2e-16 *** monthcycle[3:48] 6.307e-02 6.546e-03 9.635 < 2e-16 *** TotalDeadInjured[1:46] -2.925e-02 8.460e-03 -3.457 0.000546 ***I((TotalDeadInjured[1:46])^2) 1.218e-04 3.613e-05 3.370 0.000750 *** I((TotalDeadInjured[1:46])^3) -1.640e-07 4.961e-08 -3.306 0.000946 ***

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 78694.70 on 46 degrees of freedom
Residual deviance: 130.03 on 36 degrees of freedom
**AIC: 476.08
**
Number of Fisher Scoring iterations: 4

+++++++++++++++++++++++++

++++++++++++++++++++++++++

Call:

glm(formula = TotalDeadInjured[3:48] ~ -1 + Month[3:48] + sin(pi *

Month[3:48]/6) + cos(pi * Month[3:48]/6) + sin(pi * Month[3:48]/ 12) +

cos(pi * Month[3:48]/12) + ThousandCars[3:48] + monthcycle[3:48] + TotalDeadInjured[1:46] + I((TotalDeadInjured[1:46])^2) + I((TotalDeadInjured[1:46])^3), family = gaussian(link = identity)) Deviance Residuals: Min 1Q Median 3Q Max

-61.326 -12.012 -1.756 14.204 78.991

Coefficients:

Estimate Std. Error t value Pr(>|t|) Month[3:48] -8.111e+00 2.115e+00 -3.835 0.000487 *** sin(pi * Month[3:48]/6) -2.639e+01 1.095e+01 -2.409 0.021246 * cos(pi * Month[3:48]/6) -1.700e+01 7.138e+00 -2.382 0.022629 * sin(pi * Month[3:48]/12) 2.392e-01 6.524e+00 0.037 0.970956 cos(pi * Month[3:48]/12) 8.785e+00 6.317e+00 1.391 0.172835 ThousandCars[3:48] 2.219e+00 8.604e-01 2.579 0.014146 * monthcycle[3:48] 5.364e+00 2.494e+00 2.151 0.038301 * TotalDeadInjured[1:46] -4.974e+00 3.263e+00 -1.524 0.136171I((TotalDeadInjured[1:46])^2) 2.154e-02 1.410e-02 1.527 0.135382 I((TotalDeadInjured[1:46])^3) -2.999e-05 1.959e-05 -1.530 0.134637

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 831.6357)

Null deviance: 1927714 on 46 degrees of freedom
Residual deviance: 29939 on 36 degrees of freedom
**AIC: 450.54
**
Number of Fisher Scoring iterations: 2

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue May 24 05:03:32 2005

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