[S] summary.glm for gam object

Theo Brandsma (brandsma@knmi.nl)
Tue, 14 Jul 1998 15:09:36 +0000

Dear colleagues,

I have the following GAM model with one linear predictor and two
nonlinear predictors:

y <- gam(formula = avrain ~ tmean + lo(vort, span = 0.5) + lo(difT,
span = 0.5), family = Gamma(link = log), weights = gewyeanew)

Because I am interested in the slope of tmean, I used summary.glm (see
the output below). My question is:
(1) is this allowed (giving me the right coefficient and t-value) or do I
need something else?
(2) if summary.glm is oke, what is the meaning of the coefficients and
t-statistics of the two nonlinear predictors?

Theo Brandsma
Royal Netherlands Meteorological Institute (KNMI)
brandsma@knmi.nl

Output of summary and the summary.glm:

> summary(y,dispersion=1)
Call: gam(formula = avrain ~ tmean + lo(vort, span = 0.5) + lo(difT,
span = 0.5), family = Gamma(link = log), weights = gewyeanew) Deviance
Residuals:
Min 1Q Median 3Q Max
-2.57339 -0.9607054 -0.2057024 0.6121211 3.300363

(Dispersion Parameter for Gamma family taken to be 1 )

Null Deviance: 672.1894 on 211 degrees of freedom

Residual Deviance: 239.651 on 202.6139 degrees of freedom

Number of Local Scoring Iterations: 4

DF for Terms and Chi-squares for Nonparametric Effects

Df Npar Df Npar Chisq P(Chi)
(Intercept) 1
tmean 1
lo(vort, span = 0.5) 1 2.6 7.86971 0.03445103
lo(difT, span = 0.5) 1 2.8 54.06510 0.00000000

> summary.glm(y,dispersion=1)
Call: gam(formula = avrain ~ tmean + lo(vort, span = 0.5) + lo(difT,
span = 0.5), family = Gamma(link = log), weights =
gewyeanew)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.57339 -0.9607054 -0.2057024 0.6121211 3.300363

Coefficients:
Value Std. Error t value
(Intercept) 1.29314973 0.063986580 20.209702
tmean 0.06417742 0.005166671 12.421427
lo(vort, span = 0.5) 6.28784436 0.363913249 17.278416
lo(difT, span = 0.5) -6.43214664 0.656394283 -9.799212

(Dispersion Parameter for Gamma family taken to be 1 )

Null Deviance: 672.1894 on 211 degrees of freedom

Residual Deviance: 239.651 on 202.6139251 degrees of freedom

Number of Fisher Scoring Iterations: 4

Correlation of Coefficients:
(Intercept) tmean lo(vort, span = 0.5)
tmean -0.9722752
lo(vort, span = 0.5) -0.2398526 0.2378560
lo(difT, span = 0.5) 0.8122085 -0.8530743 -0.1315108
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