library(mgcv)
## Loading required package: nlme
## This is mgcv 1.8-18. For overview type 'help("mgcv-package")'.
set.seed(2) ## simulate some data...
dat <- gamSim(1,n=400, dist = "poisson", scale = 0.1)
## Gu & Wahba 4 term additive model
fit1 <- gam(y ~ s(x0) + s(x1) + s(x2) + s(x3), data = dat,
family = poisson(), method = "ML")
summary(fit1)
##
## Family: poisson
## Link function: log
##
## Formula:
## y ~ s(x0) + s(x1) + s(x2) + s(x3)
##
## Parametric coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.75899 0.03511 21.62 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df Chi.sq p-value
## s(x0) 2.137 2.67 5.706 0.0857 .
## s(x1) 1.000 1.00 33.832 6.01e-09 ***
## s(x2) 5.231 6.35 81.884 4.78e-15 ***
## s(x3) 1.000 1.00 3.255 0.0712 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.228 Deviance explained = 21.2%
## -ML = 715.99 Scale est. = 1 n = 400
AIC(fit1)
## [1] 1428.794
fit1$aic
## [1] 1425.752
fit2 <- gam(y ~ s(x0) + s(x1) + s(x2) + s(x3), data = dat,
family = poisson(),
method = "REML")
summary(fit2)
##
## Family: poisson
## Link function: log
##
## Formula:
## y ~ s(x0) + s(x1) + s(x2) + s(x3)
##
## Parametric coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.75761 0.03516 21.55 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df Chi.sq p-value
## s(x0) 2.559 3.190 7.027 0.0781 .
## s(x1) 1.046 1.090 33.362 1.26e-08 ***
## s(x2) 5.388 6.516 82.517 4.95e-15 ***
## s(x3) 1.414 1.713 4.260 0.1448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.232 Deviance explained = 21.6%
## -REML = 724.38 Scale est. = 1 n = 400
AIC(fit2)
## [1] 1429.832
fit2$aic
## [1] 1425.625