Last updated: 2018-10-05

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Introduction

Generalized additve model can be written as \(g(E(Y))=\beta_0+f_1(x_1)+f_2(x_2)+...+f_p(x_p)\), where \(f_i\) is smooth, either parametric, nonparametric or semi-parametric. The model is interpretable and flexible.

Let’s try GAM on smoothing poisson and binomial data.

Poisson

library(mgcv)
Loading required package: nlme
This is mgcv 1.8-24. For overview type 'help("mgcv-package")'.
set.seed(12345)
n=512
m=c(rep(3,128), rep(5, 128), rep(6, 128), rep(3, 128))
y=rpois(n,m)
x=1:n
gam.mod=gam(y~s(x,bs='cr'),family = poisson())
plot(y,col='grey80',main='cubic regression splines')
lines(gam.mod$fitted.values)
lines(m,col='grey80')

set.seed(12345)
n=512
spike.f = function(x) (0.75 * exp(-500 * (x - 0.23)^2) + 1.5 * exp(-2000 * (x - 0.33)^2) + 3 * exp(-8000 * (x - 0.47)^2) + 2.25 * exp(-16000 * 
    (x - 0.69)^2) + 0.5 * exp(-32000 * (x - 0.83)^2))
t = 1:n/n
m = spike.f(t)
y=rpois(n,m)
x=t
gam.mod=gam(y~s(x,bs='cr'),family = poisson())
plot(y,col='grey80',main='cubic regression splines')
lines(gam.mod$fitted.values)
lines(m,col='grey80')

Binomial

set.seed(12345)
p=c(rep(-2,128), rep(0, 128), rep(2, 128), rep(-2, 128))
p=exp(p)/(1+exp(p))
ntri=rpois(n,30)
y=rbinom(n,ntri,p)
gam.mod=gam(y/ntri~s(x,bs='cr'),family = binomial())
plot(y/ntri,col='grey80',main='cubic regression splines')
lines(gam.mod$fitted.values)
lines(p,col='grey80')

Session information

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] mgcv_1.8-24  nlme_3.1-137

loaded via a namespace (and not attached):
 [1] workflowr_1.1.1   Rcpp_0.12.18      lattice_0.20-35  
 [4] digest_0.6.17     rprojroot_1.3-2   R.methodsS3_1.7.1
 [7] grid_3.5.1        backports_1.1.2   git2r_0.23.0     
[10] magrittr_1.5      evaluate_0.11     stringi_1.2.4    
[13] whisker_0.3-2     R.oo_1.22.0       R.utils_2.7.0    
[16] Matrix_1.2-14     rmarkdown_1.10    tools_3.5.1      
[19] stringr_1.3.1     yaml_2.2.0        compiler_3.5.1   
[22] htmltools_0.3.6   knitr_1.20

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