simple simulation for glmnet

Last updated: 2018-05-21

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library(glmnet)

Loading required package: Matrix

Loading required package: foreach

Loaded glmnet 2.0-16

set.seed(1)
p = 100
n = 500
X = matrix(rnorm(n*p),ncol=p)
b = rnorm(p)
e = rnorm(n,0,sd=25)
Y = X %*% b + e

Y.ols = lm(Y~X) 

Y.ridge = glmnet(X,Y,alpha=0)
plot(Y.ridge)

Y.lasso = glmnet(X,Y,alpha=1)
plot(Y.lasso)

cv.ridge = cv.glmnet(X,Y,alpha=0)
plot(cv.ridge)

cv.lasso = cv.glmnet(X,Y,alpha=1)
plot(cv.lasso)

b.ridge = predict(Y.ridge, type="coefficients", s = cv.ridge$lambda.min)

b.lasso = predict(Y.lasso, type="coefficients", s = cv.lasso$lambda.min)

b.ols = Y.ols$coefficients

length(b.lasso)

[1] 101

b.lasso[1]

[1] -1.38244

mean(Y)

[1] -1.233957

btrue = c(0,b) # Here the 0 is the intercept (true value 0)

sum((btrue-0)^2) # This is error if we just estimate 0 for everything and ignore data. It is better than OLS!

[1] 85.30411

sum((btrue-Y.ols$coefficients)^2)

[1] 138.2715

sum((btrue-b.ridge)^2)

[1] 56.99797

sum((btrue-b.lasso)^2)

[1] 68.7212

sessionInfo()

R version 3.3.2 (2016-10-31)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X El Capitan 10.11.6

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] glmnet_2.0-16 foreach_1.4.4 Matrix_1.2-14

loaded via a namespace (and not attached):
 [1] workflowr_1.0.1   Rcpp_0.12.16      codetools_0.2-15 
 [4] lattice_0.20-35   digest_0.6.15     rprojroot_1.3-2  
 [7] R.methodsS3_1.7.1 grid_3.3.2        backports_1.1.2  
[10] git2r_0.21.0      magrittr_1.5      evaluate_0.10.1  
[13] stringi_1.1.7     whisker_0.3-2     R.oo_1.22.0      
[16] R.utils_2.6.0     rmarkdown_1.9     iterators_1.0.9  
[19] tools_3.3.2       stringr_1.3.0     yaml_2.1.18      
[22] htmltools_0.3.6   knitr_1.20       

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