| Type: | Package |
| Title: | Akaike Information Criterion for Sparse Estimation |
| Version: | 1.0.1 |
| Date: | 2022-10-18 |
| Author: | Shuichi Kawano 
[aut, cre],
Yoshiyuki Ninomiya [aut] |
| Maintainer: | Shuichi Kawano <skawano@math.kyushu-u.ac.jp> |
| Suggests: | MASS, glmnet, glasso |
| Description: | Computes the Akaike information criterion for the generalized linear models (logistic regression, Poisson regression, and Gaussian graphical models) estimated by the lasso. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| URL: | https://doi.org/10.1214/16-EJS1179, https://sites.google.com/site/shuichikawanoen/ |
| Repository: | CRAN |
| NeedsCompilation: | no |
| Packaged: | 2022-10-18 07:33:29 UTC; kawano |
| Date/Publication: | 2022-10-18 23:22:35 UTC |
Compute the Akaike information criterion for the lasso in generalized linear models
Description
This function computes the Akaike information criterion for generalized linear models estimated by the lasso.
Usage
sAIC(x, y=NULL, beta, family=c("binomial","poisson","ggm"))Arguments
x |
A data matrix. |
y |
A response vector. If you select family="ggm", you should omit this argument. |
beta |
An estimated coefficient vector including the intercept. If you select family="ggm", you should use an estimated precision matrix. |
family |
Response type (binomial, Poisson or Gaussian graphical model). |
Value
AIC |
The value of AIC. |
Author(s)
Shuichi Kawano
skawano@math.kyushu-u.ac.jp
References
Ninomiya, Y. and Kawano, S. (2016). AIC for the Lasso in generalized linear models. Electronic Journal of Statistics, 10, 2537–2560. doi:10.1214/16-EJS1179
Examples
library(MASS)
library(glmnet)
library(glasso)
### logistic model
set.seed(3)
n <- 100; np <- 10; beta <- c(rep(0.5,3), rep(0,np-3))
Sigma <- diag( rep(1,np) )
for(i in 1:np) for(j in 1:np) Sigma[i,j] <- 0.5^(abs(i-j))
x <- mvrnorm(n, rep(0, np), Sigma)
y <- rbinom(n,1,1-1/(1+exp(x%*%beta)))
glmnet.object <- glmnet(x,y,family="binomial",alpha=1)
coef.glmnet <- coef(glmnet.object)
### coefficients
coef.glmnet[ ,10]
### AIC
sAIC(x=x, y=y, beta=coef.glmnet[ ,10], family="binomial")
### Poisson model
set.seed(1)
n <- 100; np <- 10; beta <- c(rep(0.5,3), rep(0,np-3))
Sigma <- diag( rep(1,np) )
for(i in 1:np) for(j in 1:np) Sigma[i,j] <- 0.5^(abs(i-j))
x <- mvrnorm(n, rep(0, np), Sigma)
y <- rpois(n,exp(x%*%beta))
glmnet.object <- glmnet(x,y,family="poisson",alpha=1)
coef.glmnet <- coef(glmnet.object)
### coefficients
coef.glmnet[ ,20]
### AIC
sAIC(x=x, y=y, beta=coef.glmnet[ ,20], family="poisson")
### Gaussian graphical model
set.seed(1)
n <- 100; np <- 10; lambda_list <- 1:100/50
invSigma <- diag( rep(0,np) )
for(i in 1:np)
{
for(j in 1:np)
{
if( i == j ) invSigma[i ,j] <- 1
if( i == (j-1) || (i-1) == j ) invSigma[i ,j] <- 0.5
}
}
Sigma <- solve(invSigma)
x <- scale(mvrnorm(n, rep(0, np), Sigma))
glasso.object <- glassopath(var(x), rholist=lambda_list, trace=0)
### AIC
sAIC(x=x, beta=glasso.object$wi[,,10], family="ggm")