mAIC.LA.ridgeGLM {squeezy}

Marginal AIC of a multi-group, ridge penalised GLM

Description

Compute the marginal AIC for the marginal likelihood (ML) of multi-group, ridge penalised generalised linear models. Note: currently only implemented for linear and logistic regression.

Usage

mAIC.LA.ridgeGLM(loglambdas, XXblocks, Y, sigmasq = 1, 
                Xunpen = NULL, intrcpt = TRUE, model, minlam = 0)

Arguments

loglambdas

Logarithm of the ridge penalties as returned by ecpc or squeezy; Gx1 vector.

XXblocks

List of sample covariance matrices X_g %*% t(X_g) for groups g = 1,..., G.

Y

Response data; n-dimensional vector (n: number of samples) for linear and logistic outcomes.

sigmasq

(linear model only) Noise level (Y~N(X*beta,sd=sqrt(sigmasq))).

Xunpen

Unpenalised variables; nxp_1-dimensional matrix for p_1 unpenalised variables.

intrcpt

Should an intercept be included? Set to TRUE by default.

model

Type of model for the response; linear or logistic.

minlam

Minimum value of lambda that is added to exp(loglambdas); set to 0 as default.

Value

mAIC

mAIC of the model

Examples

#Simulate toy data
n<-100
p<-300
X <- matrix(rnorm(n*p),n,p)
Y <- rnorm(n)
groupset <- list(1:(p/2),(p/2+1):p)
sigmahat <- 2
alpha <- 0.5
tauMR <- c(0.01,0.005)

XXblocks <- lapply(groupset, function(x)X[,x]%*%t(X[,x]))

#compute the mAIC of a co-data model with multiple groups
mAIC.LA.ridgeGLM(loglambdas=log(sigmahat/tauMR), XXblocks=XXblocks, 
                 Y = Y, sigmasq = sigmahat, model="linear")

#compute the mAIC of a co-data agnostic model, i.e. only one group of covariates
mAIC.LA.ridgeGLM(loglambdas=log(sigmahat/median(tauMR)), 
                 XXblocks=list(X%*%t(X)), 
                 Y = Y, sigmasq = sigmahat, model="linear")