MMS (version 3.0.11)

lassop: L1-penalization in linear mixed models

Description

Performs a L1-penalization in linear mixed models

Usage

lassop(data,Y,z,grp,D,mu,step,fix,rand,penalty.factor,alpha,showit)

Arguments

data

Input matrix of dimension n * p; each row is an observation vector. The intercept should be included in the first column as (1,...,1). If not, it is added.

Y

Response variable of length n.

z

Random effects matrix. Of size n*q.

grp

Grouping variable of length n.

D

Logical value. If TRUE, the random effects are considered to be independent, i.e. Psi is a diagonal matrix. D=TRUE should be used with nested grouping factors.

mu

Positive regularization number to be used for the Lasso.

step

The algorithm performs at most step iterations. Default is 3000.

fix

Number of variables which are not submitted to selection. They have to be in the first columns of data. Default is 1, the selection is not performed on the intercept.

rand

A vector of length q: each entry k is the position of the random effects number k in the data matrix, 0 otherwise. If z contains variables that have both a fixed and a random effect, it is advised to not submit them to selection.

penalty.factor

Argument of 'glmnet'. Separate penalty factors can be applied to each coefficient. This is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables that are not in 1:fix.

alpha

Argument of 'glmnet'. The elasticnet mixing parameter, with \( 0\le \alpha \le 1\). alpha=1 is the lasso penalty, and alpha=0 the ridge penalty.

showit

Logical value. If TRUE, shows the iterations of the algorithm. Default is FALSE.

Value

A 'lassop' object is returned.

data

List of the user-data: the scaled matrix used in the algorithm, the first column being (1,...,1); Y and Z, which is the design matrix of the random effects.

beta

Estimation of the fixed effects.

fitted.values

Fitted values calculated with the fixed effects and the random effects.

Psi

Variance of the random effects. Matrix of dimension q*q.

sigma_e

Variance of the residuals.

it

Number of iterations of the algorithm.

converge

Logical. TRUE if the algorithm has converged, FALSE otherwise.

u

Vector of the concatenation of the estimated random effects (u_1',...,u_q')'.

call

The call that produced this object.

mu

The penalty used in the algorithm.

Details

This function performs fixed effects selection in linear mixed models through a L1-penalization of the log-likelihood of the marginal model. The method optimizes a criterion via a multicycle ECM algorithm at the regularization parameter mu. Two algorithms are available: one when the random effects are assumed to be independent (D=TRUE) and one when they are not (D=FALSE). Selection on the random is only performed when D=TRUE.

Examples

# NOT RUN {
N <- 20           # number of groups
p <- 80            # number of covariates (including intercept)
q <- 2            # number of random effect covariates
ni <- rep(6,N)    # observations per group
n <- sum(ni)   # total number of observations

grp <- factor(rep(1:N,ni)) # grouping variable
grp=rbind(grp,grp)

beta <- c(1,2,4,3,rep(0,p-3)) # fixed-effects coefficients
x <- cbind(1,matrix(rnorm(n*p),nrow=n)) # design matrix

u1=rnorm(N,0,sd=sqrt(2))
u2=rnorm(N,0,sd=sqrt(2))
bi1 <- rep(u1,ni) 
bi2 <- rep(u2,ni)
bi <- rbind(bi1,bi2)

z=x[,1:2,drop=FALSE]
   
epsilon=rnorm(120)
y <- numeric(n)
for (k in 1:n) y[k] <- x[k,]%*%beta + t(z[k,])%*%bi[,k] + epsilon[k]

########

#independent random effects
fit=lassop(x,y,z,grp,D=1,mu=0.2,fix=1,rand=c(1,2))

#dependent random effects
fit=lassop(x,y,z,grp,mu=0.2,fix=1,rand=c(1,2))
# }