# lmme: Linear mixed model estimation In MMS: Fixed Effects Selection in Linear Mixed Models

## Description

Estimation of fixed and random effects in linear mixed models

## Usage

 `1` ```lmme(data,Y,z,grp,D,step,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. `step` The algorithm performs at most `step` iterations. Default is 3000. `showit` Logical value. If TRUE, shows the convergence process of the algorithm. Default is FALSE.

## Details

`lmme` performs an ML-estimation of fixed and random effects in linear mixed models when no selection is involved. Two algorithms are available: one when the random effects are assumed to be independent (D=TRUE) and one when they are not (D=FALSE).

## Value

 `data` List of the user-data: the scaled matrix used in the algorithm, the first column being (1,...,1); Y; z and grp. `beta` Estimation of the selected fixed effects. `Psi` Variance of the random effects. Matrix of dimension q*q. `sigma_e` Variance of the noise. `fitted.values` Fitted values calculated with the fixed effects and the random effects. `it` Number of iterations of the algorithm. `converge` Did the algorithm converge? `u` Vector of the concatenation of the estimated random effects (u_1',...,u_q')'. `call` The call that produced this object.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```## 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] ######## fit=lmme(x,y,z,grp) ## End(Not run) ```

MMS documentation built on May 17, 2018, 9:05 a.m.