simplelme: simplelme
In biglme: Procedure for doing inference of one-way Linear Mixed Effects models.

Description Usage Arguments Details Value Author(s) References Examples

simplelme makes inference to a one-way Linear Mixed Effects model (assumes indepedent gaussian effect).

1 2	simplelme(dat, levelnames, phi0 = 1, eps = 10^-5, minIT = 10^2, alpha = 0.05)

`dat`	Dataset with responses, categorize (group), covariates and random effects variables. List elements: Y is Response variable, F is Categorize (name of group, X is Covariates belonging to fixed effects, Z is Covariates belonging to random effects.
`levelnames`	Name of categorized levels.
`phi0`	Startvalues of the 'phi'-parameter in the EM-algorithm. Here, 'phi' is the variance parameter of the random effect levels.
`eps`	Criterion of euclidean distance for stopping EM-algorithm.
`minIT`	Minimum number of iterations in the EM-algorithm.
`alpha`	Specifies (1-alpha/2) confidence interval of parameters.

The Maximum Likelihood are used to estimate the model using the EM-algorithm. The model assumes gaussian noise with different variance paramater for each group (heterogenous variance structure) and a gaussian independent random intercept effect with constant variance parameter.

The confidence intervals are based on normal-approximated large sample intervals. Details of the EM-algorithm and confidence intervals are found in Masterthesis of Oyvind Bleka.

Model: One individual 'j' belongs to a category-level 'i'. Let 'y_ij' be the response, 'X_ij' the covariate-vector for fixed effects, 'mu_i' is random level effect for category-level 'i'. Then the model is given as 'y_ij=X_ij*beta+mu_i + epsilon_ij'. Here, Cov(epsilon_ij,epsilon_ik)=gamma_i for j=k0 for j!=k and Cov(mu_i,mu_l)={phi for i=l}{0 for i!=l}.

Note that simplelme handels only a special case of LME models which may be fitted using genlme.

Fitted simple one-way LME model object

`est`	Maximum Likelihood estimatation of LME model
`OLSest`	Ordinary least squares estimatation of LME model
`pred`	E_mu_Y: Mean of random effects. Var_mu_Y: Variance of random effects.
`levelnames`	Categorized levelnames.
`n_i`	Datasize within each categorized levels.
`loglik`	Maximized likelihood value.
`iter`	Number of iterations in the EM-algorithm.
`timeusage`	Time spent for running function.
`modelfit`	AIC and BIC of fitted model.
`CI`	Confidence interval of parameters.

Oyvind Bleka <Oyvind.Bleka.at.fhi.no>

Master Thesis Oyvind Bleka

## Not run: 
set.seed(1)
require(biglme)
require(geoR)
Xsim <- function(p,n_i) {
 Xtype = sample(1:3,p,replace=TRUE)
 Xant = rep(0,3)
 for(i in 1:3) Xant[i] = sum(Xtype==i)
 X=NULL
 I=length(n_i)
 n=sum(n_i)
 cn_i = c(0,cumsum(n_i))+1 #startindex for each levels
 if(p) { #if having any covariables
  for(i in 1:I) { #for each levels
   Xi = matrix(NA,nrow=n_i[i],ncol=p)
   Xi[,which(Xtype==1)] = matrix(rnorm(n_i[i]*Xant[1],5,3),nrow=n_i[i],ncol=Xant[1])
  Xi[,which(Xtype==2)] = matrix(rpois(n_i[i]*Xant[2],3),nrow=n_i[i],ncol=Xant[2])
   Xi[,which(Xtype==3)] = matrix(rbinom(n_i[i]*Xant[3],1,0.3),nrow=n_i[i],ncol=Xant[3])
   if(i==1) { X = Xi
   } else { X = rbind(X,Xi) } #just add up the matrix
  }
 }
 return(X)
}
I = 30 #number of effectlevels:
levelnames = paste("place",1:I,sep="") #name of levels
nlvl = 1000 #expected number of data per level
n=I*nlvl #total number of data
n_i = c(rmultinom(1,n,runif(I,0.3,0.7))) #gen number of observations at each level
p = 4 #number of covariates
true=list(beta = rnorm(p,3,1), phi = c(3), gamma = rnorm(I,40,1)) #true parameters
X = cbind(1,Xsim(p-1,n_i)) #simulate covariate data

#Covariance Prior to level effects:
invGam = function(phi) {
 diag(rep(1,I))/phi
} #invGam(true$phi)
#Specify logarithm of determinant of inverse Covariance matrix as a function of phi:
logdetG = function(phi) {
 -I*phi
}
modelM1=list(G=invGam,ldetG=logdetG)
Z = matrix(1,ncol=1,nrow=n) #one intercept effect for each level
designM = list(X=X,Z=Z)

dat <- genlmesim(model=modelM1,true,designM,n_i,levelnames)
lmefitM1 = simplelme(dat,levelnames,phi0=8,eps=10^-5)

## End(Not run)