saemix (version 0.96.1)

fim.saemix: Computes the Fisher Information Matrix by linearisation

Description

Estimate by linearisation the Fisher Information Matrix and the standard error of the estimated parameters.

Usage

fim.saemix(saemixObject)

Arguments

saemixObject

an object returned by the saemix function

Value

• The function returns an updated version of the object saemix.fit in which the following elements have been added: [object Object],[object Object],[object Object],[object Object],[object Object]

Details

The inverse of the Fisher Information Matrix provides an estimate of the variance of the estimated parameters theta. This matrix cannot be computed in closed-form for nonlinear mixed-effect models; instead, an approximation is obtained as the Fisher Information Matrix of the Gaussian model deduced from the nonlinear mixed effects model after linearisation of the function f around the conditional expectation of the individual Gaussian parameters. This matrix is a block matrix (no correlations between the estimated fixed effects and the estimated variances).

References

Kuhn, E., and Lavielle, M. Maximum likelihood estimation in nonlinear mixed effects models. Computational Statistics and Data Analysis 49, 4 (2005), 1020-1038. Monolix32_UsersGuide.pdf (http://software.monolix.org/sdoms/software/)

See Also

SaemixObject,saemix

Examples

# Running the main algorithm to estimate the population parameters
data(theo.saemix)

saemix.data<-saemixData(name.data=theo.saemix,header=TRUE,sep="",na=NA,
  name.group=c("Id"),name.predictors=c("Dose","Time"),
  name.response=c("Concentration"),name.covariates=c("Weight","Sex"),
  units=list(x="hr",y="mg/L",covariates=c("kg","-")), name.X="Time")

model1cpt<-function(psi,id,xidep) { 
	  dose<-xidep[,1]
	  tim<-xidep[,2]  
	  ka<-psi[id,1]
	  V<-psi[id,2]
	  CL<-psi[id,3]
	  k<-CL/V
	  ypred<-dose*ka/(V*(ka-k))*(exp(-k*tim)-exp(-ka*tim))
	  return(ypred)
}

saemix.model<-saemixModel(model=model1cpt,
  description="One-compartment model with first-order absorption", 
  psi0=matrix(c(1.,20,0.5,0.1,0,-0.01),ncol=3, byrow=TRUE,
  dimnames=list(NULL, c("ka","V","CL"))),transform.par=c(1,1,1), 
  covariate.model=matrix(c(0,1,0,0,0,0),ncol=3,byrow=TRUE),fixed.estim=c(1,1,1),
  covariance.model=matrix(c(1,0,0,0,1,0,0,0,1),ncol=3,byrow=TRUE),
  omega.init=matrix(c(1,0,0,0,1,0,0,0,1),ncol=3,byrow=TRUE), error.model="constant")

saemix.options<-list(algorithm=c(1,0,0),seed=632545,save=FALSE,save.graphs=FALSE)

saemix.fit<-saemix(saemix.model,saemix.data,saemix.options)

# Estimating the Fisher Information Matrix using the result of saemix 
# & returning the result in the same object

fim.saemix(saemix.fit)