# llis.saemix: Log-likelihood using Importance Sampling In belhal/saemix: Stochastic Approximation Expectation Maximization (SAEM) Algorithm

## Description

Estimate the log-likelihood using Importance Sampling

## Usage

 `1` ```llis.saemix(saemixObject) ```

## Arguments

 `saemixObject` an object returned by the `saemix` function

## Details

The likelihood of the observations is estimated without any approximation using a Monte-Carlo approach (see documentation).

## Value

the log-likelihood estimated by Importance Sampling

## Author(s)

Emmanuelle Comets <[email protected]>, Audrey Lavenu, Marc Lavielle.

## References

Kuhn E, Lavielle M. Maximum likelihood estimation in nonlinear mixed effects models. Computational Statistics and Data Analysis 49, 4 (2005), 1020-1038.

Comets E, Lavenu A, Lavielle M. SAEMIX, an R version of the SAEM algorithm. 20th meeting of the Population Approach Group in Europe, Athens, Greece (2011), Abstr 2173.

`SaemixObject`,`saemix`,`llgq.saemix`
 ``` 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 30 31 32 33 34``` ``` # 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) # Not run (strict time constraints for CRAN) # saemix.fit<-saemix(saemix.model,saemix.data,saemix.options) # Estimating the likelihood by importance sampling using the result of saemix # & returning the result in the same object # saemix.fit<-llis.saemix(saemix.fit) ```