# llgq.saemix: Log-likelihood using Gaussian Quadrature In saemix: Stochastic Approximation Expectation Maximization (SAEM) Algorithm

 llgq.saemix R Documentation

## Log-likelihood using Gaussian Quadrature

### Description

Estimate the log-likelihood using Gaussian Quadrature (multidimensional grid)

### Usage

```llgq.saemix(saemixObject)
```

### Arguments

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

### Details

The likelihood of the observations is estimated using Gaussian Quadrature (see documentation).

### Value

the log-likelihood estimated by Gaussian Quadrature

### Author(s)

Emmanuelle Comets emmanuelle.comets@inserm.fr, Audrey Lavenu, Marc Lavielle.

### References

E Comets, A Lavenu, M Lavielle M (2017). Parameter estimation in nonlinear mixed effect models using saemix, an R implementation of the SAEM algorithm. Journal of Statistical Software, 80(3):1-41.

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

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

### See Also

`SaemixObject`,`saemix`,`llis.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(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 Gaussian Quadrature using the result of saemix
# & returning the result in the same object
# saemix.fit<-llgq.saemix(saemix.fit)

```

saemix documentation built on Aug. 5, 2022, 5:25 p.m.