# fim.saemix: Computes the Fisher Information Matrix by linearisation In belhal/saemix: Stochastic Approximation Expectation Maximization (SAEM) Algorithm

## Description

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

## Usage

 `1` ```fim.saemix(saemixObject) ```

## Arguments

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

## 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).

## Value

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

se.fixed:

standard error of fixed effects, obtained as part of the diagonal of the inverse of the Fisher Information Matrix (only when fim.saemix has been run, or when the saemix.options\$algorithms[2] is 1)

se.omega:

standard error of the variance of random effects, obtained as part of the diagonal of the inverse of the Fisher Information Matrix (only when fim.saemix has been run, or when the saemix.options\$algorithms[2] is 1)

se.res:

standard error of the parameters of the residual error model, obtained as part of the diagonal of the inverse of the Fisher Information Matrix (only when fim.saemix has been run, or when the saemix.options\$algorithms[2] is 1)

fim:

Fisher Information Matrix

ll.lin:

likelihood calculated by linearisation

## 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`
 ``` 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 35 36``` ``` # 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 Fisher Information Matrix using the result of saemix # & returning the result in the same object # fim.saemix(saemix.fit) ```