Simulate Parameters from a Theta/Omega specification

## Usage

```
rxSimThetaOmega(
params = NULL,
omega = NULL,
omegaDf = NULL,
omegaLower = as.numeric(c(R_NegInf)),
omegaUpper = as.numeric(c(R_PosInf)),
omegaIsChol = FALSE,
omegaSeparation = "auto",
omegaXform = 1L,
nSub = 1L,
thetaMat = NULL,
thetaLower = as.numeric(c(R_NegInf)),
thetaUpper = as.numeric(c(R_PosInf)),
thetaDf = NULL,
thetaIsChol = FALSE,
nStud = 1L,
sigma = NULL,
sigmaLower = as.numeric(c(R_NegInf)),
sigmaUpper = as.numeric(c(R_PosInf)),
sigmaDf = NULL,
sigmaIsChol = FALSE,
sigmaSeparation = "auto",
sigmaXform = 1L,
nCoresRV = 1L,
nObs = 1L,
dfSub = 0,
dfObs = 0,
simSubjects = TRUE,
simVariability = as.logical(c(NA_LOGICAL))
)
```

## Arguments

- params
Named Vector of rxode2 model parameters

- omega
Estimate of Covariance matrix. When omega is a list, assume it is a block matrix and convert it to a full matrix for simulations. When

`omega`

is`NA`

and you are using it with a`rxode2`

ui model, the between subject variability described by the`omega`

matrix are set to zero.- omegaDf
The degrees of freedom of a t-distribution for simulation. By default this is

`NULL`

which is equivalent to`Inf`

degrees, or to simulate from a normal distribution instead of a t-distribution.- omegaLower
Lower bounds for simulated ETAs (by default -Inf)

- omegaUpper
Upper bounds for simulated ETAs (by default Inf)

- omegaIsChol
Indicates if the

`omega`

supplied is a Cholesky decomposed matrix instead of the traditional symmetric matrix.- omegaSeparation
Omega separation strategy

Tells the type of separation strategy when simulating covariance with parameter uncertainty with standard deviations modeled in the

`thetaMat`

matrix.`"lkj"`

simulates the correlation matrix from the`rLKJ1`

matrix with the distribution parameter`eta`

equal to the degrees of freedom`nu`

by`(nu-1)/2`

`"separation"`

simulates from the identity inverse Wishart covariance matrix with`nu`

degrees of freedom. This is then converted to a covariance matrix and augmented with the modeled standard deviations. While computationally more complex than the`"lkj"`

prior, it performs better when the covariance matrix size is greater or equal to 10`"auto"`

chooses`"lkj"`

when the dimension of the matrix is less than 10 and`"separation"`

when greater than equal to 10.

- omegaXform
When taking

`omega`

values from the`thetaMat`

simulations (using the separation strategy for covariance simulation), how should the`thetaMat`

values be turned int standard deviation values:`identity`

This is when standard deviation values are directly modeled by the`params`

and`thetaMat`

matrix`variance`

This is when the`params`

and`thetaMat`

simulates the variance that are directly modeled by the`thetaMat`

matrix`log`

This is when the`params`

and`thetaMat`

simulates`log(sd)`

`nlmixrSqrt`

This is when the`params`

and`thetaMat`

simulates the inverse cholesky decomposed matrix with the`x\^2`

modeled along the diagonal. This only works with a diagonal matrix.`nlmixrLog`

This is when the`params`

and`thetaMat`

simulates the inverse cholesky decomposed matrix with the`exp(x\^2)`

along the diagonal. This only works with a diagonal matrix.`nlmixrIdentity`

This is when the`params`

and`thetaMat`

simulates the inverse cholesky decomposed matrix. This only works with a diagonal matrix.

- nSub
Number between subject variabilities (

`ETAs`

) simulated for every realization of the parameters.- thetaMat
Named theta matrix.

- thetaLower
Lower bounds for simulated population parameter variability (by default

`-Inf`

)- thetaUpper
Upper bounds for simulated population unexplained variability (by default

`Inf`

)- thetaDf
The degrees of freedom of a t-distribution for simulation. By default this is

`NULL`

which is equivalent to`Inf`

degrees, or to simulate from a normal distribution instead of a`t`

-distribution.- thetaIsChol
Indicates if the

`theta`

supplied is a Cholesky decomposed matrix instead of the traditional symmetric matrix.- nStud
Number virtual studies to characterize uncertainty in estimated parameters.

- sigma
Named sigma covariance or Cholesky decomposition of a covariance matrix. The names of the columns indicate parameters that are simulated. These are simulated for every observation in the solved system. When

`sigma`

is`NA`

and you are using it with a`rxode2`

ui model, the unexplained variability described by the`sigma`

matrix are set to zero.- sigmaLower
Lower bounds for simulated unexplained variability (by default -Inf)

- sigmaUpper
Upper bounds for simulated unexplained variability (by default Inf)

- sigmaDf
Degrees of freedom of the sigma t-distribution. By default it is equivalent to

`Inf`

, or a normal distribution.- sigmaIsChol
Boolean indicating if the sigma is in the Cholesky decomposition instead of a symmetric covariance

- sigmaSeparation
separation strategy for sigma;

Tells the type of separation strategy when simulating covariance with parameter uncertainty with standard deviations modeled in the

`thetaMat`

matrix.`"lkj"`

simulates the correlation matrix from the`rLKJ1`

matrix with the distribution parameter`eta`

equal to the degrees of freedom`nu`

by`(nu-1)/2`

`"separation"`

simulates from the identity inverse Wishart covariance matrix with`nu`

degrees of freedom. This is then converted to a covariance matrix and augmented with the modeled standard deviations. While computationally more complex than the`"lkj"`

prior, it performs better when the covariance matrix size is greater or equal to 10`"auto"`

chooses`"lkj"`

when the dimension of the matrix is less than 10 and`"separation"`

when greater than equal to 10.

- sigmaXform
When taking

`sigma`

values from the`thetaMat`

simulations (using the separation strategy for covariance simulation), how should the`thetaMat`

values be turned int standard deviation values:`identity`

This is when standard deviation values are directly modeled by the`params`

and`thetaMat`

matrix`variance`

This is when the`params`

and`thetaMat`

simulates the variance that are directly modeled by the`thetaMat`

matrix`log`

This is when the`params`

and`thetaMat`

simulates`log(sd)`

`nlmixrSqrt`

This is when the`params`

and`thetaMat`

simulates the inverse cholesky decomposed matrix with the`x\^2`

modeled along the diagonal. This only works with a diagonal matrix.`nlmixrLog`

This is when the`params`

and`thetaMat`

simulates the inverse cholesky decomposed matrix with the`exp(x\^2)`

along the diagonal. This only works with a diagonal matrix.`nlmixrIdentity`

This is when the`params`

and`thetaMat`

simulates the inverse cholesky decomposed matrix. This only works with a diagonal matrix.

- nCoresRV
Number of cores used for the simulation of the sigma variables. By default this is 1. To reproduce the results you need to run on the same platform with the same number of cores. This is the reason this is set to be one, regardless of what the number of cores are used in threaded ODE solving.

- nObs
Number of observations to simulate (with

`sigma`

matrix)- dfSub
Degrees of freedom to sample the between subject variability matrix from the inverse Wishart distribution (scaled) or scaled inverse chi squared distribution.

- dfObs
Degrees of freedom to sample the unexplained variability matrix from the inverse Wishart distribution (scaled) or scaled inverse chi squared distribution.

- simSubjects
boolean indicated rxode2 should simulate subjects in studies (

`TRUE`

, default) or studies (`FALSE`

)- simVariability
determines if the variability is simulated. When

`NA`

(default) this is determined by the solver.