nlmixr2 defaults controls for nls

Usage

nlsControl(
  maxiter = 10000,
  tol = 1e-05,
  minFactor = 1/1024,
  printEval = FALSE,
  warnOnly = FALSE,
  scaleOffset = 0,
  nDcentral = FALSE,
  algorithm = c("LM", "default", "plinear", "port"),
  ftol = sqrt(.Machine$double.eps),
  ptol = sqrt(.Machine$double.eps),
  gtol = 0,
  diag = list(),
  epsfcn = 0,
  factor = 100,
  maxfev = integer(),
  nprint = 0,
  solveType = c("grad", "fun"),
  stickyRecalcN = 4,
  maxOdeRecalc = 5,
  odeRecalcFactor = 10^(0.5),
  eventType = c("central", "forward"),
  shiErr = (.Machine$double.eps)^(1/3),
  shi21maxFD = 20L,
  useColor = crayon::has_color(),
  printNcol = floor((getOption("width") - 23)/12),
  print = 1L,
  normType = c("rescale2", "mean", "rescale", "std", "len", "constant"),
  scaleType = c("nlmixr2", "norm", "mult", "multAdd"),
  scaleCmax = 1e+05,
  scaleCmin = 1e-05,
  scaleC = NULL,
  scaleTo = 1,
  gradTo = 1,
  trace = FALSE,
  rxControl = NULL,
  optExpression = TRUE,
  sumProd = FALSE,
  literalFix = TRUE,
  returnNls = FALSE,
  addProp = c("combined2", "combined1"),
  calcTables = TRUE,
  compress = TRUE,
  adjObf = TRUE,
  ci = 0.95,
  sigdig = 4,
  sigdigTable = NULL,
  ...
)

Arguments

maxiter

A positive integer specifying the maximum number of iterations allowed.

tol

A positive numeric value specifying the tolerance level for the relative offset convergence criterion.

minFactor

A positive numeric value specifying the minimum step-size factor allowed on any step in the iteration. The increment is calculated with a Gauss-Newton algorithm and successively halved until the residual sum of squares has been decreased or until the step-size factor has been reduced below this limit.

printEval

a logical specifying whether the number of evaluations (steps in the gradient direction taken each iteration) is printed.

warnOnly

a logical specifying whether nls() should return instead of signalling an error in the case of termination before convergence. Termination before convergence happens upon completion of maxiter iterations, in the case of a singular gradient, and in the case that the step-size factor is reduced below minFactor.

scaleOffset

a constant to be added to the denominator of the relative offset convergence criterion calculation to avoid a zero divide in the case where the fit of a model to data is very close. The default value of 0 keeps the legacy behaviour of nls(). A value such as 1 seems to work for problems of reasonable scale with very small residuals.

nDcentral

only when numerical derivatives are used: logical indicating if central differences should be employed, i.e., numericDeriv(*, central=TRUE) be used.

algorithm

character string specifying the algorithm to use. The default algorithm is a Gauss-Newton algorithm. Other possible values are "plinear" for the Golub-Pereyra algorithm for partially linear least-squares models and "port" for the ‘nl2sol’ algorithm from the Port library – see the references. Can be abbreviated.

ftol

non-negative numeric. Termination occurs when both the actual and predicted relative reductions in the sum of squares are at most ftol. Therefore, ftol measures the relative error desired in the sum of squares.

ptol

non-negative numeric. Termination occurs when the relative error between two consecutive iterates is at most ptol. Therefore, ptol measures the relative error desired in the approximate solution.

gtol

non-negative numeric. Termination occurs when the cosine of the angle between result of fn evaluation $fvec$ and any column of the Jacobian is at most gtol in absolute value. Therefore, gtol measures the orthogonality desired between the function vector and the columns of the Jacobian.

diag

a list or numeric vector containing positive entries that serve as multiplicative scale factors for the parameters. Length of diag should be equal to that of par. If not, user-provided diag is ignored and diag is internally set.

epsfcn

(used if jac is not provided) is a numeric used in determining a suitable step for the forward-difference approximation. This approximation assumes that the relative errors in the functions are of the order of epsfcn. If epsfcn is less than the machine precision, it is assumed that the relative errors in the functions are of the order of the machine precision.

factor

positive numeric, used in determining the initial step bound. This bound is set to the product of factor and the $|\code{diag}*\code{par}|$ if nonzero, or else to factor itself. In most cases factor should lie in the interval (0.1,100). 100 is a generally recommended value.

maxfev

integer; termination occurs when the number of calls to fn has reached maxfev. Note that nls.lm sets the value of maxfev to 100*(length(par) + 1) if maxfev = integer(), where par is the list or vector of parameters to be optimized.

nprint

is an integer; set nprint to be positive to enable printing of iterates

solveType

tells if `nlm` will use nlmixr2's analytical gradients when available (finite differences will be used for event-related parameters like parameters controlling lag time, duration/rate of infusion, and modeled bioavailability). This can be:

- `"hessian"` which will use the analytical gradients to create a Hessian with finite differences.

- `"gradient"` which will use the gradient and let `nlm` calculate the finite difference hessian

- `"fun"` where nlm will calculate both the finite difference gradient and the finite difference Hessian

When using nlmixr2's finite differences, the "ideal" step size for either central or forward differences are optimized for with the Shi2021 method which may give more accurate derivatives

stickyRecalcN

The number of bad ODE solves before reducing the atol/rtol for the rest of the problem.

maxOdeRecalc

Maximum number of times to reduce the ODE tolerances and try to resolve the system if there was a bad ODE solve.

odeRecalcFactor

The ODE recalculation factor when ODE solving goes bad, this is the factor the rtol/atol is reduced

eventType

Event gradient type for dosing events; Can be "central" or "forward"

shiErr

This represents the epsilon when optimizing the ideal step size for numeric differentiation using the Shi2021 method

shi21maxFD

The maximum number of steps for the optimization of the forward difference step size when using dosing events (lag time, modeled duration/rate and bioavailability)

useColor

Boolean indicating if focei can use ASCII color codes

printNcol

Number of columns to printout before wrapping parameter estimates/gradient

print

Integer representing when the outer step is printed. When this is 0 or do not print the iterations. 1 is print every function evaluation (default), 5 is print every 5 evaluations.

normType

This is the type of parameter normalization/scaling used to get the scaled initial values for nlmixr2. These are used with scaleType of.

With the exception of rescale2, these come from Feature Scaling. The rescale2 The rescaling is the same type described in the OptdesX software manual.

In general, all all scaling formula can be described by:

$$v_{scaled}$$ = ($$v_{unscaled}-C_{1}$$)/$$C_{2}$$

Where

The other data normalization approaches follow the following formula

$$v_{scaled}$$ = ($$v_{unscaled}-C_{1}$$)/$$C_{2}$$

rescale2 This scales all parameters from (-1 to 1). The relative differences between the parameters are preserved with this approach and the constants are:

$$C_{1}$$ = (max(all unscaled values)+min(all unscaled values))/2

$$C_{2}$$ = (max(all unscaled values) - min(all unscaled values))/2
rescale or min-max normalization. This rescales all parameters from (0 to 1). As in the rescale2 the relative differences are preserved. In this approach:

$$C_{1}$$ = min(all unscaled values)

$$C_{2}$$ = max(all unscaled values) - min(all unscaled values)
mean or mean normalization. This rescales to center the parameters around the mean but the parameters are from 0 to 1. In this approach:

$$C_{1}$$ = mean(all unscaled values)

$$C_{2}$$ = max(all unscaled values) - min(all unscaled values)
std or standardization. This standardizes by the mean and standard deviation. In this approach:

$$C_{1}$$ = mean(all unscaled values)

$$C_{2}$$ = sd(all unscaled values)
len or unit length scaling. This scales the parameters to the unit length. For this approach we use the Euclidean length, that is:

$$C_{1}$$ = 0

$$C_{2}$$ = $$\sqrt(v_1^2 + v_2^2 + \cdots + v_n^2)$$
constant which does not perform data normalization. That is

$$C_{1}$$ = 0

$$C_{2}$$ = 1

scaleType

The scaling scheme for nlmixr2. The supported types are:

nlmixr2 In this approach the scaling is performed by the following equation:

$$v_{scaled}$$ = ($$v_{current} - v_{init}$$)*scaleC[i] + scaleTo

The scaleTo parameter is specified by the normType, and the scales are specified by scaleC.
norm This approach uses the simple scaling provided by the normType argument.
mult This approach does not use the data normalization provided by normType, but rather uses multiplicative scaling to a constant provided by the scaleTo argument.

In this case:

$$v_{scaled}$$ = $$v_{current}$$/$$v_{init}$$*scaleTo
multAdd This approach changes the scaling based on the parameter being specified. If a parameter is defined in an exponential block (ie exp(theta)), then it is scaled on a linearly, that is:

$$v_{scaled}$$ = ($$v_{current}-v_{init}$$) + scaleTo

Otherwise the parameter is scaled multiplicatively.

$$v_{scaled}$$ = $$v_{current}$$/$$v_{init}$$*scaleTo

scaleCmax

Maximum value of the scaleC to prevent overflow.

scaleCmin

Minimum value of the scaleC to prevent underflow.

scaleC

The scaling constant used with scaleType=nlmixr2. When not specified, it is based on the type of parameter that is estimated. The idea is to keep the derivatives similar on a log scale to have similar gradient sizes. Hence parameters like log(exp(theta)) would have a scaling factor of 1 and log(theta) would have a scaling factor of ini_value (to scale by 1/value; ie d/dt(log(ini_value)) = 1/ini_value or scaleC=ini_value)

For parameters in an exponential (ie exp(theta)) or parameters specifying powers, boxCox or yeoJohnson transformations , this is 1.
For additive, proportional, lognormal error structures, these are given by 0.5*abs(initial_estimate)
Factorials are scaled by abs(1/digamma(initial_estimate+1))
parameters in a log scale (ie log(theta)) are transformed by log(abs(initial_estimate))*abs(initial_estimate)

These parameter scaling coefficients are chose to try to keep similar slopes among parameters. That is they all follow the slopes approximately on a log-scale.

While these are chosen in a logical manner, they may not always apply. You can specify each parameters scaling factor by this parameter if you wish.

scaleTo

Scale the initial parameter estimate to this value. By default this is 1. When zero or below, no scaling is performed.

gradTo

this is the factor that the gradient is scaled to before optimizing. This only works with scaleType="nlmixr2".

trace

logical value indicating if a trace of the iteration progress should be printed. Default is FALSE. If TRUE the residual (weighted) sum-of-squares, the convergence criterion and the parameter values are printed at the conclusion of each iteration. Note that format() is used, so these mostly depend on getOption("digits"). When the "plinear" algorithm is used, the conditional estimates of the linear parameters are printed after the nonlinear parameters. When the "port" algorithm is used the objective function value printed is half the residual (weighted) sum-of-squares.

rxControl

`rxode2` ODE solving options during fitting, created with `rxControl()`

optExpression

Optimize the rxode2 expression to speed up calculation. By default this is turned on.

sumProd

Is a boolean indicating if the model should change multiplication to high precision multiplication and sums to high precision sums using the PreciseSums package. By default this is FALSE.

literalFix

boolean, substitute fixed population values as literals and re-adjust ui and parameter estimates after optimization; Default is `TRUE`.

returnNls

logical; when TRUE, will return the nls object instead of the nlmixr object

addProp

specifies the type of additive plus proportional errors, the one where standard deviations add (combined1) or the type where the variances add (combined2).

The combined1 error type can be described by the following equation:

$$y = f + (a + b\times f^c) \times \varepsilon$$

The combined2 error model can be described by the following equation:

$$y = f + \sqrt{a^2 + b^2\times f^{2\times c}} \times \varepsilon$$

Where:

- y represents the observed value

- f represents the predicted value

- a is the additive standard deviation

- b is the proportional/power standard deviation

- c is the power exponent (in the proportional case c=1)

calcTables

This boolean is to determine if the foceiFit will calculate tables. By default this is TRUE

compress

Should the object have compressed items

adjObf

is a boolean to indicate if the objective function should be adjusted to be closer to NONMEM's default objective function. By default this is TRUE

ci

Confidence level for some tables. By default this is 0.95 or 95% confidence.

sigdig

Optimization significant digits. This controls:

The tolerance of the inner and outer optimization is 10^-sigdig
The tolerance of the ODE solvers is 0.5*10^(-sigdig-2); For the sensitivity equations and steady-state solutions the default is 0.5*10^(-sigdig-1.5) (sensitivity changes only applicable for liblsoda)
The tolerance of the boundary check is 5 * 10 ^ (-sigdig + 1)

sigdigTable

Significant digits in the final output table. If not specified, then it matches the significant digits in the `sigdig` optimization algorithm. If `sigdig` is NULL, use 3.

...

Additional optional arguments. None are used at present.

Value

nls control object

Author

Matthew L. Fidler

Examples

# \donttest{

if (rxode2::.linCmtSensB()) {

one.cmt <- function() {
  ini({
   tka <- 0.45
   tcl <- log(c(0, 2.7, 100))
   tv <- 3.45
   add.sd <- 0.7
 })
 model({
   ka <- exp(tka)
   cl <- exp(tcl)
   v <- exp(tv)
   linCmt() ~ add(add.sd)
 })
}

# Uses nlsLM from minpack.lm if available

fit1 <- nlmixr(one.cmt, nlmixr2data::theo_sd, est="nls", nlsControl(algorithm="LM"))

# Uses port and respect parameter boundaries
fit2 <- nlmixr(one.cmt, nlmixr2data::theo_sd, est="nls", nlsControl(algorithm="port"))

# You can access the underlying nls object with `$nls`
fit2$nls
}
#>  
#>  
#>  
#>  
#> ℹ parameter labels from comments are typically ignored in non-interactive mode
#> ℹ Need to run with the source intact to parse comments
#> → loading into symengine environment...
#> → pruning branches (`if`/`else`) of nls model...
#> ✔ done
#> → calculate jacobian
#> → calculate ∂(f)/∂(θ)
#> → finding duplicate expressions in nls gradient...
#> → optimizing duplicate expressions in nls gradient...
#> → finding duplicate expressions in nls pred-only...
#>  
#>  
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  
#>  
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#> → calculating covariance
#> ✔ done
#> → loading into symengine environment...
#> → pruning branches (`if`/`else`) of full model...
#> ✔ done
#> → finding duplicate expressions in EBE model...
#> → optimizing duplicate expressions in EBE model...
#> → compiling EBE model...
#>  
#>  
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#> ✔ done
#> → Calculating residuals/tables
#> ✔ done
#> → compress origData in nlmixr2 object, save 5952
#> → compress parHistData in nlmixr2 object, save 2320
#>  
#>  
#>  
#>  
#> ℹ parameter labels from comments are typically ignored in non-interactive mode
#> ℹ Need to run with the source intact to parse comments
#> → loading into symengine environment...
#> → pruning branches (`if`/`else`) of nls model...
#> ✔ done
#> → calculate jacobian
#> → calculate ∂(f)/∂(θ)
#> → finding duplicate expressions in nls gradient...
#> → optimizing duplicate expressions in nls gradient...
#> → finding duplicate expressions in nls pred-only...
#>  
#>  
#>  
#>  
#> → loading into symengine environment...
#> → pruning branches (`if`/`else`) of full model...
#> ✔ done
#> → finding duplicate expressions in EBE model...
#> → optimizing duplicate expressions in EBE model...
#> → compiling EBE model...
#>  
#>  
#> ✔ done
#> → Calculating residuals/tables
#> ✔ done
#> → compress origData in nlmixr2 object, save 5952
#> → compress parHistData in nlmixr2 object, save 2296
#> Nonlinear regression model
#>   model: 0 ~ nlmixr2est::.nlmixrNlsFunValGrad(DV, tka, tcl, tv)
#>    data: nlmixr2est::.nlmixrNlsData()
#>     tka     tcl      tv 
#> -1.0097 -0.6696  1.0423 
#>  residual sum-of-squares: 249.7
#> 
#> Algorithm "port", convergence message: relative convergence (4)
# }