Control Options for FOCEi

Usage

foceiControl(
  sigdig = 4,
  ...,
  epsilon = NULL,
  maxInnerIterations = 1000,
  maxOuterIterations = 5000,
  n1qn1nsim = NULL,
  print = 1L,
  printNcol = NULL,
  scaleTo = 1,
  scaleObjective = 0,
  normType = c("rescale2", "mean", "rescale", "std", "len", "constant"),
  scaleType = c("nlmixr2", "norm", "mult", "multAdd"),
  scaleCmax = 1e+05,
  scaleCmin = 1e-05,
  scaleC = NULL,
  scaleC0 = 1e+05,
  derivEps = rep(20 * sqrt(.Machine$double.eps), 2),
  derivMethod = c("switch", "forward", "central"),
  derivSwitchTol = NULL,
  covDerivMethod = c("central", "forward"),
  covMethod = c("r,s", "r", "s", ""),
  hessEps = (.Machine$double.eps)^(1/3),
  hessEpsLlik = (.Machine$double.eps)^(1/3),
  optimHessType = c("central", "forward"),
  optimHessCovType = c("central", "forward"),
  eventType = c("central", "forward"),
  centralDerivEps = rep(20 * sqrt(.Machine$double.eps), 2),
  lbfgsLmm = 7L,
  lbfgsPgtol = 0,
  lbfgsFactr = NULL,
  eigen = TRUE,
  diagXform = c("sqrt", "log", "identity"),
  iovXform = c("sd", "var", "logsd", "logvar"),
  sumProd = FALSE,
  optExpression = TRUE,
  literalFix = TRUE,
  literalFixRes = TRUE,
  ci = 0.95,
  useColor = NULL,
  boundTol = NULL,
  calcTables = TRUE,
  noAbort = TRUE,
  interaction = TRUE,
  cholSEtol = (.Machine$double.eps)^(1/3),
  cholAccept = 0.001,
  resetEtaP = 0.15,
  resetThetaP = 0.05,
  resetThetaFinalP = 0.15,
  diagOmegaBoundUpper = 5,
  diagOmegaBoundLower = 100,
  cholSEOpt = FALSE,
  cholSECov = FALSE,
  fo = FALSE,
  covTryHarder = FALSE,
  outerOpt = c("lbfgsb3c", "nlminb", "bobyqa", "L-BFGS-B", "mma", "lbfgsbLG", "slsqp",
    "Rvmmin", "uobyqa", "newuoa"),
  innerOpt = c("n1qn1", "BFGS"),
  rhobeg = 0.2,
  rhoend = NULL,
  npt = NULL,
  rel.tol = NULL,
  x.tol = NULL,
  eval.max = 4000,
  iter.max = 2000,
  abstol = NULL,
  reltol = NULL,
  resetHessianAndEta = FALSE,
  muModel = c("none", "irls", "lin"),
  muRefCovAlg = TRUE,
  muModelTol = 0.001,
  muModelMaxCycles = 10L,
  stateTrim = Inf,
  shi21maxOuter = 0L,
  shi21maxInner = 20L,
  shi21maxInnerCov = 20L,
  shi21maxFD = 20L,
  gillK = 10L,
  gillStep = 4,
  gillFtol = 0,
  gillRtol = sqrt(.Machine$double.eps),
  gillKcov = 10L,
  gillKcovLlik = 10L,
  gillStepCovLlik = 4.5,
  gillStepCov = 2,
  gillFtolCov = 0,
  gillFtolCovLlik = 0,
  rmatNorm = TRUE,
  rmatNormLlik = TRUE,
  smatNorm = TRUE,
  smatNormLlik = TRUE,
  covGillF = TRUE,
  optGillF = TRUE,
  covSmall = 1e-05,
  adjLik = TRUE,
  gradTrim = Inf,
  maxOdeRecalc = 5,
  odeRecalcFactor = 10^(0.5),
  gradCalcCentralSmall = 1e-04,
  gradCalcCentralLarge = 10000,
  etaNudge = qnorm(1 - 0.05/2)/sqrt(3),
  etaNudge2 = qnorm(1 - 0.05/2) * sqrt(3/5),
  nRetries = 3,
  seed = 42,
  resetThetaCheckPer = 0.1,
  etaMat = NULL,
  repeatGillMax = 1,
  stickyRecalcN = 4,
  indTolRelax = TRUE,
  gradProgressOfvTime = 10,
  addProp = c("combined2", "combined1"),
  badSolveObjfAdj = 100,
  compress = FALSE,
  rxControl = NULL,
  sigdigTable = NULL,
  fallbackFD = FALSE,
  smatPer = 0.6,
  sdLowerFact = 0.001,
  zeroGradFirstReset = TRUE,
  zeroGradRunReset = TRUE,
  zeroGradBobyqa = TRUE,
  mceta = -1L,
  nAGQ = 0,
  agqLow = -Inf,
  agqHi = Inf,
  eventSens = c("jump", "fd"),
  boundedTransform = TRUE
)

Arguments

sigdig

Optimization significant digits; controls the inner/outer optimization tolerance (10^-sigdig), ODE solver tolerance (0.5*10^(-sigdig-2), or 0.5*10^(-sigdig-1.5) for sensitivity/steady-state with liblsoda), and boundary check tolerance (5*10^(-sigdig+1)).

...

Ignored parameters

epsilon

Precision of estimate for n1qn1 optimization.

maxInnerIterations

Number of iterations for n1qn1 optimization.

maxOuterIterations

Maximum number of L-BFGS-B optimization for outer problem.

n1qn1nsim

Number of function evaluations for n1qn1 optimization.

print

Either a scalar print-frequency (`0` = suppress, `1` (default) = every evaluation, `N` = every Nth), OR a pre-built [iterPrintControl()] object. Equivalent to `iterPrintControl(every = print, ncol = printNcol, useColor = useColor)`.

printNcol

Integer (or `NULL`) parameter columns per row before wrapping. `NULL` (default) uses `floor((getOption("width") - 23) / 12)`.

scaleTo

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

scaleObjective

Scale the initial objective function to this value. By default this is 0 (meaning do not scale)

normType

Parameter normalization/scaling used to get scaled initial values for scaleType, of the form Vscaled = (Vunscaled-C1)/C2 (see Feature Scaling; rescale2 follows the OptdesX manual): "rescale2" scales all parameters to (-1, 1); "rescale" (min-max) scales to (0, 1); "mean" centers on the mean with range (0, 1); "std" standardizes by mean/sd; "len" scales to unit (Euclidean) length; "constant" performs no normalization (C1=0, C2=1).

scaleType

The scaling scheme for nlmixr2: "nlmixr2" (default) scales as (current-init)*scaleC[i] + scaleTo, with scaleTo from normType and scales from scaleC; "norm" uses the simple scaling from normType; "mult" scales multiplicatively as current/init*scaleTo; "multAdd" scales linearly ((current-init)+scaleTo) for parameters in an exponential block (e.g. exp(theta)) and multiplicatively otherwise.

scaleCmax

Maximum value of the scaleC to prevent overflow.

scaleCmin

Minimum value of the scaleC to prevent underflow.

scaleC

Scaling constant used with scaleType="nlmixr2"; when not specified, chosen by parameter type to keep gradient sizes similar on a log scale: `1` for exp()-transformed/power/boxCox/ yeoJohnson parameters, `0.5*abs(est)` for additive/proportional/ lognormal error parameters, `abs(1/digamma(est+1))` for factorials, and `log(abs(est))*abs(est)` for log-scale parameters. May be set explicitly per parameter if these defaults don't apply well.

scaleC0

Number to adjust the scaling factor by if the initial gradient is zero.

derivEps

Forward difference tolerances (relative, absolute); step size h = abs(x)*derivEps[1] + derivEps[2].

derivMethod

Derivative method for the outer problem: "switch", "central", or "forward". "switch" starts forward and toggles to central when abs(delta(OFV)) <= derivSwitchTol.

derivSwitchTol

The tolerance to switch forward to central differences.

covDerivMethod

indicates the method for calculating the derivatives while calculating the covariance components (Hessian and S).

covMethod

Method for calculating covariance, where R is the Hessian and S the sum of individual gradient cross-products (at the empirical Bayes estimates): "r,s" sandwich (solve(R)%*%S%*%solve(R)), "r" Hessian-based (2%*%solve(R)), "s" cross-product-based (4%*%solve(S)), or "" to skip the covariance step.

hessEps

is a double value representing the epsilon for the Hessian calculation. This is used for the R matrix calculation.

hessEpsLlik

is a double value representing the epsilon for the Hessian calculation when doing focei generalized log-likelihood estimation. This is used for the R matrix calculation.

optimHessType

Hessian type for numeric-difference individual Hessians in generalized log-likelihood estimation: "central" (matches R's `optimHess()`, default) or "forward" (faster).

optimHessCovType

Hessian type for numeric-difference individual Hessians used for the covariance step/final likelihood: "central" (more accurate, used here) or "forward".

eventType

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

centralDerivEps

Central difference tolerances (relative, absolute); step size h = abs(x)*derivEps[1] + derivEps[2].

lbfgsLmm

An integer giving the number of BFGS updates retained in the "L-BFGS-B" method, It defaults to 7.

lbfgsPgtol

Projected-gradient convergence tolerance for "L-BFGS-B": iteration stops when max(| proj g_i |) <= lbfgsPgtol. Defaults to `0` (check suppressed).

lbfgsFactr

Convergence factor for "L-BFGS-B": converges when the objective reduction is within lbfgsFactr * .Machine$double.eps. Default `1e10` (~4 sigdigs, 2e-6).

eigen

A boolean indicating if eigenvectors are calculated to include a condition number calculation.

diagXform

Transformation used on the diagonal of chol(solve(omega)) (the FOCEi-estimated parameters): one of "sqrt" (default), "log", or "identity".

iovXform

Transformation used on the diagonal of the IOV: one of "sd", "var", "logsd", or "logvar".

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.

optExpression

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

literalFix

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

literalFixRes

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

ci

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

useColor

Logical (or `NULL`) emit ANSI bold/color escapes in the iteration print. `NULL` (default) defers to [crayon::has_color()].

boundTol

Tolerance for boundary issues.

calcTables

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

noAbort

Boolean to indicate if you should abort the FOCEi evaluation if it runs into troubles. (default TRUE)

interaction

Boolean indicate FOCEi should be used (TRUE) instead of FOCE (FALSE)

cholSEtol

tolerance for Generalized Cholesky Decomposition. Defaults to suggested (.Machine$double.eps)^(1/3)

cholAccept

Tolerance to accept a Generalized Cholesky Decomposition for a R or S matrix.

resetEtaP

P-value for resetting an individual ETA to 0 during optimization, based on a z-test of chol(omega^-1) %*% eta or eta/sd(allEtas). `0` = never reset, `1` = always reset.

resetThetaP

P-value for resetting mu-referenced THETAs based on ETA drift, checked at the start and near a local minimum (see resetThetaCheckPer). `0` = never reset; `1` is not allowed.

resetThetaFinalP

represents the p-value for reseting the population mu-referenced THETA parameters based on ETA drift during optimization, and resetting the optimization one final time.

diagOmegaBoundUpper

Upper bound of the diagonal omega matrix, as diag(omega)*diagOmegaBoundUpper. `1` = no upper bound.

diagOmegaBoundLower

Lower bound of the diagonal omega matrix, as diag(omega)/diagOmegaBoundLower. `1` = no lower bound.

cholSEOpt

Boolean indicating if the generalized Cholesky should be used while optimizing.

cholSECov

Boolean indicating if the generalized Cholesky should be used while calculating the Covariance Matrix.

fo

is a boolean indicating if this is a FO approximation routine.

covTryHarder

If the R matrix is non-positive definite and cannot be corrected to be non-positive definite try estimating the Hessian on the unscaled parameter space.

outerOpt

optimization method for the outer problem

innerOpt

optimization method for the inner problem (not implemented yet.)

rhobeg

Initial trust region radius for the bobyqa outer optimizer (with `rhoend`, must satisfy `0 < rhoend < rhobeg`). Default `0.2` (20 `abs(upper-lower)/2`. (bobyqa)

rhoend

Final trust region radius. If not defined, `10^(-sigdig-1)` is used. (bobyqa)

npt

Number of points for bobyqa's quadratic approximation to the objective; must be in `[n+2, (n+1)(n+2)/2]`. Defaults to `2*n + 1`. (bobyqa)

rel.tol

Relative tolerance before nlminb stops (nlmimb).

x.tol

X tolerance for nlmixr2 optimizer

eval.max

Number of maximum evaluations of the objective function (nlmimb)

iter.max

Maximum number of iterations allowed (nlmimb)

abstol

Absolute tolerance for nlmixr2 optimizer (BFGS)

reltol

tolerance for nlmixr2 (BFGS)

resetHessianAndEta

is a boolean representing if the individual Hessian is reset when ETAs are reset using the option resetEtaP.

muModel

Selects the mu-referenced-FOCEI-family regression variant for theta/eta in a mu-ref covariate relationship (see muRefCovAlg): "none" (default, ordinary FOCEI); "lin" (mufocei/mufoce/muagq/ mulaplace: population theta and covariate coefficient(s) per mu-ref-covariate group are excluded from the outer optimizer and re-derived in C++ by closed-form OLS regression of each subject's back-calculated value on the covariate(s), residual becomes that subject's eta; repeats until convergence, see muModelTol/ muModelMaxCycles); or "irls" (irlsfocei/irlsfoce/irlsagq/irlslaplace: same mechanism, reweighted by inner-optimization curvature).

A mu-ref-covariate theta with a finite bound falls back to ordinary bounded outer-optimizer handling with a warning (a bound on the group's population theta excludes the whole group; a bound on one covariate coefficient excludes only that covariate).

muRefCovAlg

When `TRUE` (default), algebraic expressions that can be mu-referenced are internally rewritten as mu-referenced covariates and restored after optimization. Mirrors saemControl(muRefCovAlg=)/nlmeControl(muRefCovAlg=); for foceiControl() only takes effect when muModel != "none".

muModelTol

Convergence tolerance for the mu-referenced-FOCEI-family "re-optimize etas, then regress" cycle (muModel != "none"): repeats until the max mu-group theta change drops below this value or muModelMaxCycles is reached.

muModelMaxCycles

Maximum number of "re-optimize etas, regress" cycles per outer iteration (see muModel, muModelTol).

stateTrim

Trim state amounts/concentrations to this value.

shi21maxOuter

The maximum number of steps for the optimization of the forward-difference step size. When not zero, use this instead of Gill differences.

shi21maxInner

The maximum number of steps for the optimization of the individual Hessian matrices in the generalized likelihood problem. When 0, un-optimized finite differences are used.

shi21maxInnerCov

The maximum number of steps for the optimization of the individual Hessian matrices in the generalized likelihood problem for the covariance step. When 0, un-optimized finite differences are used.

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)

gillK

Max steps to determine the optimal forward/central difference step size per parameter (Gill 1983). `0` = no optimal step size determined.

gillStep

When looking for the optimal forward difference step size, this is This is the step size to increase the initial estimate by. So each iteration the new step size = (prior step size)*gillStep

gillFtol

The gillFtol is the gradient error tolerance that is acceptable before issuing a warning/error about the gradient estimates.

gillRtol

The relative tolerance used for Gill 1983 determination of optimal step size.

gillKcov

Max steps to determine the optimal forward/central difference step size per parameter (Gill 1983) during the covariance step. `0` = no optimal step size determined.

gillKcovLlik

Same as gillK but for the generalized focei log-likelihood method (Gill 1986).

gillStepCovLlik

Same as above but during generalized focei log-likelihood

gillStepCov

When looking for the optimal forward difference step size, this is This is the step size to increase the initial estimate by. So each iteration during the covariance step is equal to the new step size = (prior step size)*gillStepCov

gillFtolCov

The gillFtol is the gradient error tolerance that is acceptable before issuing a warning/error about the gradient estimates during the covariance step.

gillFtolCovLlik

Same as above but applied during generalized log-likelihood estimation.

rmatNorm

A parameter to normalize gradient step size by the parameter value during the calculation of the R matrix

rmatNormLlik

A parameter to normalize gradient step size by the parameter value during the calculation of the R matrix if you are using generalized log-likelihood Hessian matrix.

smatNorm

A parameter to normalize gradient step size by the parameter value during the calculation of the S matrix

smatNormLlik

A parameter to normalize gradient step size by the parameter value during the calculation of the S matrix if you are using the generalized log-likelihood.

covGillF

Use the Gill calculated optimal Forward difference step size for the instead of the central difference step size during the central difference gradient calculation.

optGillF

Use the Gill calculated optimal Forward difference step size for the instead of the central difference step size during the central differences for optimization.

covSmall

Small number used to compare covariance estimates (sandwich vs R/S matrix) before rejecting one as too small to be the final covariance estimate.

adjLik

When `TRUE`, adjusts the likelihood by the 2*pi constant nlmixr2's objective function otherwise omits (to match NONMEM), more closely matching nlme/SAS likelihood approximations. The objective function itself always matches NONMEM regardless.

gradTrim

The parameter to adjust the gradient to if the |gradient| is very large.

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

gradCalcCentralSmall

A small number that represents the value where |grad| < gradCalcCentralSmall where forward differences switch to central differences.

gradCalcCentralLarge

A large number that represents the value where |grad| > gradCalcCentralLarge where forward differences switch to central differences.

etaNudge

When n1qn1 optimization of an ETA (starting at zero) misbehaves, reset the Hessian and nudge the ETA up by this value, then down if it still doesn't move. Defaults to `qnorm(1-0.05/2)*1/sqrt(3)`. Falls back to etaNudge2, then to zero (stop optimizing) if unsuccessful.

etaNudge2

This is the second eta nudge. By default it is qnorm(1-0.05/2)*sqrt(3/5), which is the n=3 quadrature point (excluding zero) times by the 0.95% normal region

nRetries

If FOCEi doesn't fit with the current parameter estimates, randomly sample new parameter estimates and restart the problem. This is similar to 'PsN' resampling.

seed

an object specifying if and how the random number generator should be initialized

resetThetaCheckPer

represents objective function % percentage below which resetThetaP is checked.

etaMat

Initial (or final) ETA estimates; can also be a prior fit, whose final ETAs are then used as initial values. By default, uses the last fit's ETAs if supplied, else all ETAs start at zero (`NULL`). `NA` disables reuse from a prior fit.

repeatGillMax

If the tolerances were reduced when calculating the initial Gill differences, the Gill difference is repeated up to a maximum number of times defined by this parameter.

stickyRecalcN

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

indTolRelax

When `TRUE` (default), only subjects whose ODE solve produced NaN/Inf have their tolerances relaxed, and the relaxed tolerance persists across optimizer calls (sticky). When `FALSE`, all subjects have their tolerances relaxed on each retry and tolerances are reset afterward.

gradProgressOfvTime

This is the time for a single objective function evaluation (in seconds) to start progress bars on gradient evaluations

addProp

Type of additive-plus-proportional error: `"combined1"`, where standard deviations add: $$y = f + (a + b\times f^c) \times \varepsilon$$; or `"combined2"`, where variances add: $$y = f + \sqrt{a^2 + b^2\times f^{2\times c}} \times \varepsilon$$. Here y = observed, f = predicted, a = additive sd, b = proportional/power sd, c = power exponent (1 in the proportional case).

badSolveObjfAdj

The objective function adjustment when the ODE system cannot be solved. It is based on each individual bad solve.

compress

Should the object have compressed items

rxControl

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

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.

fallbackFD

Fallback to the finite differences if the sensitivity equations do not solve.

smatPer

Percentage of failed per-individual parameter gradients (replaced with the overall parameter gradient) out of the total (`ntheta*nsub`) above which the S matrix is considered bad.

sdLowerFact

Factor multiplying the estimate when the lower bound is zero for a standard-deviation error parameter (add.sd, prop.sd, etc); e.g. estimate 0.15 with lower bound 0 assumes a lower bound of 0.00015. `0` disables this.

zeroGradFirstReset

When `TRUE` (default), reset a zero first gradient to `sqrt(.Machine$double.eps)` instead of erroring; `FALSE` errors; `NA` ignores it only on the last reset attempt.

zeroGradRunReset

When `TRUE` (default), reset a zero gradient encountered mid-run to `sqrt(.Machine$double.eps)` instead of erroring.

zeroGradBobyqa

When `TRUE` (default), a zero-gradient reset switches to the gradient-free bobyqa method; `NA` only does so for the first zero gradient.

mceta

Monte Carlo sampling for the best initial ETA estimate (based on `omega`): `-1` (default) uses the last eta; `0` uses eta=0 for each inner optimization; for `n>0`, the last eta, eta=0, and n-1 etas sampled from omega are each evaluated and the best (by inner objective) is used.

nAGQ

Number of Gauss-Hermite adaptive quadrature points. `0` disables AGQ; `1` is equivalent to Laplace. Cost grows quickly with ETAs: once the EBE is found, expect `nAGQ^neta` (even `nAGQ`) or `(nAGQ^neta)-1` (odd `nAGQ`) additional evaluations per subject.

agqLow

The lower bound for adaptive quadrature log-likelihood. By default this is -Inf; in the original nlmixr's gnlmm it was -700.

agqHi

The upper bound for adaptive quadrature log-likelihood. By default this is Inf; in the original nlmixr's gnlmm was 400.

eventSens

Controls how dosing/event-parameter (`alag`, `F`, `rate`, `dur`) sensitivities are computed for THETA/ETA gradients: `"jump"` (default) uses rxode2's analytic event sensitivities; `"fd"` uses the legacy finite-difference behavior.

boundedTransform

When `TRUE` (default), bounded parameters are transformed for unbounded optimization methods and back-transformed for final estimates. `FALSE` optimizes on the original scale with bounds passed to the optimizer. `NA` transforms for optimization but skips the final back-transform.

Value

The control object that changes the options for the FOCEi family of estimation methods

Details

Uses R's L-BFGS-B (optim) for the outer problem and BFGS n1qn1 (restoring the prior individual Hessian) for the inner problem, which is left unscaled since eta estimates start near zero. The covariance step is performed on the unscaled problem, so its condition number may differ from the scaled problem's.

References

Gill, P.E., Murray, W., Saunders, M.A., & Wright, M.H. (1983). Computing Forward-Difference Intervals for Numerical Optimization. Siam Journal on Scientific and Statistical Computing, 4, 310-321.

Shi, H.M., Xie, Y., Xuan, M.Q., & Nocedal, J. (2021). Adaptive Finite-Difference Interval Estimation for Noisy Derivative-Free Optimization.

Author

Matthew L. Fidler