Control Options for SAEM

Usage

saemControl(
  seed = 99,
  nBurn = 200,
  nEm = 300,
  nmc = 3,
  nu = c(2, 2, 2),
  print = 1L,
  trace = 0,
  covMethod = c("linFim", "fim", "sa", "r,s", "r", "s", ""),
  covFull = TRUE,
  nSaCov = 500L,
  calcTables = TRUE,
  logLik = FALSE,
  nnodesGq = 3,
  nsdGq = 1.6,
  optExpression = TRUE,
  literalFix = FALSE,
  adjObf = TRUE,
  sumProd = FALSE,
  addProp = c("combined2", "combined1"),
  tol = 1e-06,
  itmax = 30,
  type = c("newuoa", "nelder-mead"),
  powRange = 10,
  lambdaRange = 3,
  odeRecalcFactor = 10^(0.5),
  maxOdeRecalc = 5L,
  indTolRelax = TRUE,
  perSa = 0.75,
  perNoCor = 0.75,
  perFixOmega = 0.1,
  perFixResid = 0.1,
  compress = TRUE,
  rxControl = NULL,
  sigdig = NULL,
  sigdigTable = NULL,
  ci = 0.95,
  muRefCov = TRUE,
  muRefCovAlg = TRUE,
  handleUninformativeEtas = TRUE,
  iovXform = c("sd", "var", "logsd", "logvar"),
  boundedTransform = TRUE,
  eventSens = c("jump", "fd"),
  mixProbMethod = c("regularized", "annealed"),
  mixProbStepExp = 1,
  mixProbPriorN = 20,
  mixSampleMethod = c("parallel", "msaem"),
  censOption = c("gauss", "laplace"),
  fast = FALSE,
  fastKernel = c("firstN", "throughout", "additive"),
  fastCov = c("auto", "jacobian", "hessian"),
  fastIter = 20L,
  fastLik = c("focei", "foce", "focep"),
  lbfgsLmm = 5L,
  lbfgsFactr = NULL,
  lbfgsPgtol = NULL,
  lbfgsMaxIter = 20L,
  nRetry = 10L,
  ...
)

Arguments

seed

Random Seed for SAEM step. (Needs to be set for reproducibility.) By default this is 99.

nBurn

Number of iterations in the first phase, ie the MCMC/Stochastic Approximation steps. This is equivalent to Monolix's K_0 or K_b.

nEm

Number of iterations in the Expectation-Maximization (EM) Step. This is equivalent to Monolix's K_1.

nmc

Number of Markov Chains. By default this is 3. When you increase the number of chains the numerical integration by MC method will be more accurate at the cost of more computation. In Monolix this is equivalent to L.

nu

This is a vector of 3 integers. They represent the numbers of transitions of the three different kernels used in the Hasting-Metropolis algorithm. The default value is c(2,2,2), representing 40 for each transition initially (each value is multiplied by 20).

The first value represents the initial number of multi-variate Gibbs samples are taken from a normal distribution.

The second value represents the number of uni-variate, or multi- dimensional random walk Gibbs samples are taken.

The third value represents the number of bootstrap/reshuffling or uni-dimensional random samples are taken.

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)`.

trace

An integer indicating if you want to trace(1) the SAEM algorithm process. Useful for debugging, but not for typical fitting.

covMethod

Method for calculating covariance. In this discussion, R is the Hessian matrix of the objective function. The S matrix is the sum of each individual's gradient cross-product (evaluated at the individual empirical Bayes estimates).

"linFim" Use the Linearized Fisher Information Matrix to calculate the covariance.

"fim" Use the Fisher Information Matrix accumulated during SAEM estimation to calculate the covariance. Like sa it inverts the observed information to a full theta + Omega diagonal + residual covariance, but uses the (noisier) estimation-phase matrix rather than a dedicated cov phase.

"sa" Use the stochastic-approximation Fisher Information Matrix. After estimation, a dedicated covariance phase (nSaCov iterations) holds the parameters at the converged estimate and keeps resimulating the individual parameters, Monte-Carlo averaging the Louis observed-information integrand into a converged FIM decoupled from the cooling schedule (the approach used by Monolix; Kuhn & Lavielle 2005). Always includes every estimated population parameter (theta, the Omega diagonal variances, and residual).

For both fim and sa the simulation-based Fisher information covers the structural theta, the Omega diagonal variances, and additive residual error. Off-diagonal Omega covariances and proportional/combined residual error are not estimated reliably by the simulation FIM (the complete-data correction is unstable when between-subject variability dominates the residual), so those variance-block standard errors are spliced in from the linearized FIM (linFim).

"r,s" Uses the sandwich matrix to calculate the covariance, that is: $R^-1 \times S \times R^-1$

"r" Uses the Hessian matrix to calculate the covariance as $2\times R^-1$

"s" Uses the crossproduct matrix to calculate the covariance as $4\times S^-1$

"" Does not calculate the covariance step.

covFull

Boolean (default TRUE) indicating the covariance should include every estimated population parameter – the structural and residual thetas plus the Omega variance/covariance elements – named om.<eta> / cov.<eta>.<eta>. When FALSE the legacy structural-theta-only covariance is reported. Ignored by covMethod="sa", which is always full.

nSaCov

Number of iterations in the dedicated stochastic-approximation covariance phase used by covMethod="sa" (default 500). These iterations run at the converged estimate (parameters frozen) and only resimulate the individual parameters to build the observed Fisher information; a larger value gives a less noisy covariance. Ignored by other covariance methods.

calcTables

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

logLik

boolean indicating that log-likelihood should be calculate by Gaussian quadrature.

nnodesGq

number of nodes to use for the Gaussian quadrature when computing the likelihood with this method (defaults to 1, equivalent to the Laplacian likelihood)

nsdGq

span (in SD) over which to integrate when computing the likelihood by Gaussian quadrature. Defaults to 3 (eg 3 times the SD)

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`.

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

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.

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).

tol

This is the tolerance for the regression models used for complex residual errors (ie add+prop etc)

itmax

This is the maximum number of iterations for the regression models used for complex residual errors. The number of iterations is itmax*number of parameters

type

indicates the type of optimization for the residuals; Can be one of c("nelder-mead", "newuoa")

powRange

This indicates the range that powers can take for residual errors; By default this is 10 indicating the range is c(-10, 10)

lambdaRange

This indicates the range that Box-Cox and Yeo-Johnson parameters are constrained to be; The default is 3 indicating the range c(-3,3)

odeRecalcFactor

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

maxOdeRecalc

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

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.

perSa

This is the percent of the time the `nBurn` iterations in phase runs runs a simulated annealing.

perNoCor

This is the percentage of the MCMC phase of the SAEM algorithm where the variance/covariance matrix has no correlations. By default this is 0.75 or 75 Monte-carlo iteration.

perFixOmega

This is the percentage of the `nBurn` phase where the omega values are unfixed to allow better exploration of the likelihood surface. After this time, the omegas are fixed during optimization.

perFixResid

This is the percentage of the `nBurn` phase where the residual components are unfixed to allow better exploration of the likelihood surface.

compress

Should the object have compressed items

rxControl

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

sigdig

Specifies the "significant digits" that the ode solving requests. When specified this controls the relative and absolute tolerances of the ODE solvers. By default the tolerance is 0.5*10^(-sigdig-2) for regular ODEs. For the sensitivity equations the default is 0.5*10\^(-sigdig-1.5) (sensitivity changes only applicable for liblsoda). This also controls the atol/rtol of the steady state solutions. The ssAtol/ssRtol is 0.5*10\^(-sigdig) and for the sensitivities 0.5*10\^(-sigdig+0.625). By default this is unspecified (NULL) and uses the standard atol/rtol.

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.

ci

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

muRefCov

This controls if mu-referenced covariates in `saem` are handled differently than non mu-referenced covariates. When `TRUE`, mu-referenced covariates have special handling. When `FALSE` mu-referenced covariates are treated the same as any other input parameter.

muRefCovAlg

This controls if algebraic expressions that can be mu-referenced are treated as mu-referenced covariates by:

1. Creating a internal data-variable `nlmixrMuDerCov#` for each algebraic mu-referenced expression

2. Change the algebraic expression to `nlmixrMuDerCov# * mu_cov_theta`

3. Use the internal mu-referenced covariate for saem

4. After optimization is completed, replace `model()` with old `model()` expression

5. Remove `nlmixrMuDerCov#` from nlmix2 output

In general, these covariates should be more accurate since it changes the system to a linear compartment model. Therefore, by default this is `TRUE`.

handleUninformativeEtas

boolean that tells nlmixr2's saem to calculate uninformative etas and handle them specially (default is `TRUE`).

iovXform

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

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.

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.

mixProbMethod

For mixture models (`mix()`, more than one component), stabilizes the mixing-probability estimate against collapsing onto a single component (the responsibility used to update it is itself weighted by the current mixing probability, which can create a runaway feedback loop). Two options:

* `"regularized"` (default): blend `mixProbPriorN` pseudo-subjects, distributed per the initial mixing probability, into the responsibility average each iteration (Dirichlet/MAP-EM-style). Prevents collapse even in difficult cases, at the cost of some bias toward the initial guess; may need larger `nBurn`/`nEm`.

* `"annealed"`: give the mixing-probability update its own decaying step-size schedule (`mixProbStepExp`) instead of the full-replacement step used during `nBurn`. Lower bias, but does not by itself fix a systematic (non-noise-driven) collapse.

mixProbStepExp

Only used when `mixProbMethod="annealed"`. Decay exponent for the mixing-probability step size (`1/iteration^mixProbStepExp`), applied from iteration 1. Default 1; smaller values decay more slowly.

mixProbPriorN

Only used when `mixProbMethod="regularized"`. Number of pseudo-subjects blended into the responsibility average each iteration. Larger values are more robust to collapse but bias the estimate more and need more `nBurn`/`nEm`. Default 20.

mixSampleMethod

For mixture models with per-component etas (split-ETA, e.g. `cl <- mix(tcl1 + eta.cl1, p1, tcl2 + eta.cl2)`), controls the MCMC/sufficient-statistic architecture for the individual random effects, independent of `mixProbMethod`. BSV (`$omega`) for split components is unreliable under `"parallel"` regardless of `mixProbMethod`.

* `"parallel"` (default): one full MCMC chain per component per subject per iteration, blended post hoc by responsibility. Mirrors NONMEM's `$MIX` and correctly estimates BSV shared across components, but cannot cleanly separate per-component BSV for split-ETA models (each "wrong-hypothesis" chain still explores its non-owned column(s) as unconstrained prior noise).

* `"msaem"` (experimental): the MSAEM algorithm (Lavielle & Mbogning 2014), as used by Monolix. Simulates one random-effects trajectory per subject per iteration (label marginalized out via a closed-form responsibility) instead of parallel per-component chains, so no post-hoc blending is needed. Not compute-matched to `"parallel"` at equal `nmc` – set `nmc` to roughly `nMix` times its default for a fair comparison. Uses a model-aware stratified initialization for split-ETA components that reliably achieves full theta/fixed-effect separation. Split-ETA BSV recovery is improved (two numerical bugs fixed: an `IGamma2_phi1` blowup that locked variance to exactly zero, and an inverted responsibility sign) but still not reliable – it often settles at a safety-floor value rather than the true variance. Prefer `"parallel"` unless specifically evaluating this method.

censOption

Treatment of the second derivative for censored (M2/M3/M4/BLQ) observations in the FOCEI family. "gauss" (the default) keeps the historic uncensored Gauss-Newton curvature, matching common PMx tools; "laplace" uses the exact censored second derivative of the objective (a proper Laplace inner Hessian and analytic covariance). Accepted by saemControl/nlmControl for a uniform interface but inert there – SAEM (stochastic EM) has no Laplace inner Hessian, and NLM uses a finite-difference Hessian that already reflects censoring exactly.

fast

Boolean enabling the fast-SAEM (f-SAEM) simulation step (Karimi, Lavielle and Moulines 2020). When `TRUE`, the MCMC simulation of the individual random effects uses an independent Metropolis-Hastings proposal centered at each subject's conditional MAP estimate with a Laplace/linearization covariance, which converges in far fewer SAEM iterations than the default random-walk Metropolis. The `est="fsaem"` method is sugar for `saemControl(fast=TRUE)`. By default this is `FALSE` (standard SAEM). The `fast*` options below are only consulted when `fast=TRUE`.

fastKernel

Schedule for the f-SAEM independent Metropolis-Hastings (IMH) kernel:

* `"firstN"` (default): use the IMH kernel for the first `fastIter` iterations, then revert to the standard random-walk kernels. This is the recipe used in the f-SAEM paper – the early iterations only need an approximate posterior, so the fast kernel accelerates the initial convergence and the steady-state behavior is unchanged.

* `"throughout"`: use the IMH kernel on every iteration for the whole run. Simpler, but recomputing the MAP/covariance every iteration is costlier and unnecessary near convergence.

* `"additive"`: append the IMH kernel alongside the standard random-walk kernels on every iteration. Most mixing, most cost.

fastCov

Covariance used for the IMH Gaussian proposal:

* `"auto"` (default): Jacobian linearization for continuous-data endpoints, Hessian (Laplace) for non-continuous endpoints.

* `"jacobian"`: `Gamma_i = (J' Sigma^-1 J + Omega^-1)^-1` from the structural-model Jacobian at the MAP (continuous data only).

* `"hessian"`: `Gamma_i = (-H + Omega^-1)^-1` from the Hessian of the individual log-likelihood at the MAP (any data type).

fastIter

Integer number of initial iterations to run the IMH kernel when `fastKernel="firstN"` (default 20). Ignored by the other schedules.

fastLik

Inner likelihood used for the Hessian proposal path, one of `"focei"` (default), `"foce"` or `"focep"`. Selects which FOCEI-family individual likelihood is reused to build the proposal (and, when the Hessian path is active, reported by SAEM).

lbfgsLmm

Integer number of BFGS corrections (the L-BFGS-B `lmm` memory) used when refining the fixed-effect-only parameters of a general log-likelihood model (`ll(name) ~ <expr>`) by direct L-BFGS-B optimization of the observation likelihood. Default 5.

lbfgsFactr

Convergence tolerance on the relative reduction in the objective for that L-BFGS-B refinement (the `factr` control, in units of machine epsilon). When `NULL` (default) it is derived from `sigdig` the same way as `foceiControl()` (`10^(-sigdig - 1) / .Machine$double.eps`).

lbfgsPgtol

Convergence tolerance on the projected gradient for that L-BFGS-B refinement (the `pgtol` control). When `NULL` (default) it is derived from `sigdig` (`10^(-sigdig - 1)`).

lbfgsMaxIter

Integer maximum number of iterations for that L-BFGS-B refinement. Default 20.

nRetry

Integer number of times a bounded log-likelihood parameter's f-SAEM IMH proposal is re-drawn when it lands outside the parameter's bounds before being clamped to the violated boundary. Default 10.

...

Other arguments to control SAEM.

Value

List of options to be used in nlmixr2 fit for SAEM.

References

Kuhn E, Lavielle M (2005). "Maximum likelihood estimation in nonlinear mixed effects models." Computational Statistics & Data Analysis, 49(4), 1020-1038. doi:10.1016/j.csda.2004.07.002

Jiang L, Roy A, Balasubramanian K, Davis D, Drusvyatskiy D, Na S (2025). "Online Covariance Estimation in Nonsmooth Stochastic Approximation." arXiv:2502.05305. doi:10.48550/arXiv.2502.05305

Author

Wenping Wang & Matthew L. Fidler