Control for lbfgsb3c estimation method in nlmixr2

## Usage

```
lbfgsb3cControl(
trace = 0,
factr = 1e+07,
pgtol = 0,
abstol = 0,
reltol = 0,
lmm = 5L,
maxit = 10000L,
returnLbfgsb3c = FALSE,
stickyRecalcN = 4,
maxOdeRecalc = 5,
odeRecalcFactor = 10^(0.5),
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,
rxControl = NULL,
optExpression = TRUE,
sumProd = FALSE,
literalFix = TRUE,
addProp = c("combined2", "combined1"),
calcTables = TRUE,
compress = TRUE,
covMethod = c("r", ""),
adjObf = TRUE,
ci = 0.95,
sigdig = 4,
sigdigTable = NULL,
...
)
```

## Arguments

- trace
If positive, tracing information on the progress of the optimization is produced. Higher values may produce more tracing information: for method "L-BFGS-B" there are six levels of tracing. (To understand exactly what these do see the source code: higher levels give more detail.)

- factr
controls the convergence of the "L-BFGS-B" method. Convergence occurs when the reduction in the objective is within this factor of the machine tolerance. Default is 1e7, that is a tolerance of about 1e-8.

- pgtol
helps control the convergence of the "L-BFGS-B" method. It is a tolerance on the projected gradient in the current search direction. This defaults to zero, when the check is suppressed.

- abstol
helps control the convergence of the "L-BFGS-B" method. It is an absolute tolerance difference in x values. This defaults to zero, when the check is suppressed.

- reltol
helps control the convergence of the "L-BFGS-B" method. It is an relative tolerance difference in x values. This defaults to zero, when the check is suppressed.

- lmm
is an integer giving the number of BFGS updates retained in the "L-BFGS-B" method, It defaults to 5.

- maxit
maximum number of iterations.

- returnLbfgsb3c
return the lbfgsb3c output instead of the nlmixr2 fit

- 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

- useColor
Boolean indicating if focei can use ASCII color codes

- printNcol
Number of columns to printout before wrapping parameter estimates/gradient

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".

- 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`.

- 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

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

"

`r,s`

" Uses the sandwich matrix to calculate the covariance, that is:`solve(R) %*% S %*% solve(R)`

"

`r`

" Uses the Hessian matrix to calculate the covariance as`2 %*% solve(R)`

"

`s`

" Uses the cross-product matrix to calculate the covariance as`4 %*% solve(S)`

"" Does not calculate the covariance step.

- 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 arguments passed to

`nlmixr2est::lbfgsb3cControl()`

.

## Examples

```
# \donttest{
# A logit regression example with emax model
dsn <- data.frame(i=1:1000)
dsn$time <- exp(rnorm(1000))
dsn$DV=rbinom(1000,1,exp(-1+dsn$time)/(1+exp(-1+dsn$time)))
mod <- function() {
ini({
E0 <- 0.5
Em <- 0.5
E50 <- 2
g <- fix(2)
})
model({
v <- E0+Em*time^g/(E50^g+time^g)
ll(bin) ~ DV * v - log(1 + exp(v))
})
}
fit2 <- nlmixr(mod, dsn, est="lbfgsb3c")
#>
#>
#>
#>
#> 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 population log-likelihood model...
#> ✔ done
#> → calculate jacobian
#> → calculate ∂(f)/∂(θ)
#> → finding duplicate expressions in nlm llik gradient...
#> → optimizing duplicate expressions in nlm llik gradient...
#> → finding duplicate expressions in nlm pred-only...
#> → optimizing duplicate expressions in nlm 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...
#>
#>
#> ✔ done
#> → Calculating residuals/tables
#> ✔ done
#> → compress origData in nlmixr2 object, save 9104
#> → compress parHistData in nlmixr2 object, save 3496
print(fit2)
#> ── nlmixr² log-likelihood lbfgsb3c ──
#>
#> OBJF AIC BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> lPop -667.8633 1176.014 1190.737 -585.0069 141441.6 1203.715
#>
#> ── Time (sec $time): ──
#>
#> setup table compress other
#> elapsed 0.003027 0.05 0.01 2.899973
#>
#> ── ($parFixed or $parFixedDf): ──
#>
#> Est. SE %RSE Back-transformed(95%CI) BSV(SD) Shrink(SD)%
#> E0 -0.5031 0.2098 41.69 -0.5031 (-0.9142, -0.09196)
#> Em 18.29 50.71 277.3 18.29 (-81.1, 117.7)
#> E50 7.124 11.52 161.7 7.124 (-15.46, 29.71)
#> g 2 FIXED FIXED 2
#>
#> Covariance Type ($covMethod): r
#> Censoring ($censInformation): No censoring
#> Minimization message ($message):
#> CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH
#>
#> ── Fit Data (object is a modified tibble): ──
#> # A tibble: 1,000 × 5
#> ID TIME DV IPRED v
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 1 0.0323 0 -0.473 -0.503
#> 2 1 0.0398 1 -0.976 -0.503
#> 3 1 0.0418 0 -0.473 -0.502
#> # ℹ 997 more rows
# you can also get the nlm output with fit2$lbfgsb3c
fit2$lbfgsb3c
#> $par
#> E0 Em E50
#> -0.5030809 18.2865802 7.1241967
#>
#> $grad
#> [1] 4.850456e-06 6.125312e-07 -3.999022e-06
#>
#> $value
#> [1] 585.0069
#>
#> $counts
#> [1] 26 26
#>
#> $convergence
#> [1] 0
#>
#> $message
#> [1] "CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH"
#>
#> $scaleC
#> [1] 0.002809357 0.034120069 0.030608991
#>
#> $par.scaled
#> E0 Em E50
#> -358.0500 520.2938 168.4082
#>
#> $hessian
#> E0 Em E50
#> E0 0.0016250688 0.0005134493 -0.002197546
#> Em 0.0005134493 0.0004406288 -0.001789955
#> E50 -0.0021975460 -0.0017899552 0.007311689
#>
#> $covMethod
#> [1] "r"
#>
#> $cov.scaled
#> E0 Em E50
#> E0 5574.769 56159.38 15423.74
#> Em 56159.379 2208699.19 557584.61
#> E50 15423.738 557584.61 141683.52
#>
#> $cov
#> E0 Em E50
#> E0 0.04399879 5.383183 1.326312
#> Em 5.38318250 2571.321424 582.330707
#> E50 1.32631163 582.330707 132.744751
#>
#> $r
#> E0 Em E50
#> E0 0.0008125344 0.0002567246 -0.0010987730
#> Em 0.0002567246 0.0002203144 -0.0008949776
#> E50 -0.0010987730 -0.0008949776 0.0036558447
#>
# The nlm control has been modified slightly to include
# extra components and name the parameters
# }
```