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Title:

Nonlinear Least Squares Estimation for Emax Regression Models

Version:

0.1.1

Description:

Provides estimation and covariate selection tools for Emax regression models using nonlinear least squares methods. Supported optimization algorithms are Gauss-Newton, Levenberg-Marquardt, and the port library for bounded optimization. The package also provides tools to assist in simulation work using Emax regression.

License:

MIT + file LICENSE

URL:

https://github.com/djnavarro/emaxnls, https://emaxnls.djnavarro.net/

BugReports:

https://github.com/djnavarro/emaxnls/issues

Depends:

R (≥ 3.5)

Imports:

Deriv, minpack.lm, mvtnorm, rlang, stats, tibble, utils

Suggests:

spelling, testthat (≥ 3.0.0)

Config/Needs/website:

djnavarro/waeponwifestre

Config/testthat/edition:

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.3.3

Language:

en-US

NeedsCompilation:

Packaged:

2026-06-25 12:45:44 UTC; danielle

Author:

Danielle Navarro

[aut, cre, cph]

Maintainer:

Danielle Navarro <djnavarro@protonmail.com>

Repository:

CRAN

Date/Publication:

2026-06-30 20:10:02 UTC

Akaike information criterion / Bayesian information criterion

Description

Akaike information criterion / Bayesian information criterion

Usage

## S3 method for class 'emaxnls'
AIC(object, ..., k = 2)

## S3 method for class 'emaxnls'
BIC(object, ...)

Arguments

object

An emaxnls object

...

Optionally, more fitted model objects

k

Penalty per parameter in the AIC

Value

If just one object is provided, a numeric value with the corresponding AIC (or BIC). If multiple objects are provided, a data.frame with rows corresponding to the objects and columns representing the number of parameters in the model (df) and the AIC or BIC.

Examples

mod_0 <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ 1, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
mod_1 <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)

# calculate AIC for individual models
AIC(mod_0)
AIC(mod_1)

# calculate AIC for a sequence of models
AIC(mod_0, mod_1)

# calculate BIC for individual models
BIC(mod_0)
BIC(mod_1)

# calculate BIC for a sequence of models
BIC(mod_0, mod_1)

Analysis of variance for Emax regression models

Description

Analysis of variance for Emax regression models

Usage

## S3 method for class 'emaxnls'
anova(object, ...)

Arguments

object

An emaxnls object

...

Additional fitted model objects

Value

Analysis of variance tables for a sequence of emaxnls models

Examples


mod_0 <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ 1, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
mod_1 <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)

anova(mod_0, mod_1)

Coefficients for an Emax regression

Description

Coefficients for an Emax regression

Usage

## S3 method for class 'emaxnls'
coef(object, back_transform = FALSE, ...)

Arguments

object

An emaxnls object

back_transform

Should log-scaled parameters (logEC50, logHill) be back-transformed to original scale?

...

Ignored

Value

A vector of coefficients

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)

# coefficients on the estimation scale
coef(mod)

# coefficients with log-scale parameters back-transformed
coef(mod, back_transform = TRUE)

Confidence intervals for Emax regression model parameters

Description

Confidence intervals for Emax regression model parameters

Usage

## S3 method for class 'emaxnls'
confint(object, parm = NULL, level = 0.95, back_transform = FALSE, ...)

Arguments

object

An emaxnls object

parm

A specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If parm = NULL, all parameters are considered.

level

The confidence level required

back_transform

Should log-scaled parameters (logEC50, logHill) be back-transformed to original scale?

...

Ignored

Value

A matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labeled as (1-level)/2 and 1 - (1-level)/2 in % (by default 2.5% and 97.5%).

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)

# 95% confidence interval on the estimation scale
confint(mod)

# 90% confidence interval on the estimation scale
confint(mod, level = 0.9)

# 95% confidence interval with log-scale parameters back-transformed
confint(mod, back_transform = TRUE)

Model deviance for an Emax regression

Description

Model deviance for an Emax regression

Usage

## S3 method for class 'emaxnls'
deviance(object, ...)

Arguments

object

An emaxnls object

...

Ignored

Value

Numeric

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
deviance(mod)

Residual degrees of freedom for an Emax regression model

Description

Residual degrees of freedom for an Emax regression model

Usage

## S3 method for class 'emaxnls'
df.residual(object, ...)

Arguments

object

An emaxnls object

...

Ignored

Value

Numeric

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
df.residual(mod)

Check Emax regression model for convergence status

Description

Check Emax regression model for convergence status

Usage

emax_converged(mod)

Arguments

mod

An emaxnls object

Details

This is a convenience function that takes an Emax regression object as input. It returns TRUE if the optimization routine converged during model fitting, and FALSE if it did not.

Value

Logical value

Sample simulated data for Emax exposure-response models with covariates.

Description

Sample simulated data for Emax exposure-response models with covariates.

Usage

emax_df

Format

A data frame with columns:

id: Identifier column
dose: Nominal dose, units not specified
exp_1: Exposure value, units and metric not specified
exp_2: Exposure value, units and metric not specified, but different from exp_1
rsp_1: Continuous response value (units not specified)
rsp_2: Binary response value (group labels not specified)
cnt_a: Continuous valued covariate
cnt_b: Continuous valued covariate
cnt_c: Continuous valued covariate
bin_d: Binary valued covariate
bin_e: Binary valued covariate
cat_f: Categorical covariate

Details

This simulated dataset is entirely synthetic. It is a generic data set that can be used to illustrate Emax modeling. It contains variables corresponding to dose and exposure, and includes both a continuous response variable and a binary response variable. Three continuous valued covariates are included, along with two binary covariates.

You can find the data generating code in the package source code, under R/data.R

Examples

emax_df

Construct Emax prediction function from model object

Description

Construct Emax prediction function from model object

Usage

emax_fun(mod)

Arguments

mod

An emaxnls object

Value

A function f with arguments data and params. The data argument defaults to the data used to estimate the model, and the params argument defaults to the estimated parameter values. Both can be customized, as long as data contains columns corresponding to each of the variables used by the model, and params is a named numeric vector of the appropriate length. The names for params must exactly match the names of the vector returned by coef(mod).

The return value for f is a numeric vector of model predictions for each row in data, evaluated at parameters params.

Examples


mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)

# the emax simulation function can only be extracted if the
# optimization routine converged
if (emax_converged(mod)) {

  par <- coef(mod)
  
  # customizable emax function with the same structural 
  # model and same covariate model, defaulting to the 
  # same data and parameters as the original model, but
  # allowing user to pass their own data and parameters  
  mod_fn <- emax_fun(mod)
  
  # apply the function to a few rows of the original data
  out_1 <- mod_fn(
    data = emax_df[120:125, ],
    param = par
  )
  print(out_1)
  
  # adjust the parameters
  new_par <- par
  new_par["E0_Intercept"] <- 0
  
  # simulate the model with the adjusted parameters
  out_2 <- mod_fn(
    data = emax_df[120:125, ],
    param = new_par
  )
  print(out_2)

}

Estimate parameters for an Emax regression model

Description

Estimate parameters for an Emax regression model

Usage

emax_nls(structural_model, covariate_model, data, init = NULL, opts = NULL)

Arguments

structural_model

A two-sided formula of the form response ~ exposure

covariate_model

A list of two-sided formulas, each of specifying a covariate model for a structural parameter

data

A data frame that includes all relevant variables

init

Initial values and bounds for parameters. See emax_nls_init()

opts

Model fitting and optimization options. See emax_nls_options()

Details

The emax_nls() function is the workhorse function for estimating an Emax regression model. Pass a two-sided formula to the structural_model argument to specify the exposure variable and the response variable (e.g., response ~ exposure), and pass a list of formulas to the covariate_model argument to specify covariates of interest. At a minimum the covariate model requires specification of the covariate model for the E0 parameter, the Emax parameter, and the logEC50 parameter. For example, a formula like E0 ~ age + group would indicate that age and group should both be included as covariates on the baseline response E0. When no covariates are to be added, use a formula like Emax ~ 1.

The emax_nls() function can support sigmoidal emax models as well as hyperbolic models. To build a sigmoidal model (where the Hill parameter) is estimated from the data, the covariate_model argument must also include a formula for the logHill parameter. For instance, if the covariate model includes logHill ~ 1, the model will estimate the value of the Hill parameter (with no covariates on it) from the data set.

At present, emax_nls() does not support binary response variables, nor is it possible to specify interaction terms in the covariate model.

When estimating model parameters, the init argument can be used to specify the starting values for the optimization. If unspecified, the emax_nls_init() function is used to automatically guess sensible starting values. Please see the documentation of that function for additional details on manually specifying the initial values.

The emax_nls() function currently supports three optimization methods: the Gauss-Newton algorithm, the Levenberg-Marquardt algorithm, and the 'nl2sol' algorithm from the Port library. For more information on how to customize the optimization procedure, please see the documentation for emax_nls_options().

Value

An object of class emaxnls

Examples

emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)

Construct an initial guess for the Emax model parameters

Description

Construct an initial guess for the Emax model parameters

Usage

emax_nls_init(structural_model, covariate_model, data)

Arguments

structural_model

A two-sided formula of the form response ~ exposure

covariate_model

A list of two-sided formulas, each of specifying a covariate model for a structural parameter

data

A data frame

Details

The emax_nls() function requires that the user specify the initial values for the model parameters. Specifically, it expects to be supplied with a data frame with columns named parameter, covariate, and start. If a bounded optimization method is used (e.g. if the "port" method is used), the data frame also needs to have columns named lower and upper. The data frame should contain one row per parameter. In most cases the user does not need to define this manually, because emax_nls_init() can use heuristics to make a sensible guess about what to use as starting values. By default this is what emax_nls() relies upon, automatically calling emax_nls_init() using the appropriate values for the structural_model, the covariate_model, and the data.

Value

A data frame

Examples

# use a heuristic to construct sensible start values, and plausible
# upper and lower bounds within which the estimate is expected to fall 
emax_nls_init(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)

# compare to the values estimated:
coef(emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
))

Settings used to estimate Emax model

Description

Settings used to estimate Emax model

Usage

emax_nls_options(
  optim_method = "gauss",
  optim_control = NULL,
  quiet = FALSE,
  weights = NULL,
  na.action = options("na.action")
)

Arguments

optim_method

Character string specifying the algorithm used to solve the nonlinear least squares optimization problem. Supported options are "gauss" (the default), "port", and "levenberg". See details.

optim_control

A list of arguments used to control the behavior of the optimization algorithm. Allowed values differ depending on which algorithm is used

quiet

When quiet=TRUE, messages are suppressed

weights

Numeric vector providing the weights for observations. When specified, weighted least squares is used

na.action

How should missing values in the data be handled?

Details

At present there are three supported values for optim_method:

"gauss": Estimate parameters using the Gauss-Newton algorithm. This is equivalent to the using "default" option in nls()
"port": Estimate parameters using bounded optimization with the "nl2sol" algorithm from from the the Port library. Equivalent to "port" in nls()
"levenberg": Estimate parameters using the Levenberg-Marquardt algorithm. This is equivalent to using nlsLM() from the "minpack.lm" package.

Note that the Golub-Pereyra algorithm for partially linear least-squares (i.e. the "plinear" option in nls()) is not currently supported for Emax regression. Informal testing suggests it does not perform well for these models, and rarely converges.

The optim_control argument mirrors the corresponding control arguments for the respective optimization methods:

For "gauss" and "port": the list should match the output of stats::nls.control()
For "levenberg": the list should match the output of minpack.lm::nls.lm.control()

If optim_control = NULL, the default settings are used for the relevant function.

Value

A list of settings

Examples

# default options
emax_nls_options()

# switch to levenberg-marquardt
if (require("minpack.lm", quietly = TRUE)) emax_nls_options(optim_method = "levenberg")

Stepwise covariate modeling for Emax regression

Description

Stepwise covariate modeling for Emax regression

Usage

emax_scm_forward(mod, candidates, threshold = 0.01, seed = NULL)

emax_scm_backward(mod, candidates, threshold = 0.001, seed = NULL)

emax_scm_history(mod)

Arguments

mod

An emaxnls object

candidates

A list of candidate covariates

threshold

Threshold for addition or removal

seed

Seed for the RNG state

Details

The emaxnls package supports stepwise covariate modeling via forward addition and backward elimination. The emax_scm_forward() function supports forward addition, the emax_scm_backward() function supports backward elimination, and the syntax is designed to allow forward-backward procedures by piping a base model to emax_scm_forward() and then to emax_scm_backward(). In both cases, the function takes an emaxnls regression object as the first argument, as well as a list of candidate covariates to be considered for addition (in the forward addition case) or deletion (backward elimination). The input must be a named list, with the names corresponding to the relevant structural parameter, and the values should be character vector specifying covariates of interest. See the examples for an illustration of how this argument should be specified.

As present, these functions only support stepwise regression using p-values as the criterion for addition or deletion. The threshold argument corresponds to the threshold p-value to be used. In future, other methods (e.g., selection on the basis of AIC values) may be supported.

The seed argument is used to control the RNG state for stochastic components of the stepwise procedure. However, please note that the seed argument is currently experimental, and may be removed in future releases.

A key feature of the stepwise covariate modeling functions is that they keep track of every tested model, and store information about this history internally within the emaxnls object that gets returned. Use the emax_scm_history() function to extract this history.

Value

An object of class emaxnls

Examples

base_model <- emax_nls(rsp_1 ~ exp_1, list(E0 ~ 1, Emax ~ 1, logEC50 ~ 1), emax_df)

covariate_list <- list(
  E0 = c("cnt_a", "cnt_b", "cnt_c", "bin_d", "bin_e"),
  Emax = c("cnt_a", "cnt_b", "cnt_c", "bin_d", "bin_e")
)

# add covariates to the base model using forward addition
forward_model <- emax_scm_forward(
  mod = base_model,
  candidates = covariate_list, 
  threshold = .01
)
forward_model

# remove covariates from the forward model using backward deletion
final_model <- emax_scm_backward(
  mod = forward_model,
  candidates = covariate_list, 
  threshold = .001
) 
final_model

# show the history of all models tested during the forward addition
# step and the backward deletion step
emax_scm_history(final_model)

Add or remove a covariate term from an Emax regression

Description

Add or remove a covariate term from an Emax regression

Usage

emax_add_term(mod, formula)

emax_remove_term(mod, formula)

Arguments

mod

An emaxnls object

formula

A formula such as E0 ~ AGE

Details

The emax_add_term() and emax_remove_term() functions take an existing Emax regression object, and allow the user to add or remove a specific term to the model. It is not expected that users will need these functions very often, but they provide the basis for the stepwise covariate modeling procedures that are very commonly used when building Emax regressions.

Value

An object of class emaxnls

Examples

mod_0 <- emax_nls(rsp_1 ~ exp_1, list(E0 ~ 1, Emax ~ 1, logEC50 ~ 1), emax_df)
mod_1 <- emax_nls(rsp_1 ~ exp_1, list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), emax_df)

if (emax_converged(mod_0)) emax_add_term(mod_0, E0 ~ cnt_a)

if (emax_converged(mod_1)) emax_remove_term(mod_1, E0 ~ cnt_a)

Fitted values for an Emax regression

Description

Fitted values for an Emax regression

Usage

## S3 method for class 'emaxnls'
fitted(object, ...)

Arguments

object

An emaxnls object

...

Ignored

Value

Numeric vector of fitted values

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
fit <- fitted(mod)
fit[1:20]

Log-likelihood for an Emax regression model

Description

Log-likelihood for an Emax regression model

Usage

## S3 method for class 'emaxnls'
logLik(object, REML = FALSE, ...)

Arguments

object

An emaxnls object

REML

For nls objects only REML = FALSE is supported

...

Ignored

Value

Returns an object of class logLik. This is a number with at least one attribute, "df" (degrees of freedom), giving the number of (estimated) parameters in the model.

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
logLik(mod)

Number of observations for an Emax regression model

Description

Number of observations for an Emax regression model

Usage

## S3 method for class 'emaxnls'
nobs(object, ...)

Arguments

object

An emaxnls object

...

Ignored

Value

Numeric

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
nobs(mod)

Predicting from Emax regression models

Description

Predicting from Emax regression models

Usage

## S3 method for class 'emaxnls'
predict(
  object,
  newdata = NULL,
  se.fit = FALSE,
  interval = "none",
  level = 0.95,
  ...
)

Arguments

object

An emaxnls object

newdata

A named list or data frame in which to look for variables with which to predict. If newdata is missing the fitted values at the original data points are returned.

se.fit

A switch indicating if standard errors are required.

interval

A character string indicating if prediction intervals or a confidence interval on the mean responses are to be calculated. Can be "none", "confidence", or "prediction"

level

A numeric scalar between 0 and 1 giving the confidence level for the intervals (if any) to be calculated.

...

Ignored

Value

The return value differs slightly depending on inputs. When se.fit = FALSE, it produces a vector or matrix of predictions with column names fit, lwr and upr if the interval argument is set. When se.fit = TRUE, it returns a list with the following components:

fit: vector or matrix as above
se.fit: standard error of the predicted means
residual.scale: residual standard deviation
df: residual degrees of freedom

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)

# return a vector of predictions
pred <- predict(mod)
pred[1:20]

# return a matrix with confidence intervals
predict(mod, interval = "confidence", se.fit = FALSE)

Print an Emax regression model object

Description

Print an Emax regression model object

Usage

## S3 method for class 'emaxnls'
print(x, ...)

Arguments

x

An emaxnls object

...

Ignored

Value

Invisibly returns the original object

Residuals for an Emax regression

Description

Residuals for an Emax regression

Usage

## S3 method for class 'emaxnls'
residuals(object, ...)

Arguments

object

An emaxnls object

...

Ignored

Value

Numeric vector of residuals

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
res <- residuals(mod)
res[1:20]

Residual standard deviation for Emax regression models

Description

Residual standard deviation for Emax regression models

Usage

## S3 method for class 'emaxnls'
sigma(object, ...)

Arguments

object

An emaxnls object

...

Ignored

Value

Numeric

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
sigma(mod)

Simulate responses from Emax regression model

Description

Simulate responses from Emax regression model

Usage

## S3 method for class 'emaxnls'
simulate(object, nsim = 1, seed = NULL, ...)

Arguments

object

An emaxnls object

nsim

Number of replicates

seed

Used to set RNG seed

...

Ignored

The simulate() method for an emaxnls object simulates new values for the response, using new parameter values that sampled using the variance-covariance matrix associated with the parameter estimates. It uses mvtnorm::rmvnorm() to generate multivariate normal variates.

Value

A data frame or tibble

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
if (requireNamespace("mvtnorm", quietly = TRUE)) simulate(mod)

Summary of an Emax regression model

Description

Summary of an Emax regression model

Usage

## S3 method for class 'emaxnls'
summary(object, conf_level = 0.95, back_transform = FALSE, ...)

Arguments

object

An emaxnls object

conf_level

Confidence level for interval estimates

back_transform

Should log-scaled parameters (logEC50, logHill) be back-transformed to original scale?

...

Ignored

Value

A data frame or tibble containing a table of parameter estimates and other statistical summaries. Please note that the summary() method is experimental (moreso than other methods), and the return value may be modified in future releases as the package matures.

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)

# standard summary
summary(mod)

# summary with adjusted confidence level
summary(mod, conf_level = 0.99)

# summary with log-scale parameters transformed to original scale
summary(mod, back_transform = TRUE)

Variance-covariance matrix for an Emax regression

Description

Variance-covariance matrix for an Emax regression

Usage

## S3 method for class 'emaxnls'
vcov(object, ...)

Arguments

object

An emaxnls object

...

Ignored

Value

A matrix

Examples

mod <- emax_nls(
  structural_model = rsp_1 ~ exp_1, 
  covariate_model = list(E0 ~ cnt_a, Emax ~ 1, logEC50 ~ 1), 
  data = emax_df
)
vcov(mod)

Package {emaxnls}

Akaike information criterion / Bayesian information criterion

Description

Usage

Arguments

Value

Examples

Analysis of variance for Emax regression models

Description

Usage

Arguments

Value

Examples

Coefficients for an Emax regression

Description

Usage

Arguments

Value

Examples

Confidence intervals for Emax regression model parameters

Description

Usage

Arguments

Value

Examples

Model deviance for an Emax regression

Description

Usage

Arguments

Value

Examples

Residual degrees of freedom for an Emax regression model

Description

Usage

Arguments

Value

Examples

Check Emax regression model for convergence status

Description

Usage

Arguments

Details

Value

Sample simulated data for Emax exposure-response models with covariates.

Description

Usage

Format

Details

Examples

Construct Emax prediction function from model object

Description

Usage

Arguments

Value

See Also

Examples

Estimate parameters for an Emax regression model

Description

Usage

Arguments

Details

Value

See Also

Examples

Construct an initial guess for the Emax model parameters

Description

Usage

Arguments

Details

Value

See Also

Examples

Settings used to estimate Emax model

Description

Usage

Arguments

Details

Value

See Also

Examples