Package 'optedr' reference manual

Title:	Calculating Optimal and D-Augmented Designs
Description:	Calculates D-, Ds-, A- and I-optimal designs for non-linear models, via an implementation of the cocktail algorithm (Yu, 2011, <doi:10.1007/s11222-010-9183-2>). Compares designs via their efficiency, and D-augments any design with a controlled efficiency. An efficient rounding function has been provided to transform approximate designs to exact designs.
Authors:	Carlos de la Calle-Arroyo [aut, cre] , Jesús López-Fidalgo [aut] , Licesio J. Rodríguez-Aragón [aut]
Maintainer:	Carlos de la Calle-Arroyo <[email protected]>
License:	GPL-3
Version:	2.1.1
Built:	2024-11-09 05:54:10 UTC
Source:	https://github.com/kezrael/optedr

Add two designs

Description

Add two designs

Usage

add_design(design_1, design_2, alpha)
add_design(design_1, design_2, alpha)

Arguments

`design_1`	A dataframe with 'Point' and 'Weight' as columns that represent the first design to add
`design_2`	A dataframe with 'Point' and 'Weight' as columns that represent the second design to add
`alpha`	Weight of the first design

Value

A design as a dataframe with the weighted addition of the two designs

Update design given crosspoints and alpha

Description

Given a set of points, a weight and the design, the function adds these points to the new design with uniform weight, and combined weight alpha

Usage

add_points(points, alpha, design)
add_points(points, alpha, design)

Arguments

`points`	Points to be added to the design
`alpha`	Combined weight of the new points to be added to the design
`design`	A design as a dataframe with "Point" and "Weight" columns

Value

A design as a dataframe with "Point" and "Weight" columns that is the addition of the design and the new points

Augments a design. The user gives an initial design for which he would like to add points and specifies the weight of the new points. Then he is prompted to choose a minimum efficiency. After that, the candidate points region is calculated and the user can choose the points and weights to add.

Usage

augment_design(
  criterion,
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  par_int = NA,
  matB = NULL,
  distribution = NA,
  weight_fun = function(x) 1
)
augment_design(
  criterion,
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  par_int = NA,
  matB = NULL,
  distribution = NA,
  weight_fun = function(x) 1
)

Arguments

`criterion`	character variable with the chosen optimality criterion. Can be one of the following: 'D-Optimality' 'Ds-Optimality' 'A-Optimality' 'I-Optimality' 'L-Optimality'
`init_design`	dataframe with "Point" and "Weight" columns that represents the initial design to augment
`alpha`	combined weight of the new points
`model`	formula that represents the model with x as the independent variable
`parameters`	character vector with the unknown parameters of the model to estimate
`par_values`	numeric vector with the initial values of the unknown parameters
`design_space`	numeric vector with the limits of the space of the design
`calc_optimal_design`	boolean parameter, if TRUE, the optimal design is calculated and efficiencies of the initial and augmented design are given
`par_int`	optional numeric vector with the index of the `parameters` of interest for Ds-optimality.
`matB`	optional matrix of dimensions k x k, for L-optimality.
`distribution`	character specifying the probability distribution of the response. Can be one of the following: 'Homoscedasticity' 'Gamma', which can be used for exponential or normal heteroscedastic with constant relative error 'Poisson' 'Logistic' 'Log-Normal' (work in progress)
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A dataframe that represents the D-augmented design

Examples

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
augment_design("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
augment_design("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)
init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
augment_design("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
augment_design("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)

Check Inputs

Description

Function to check that the inputs given to the function opt_des are correct. If not, throws the correspondent error message.

Usage

check_inputs(
  criterion,
  model,
  parameters,
  par_values,
  design_space,
  init_design,
  join_thresh,
  delete_thresh,
  delta,
  tol,
  tol2,
  par_int,
  matB,
  reg_int,
  desired_output,
  weight_fun
)
check_inputs(
  criterion,
  model,
  parameters,
  par_values,
  design_space,
  init_design,
  join_thresh,
  delete_thresh,
  delta,
  tol,
  tol2,
  par_int,
  matB,
  reg_int,
  desired_output,
  weight_fun
)

Arguments

`criterion`	character variable with the chosen optimality criterion. Can be one of the following: 'D-Optimality' 'Ds-Optimality' 'A-Optimality' 'I-Optimality' 'L-Optimality'
`model`	formula describing the model to calculate the optimal design. Must use x as the variable.
`parameters`	character vector with the parameters of the models, as written in the `formula`.
`par_values`	numeric vector with the parameters nominal values, in the same order as given in `parameters`.
`design_space`	numeric vector with the limits of the space of the design.
`init_design`	optional dataframe with the initial design for the algorithm. A dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`join_thresh`	optional numeric value that states how close, in real units, two points must be in order to be joined together by the join heuristic.
`delete_thresh`	optional numeric value with the minimum weight, over 1 total, that a point needs to have in order to not be deleted from the design.
`delta`	optional numeric value in (0, 1), parameter of the algorithm.
`tol`	optional numeric value for the convergence of the weight optimizing algorithm.
`tol2`	optional numeric value for the stop criterion: difference between maximum of sensitivity function and optimality criterion.
`par_int`	optional numeric vector with the index of the `parameters` of interest for Ds-optimality.
`matB`	optional matrix of dimensions k x k, for L-optimality.
`reg_int`	optional numeric vector of two components with the bounds of the interest region for I-Optimality.
`desired_output`	not functional yet: decide which kind of output you want.
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response.

Combinatorial round

Description

Given an approximate design and a number of points, computes all the possible combinations of roundings of each point to the nearest integer, keeps the ones that amount to the requested number of points, and returns the one with the best value for the criterion function

Usage

combinatorial_round(
  design,
  n,
  criterion = NULL,
  model = NULL,
  parameters = NULL,
  par_values = NULL,
  weight_fun = function(x) 1,
  par_int = NULL,
  reg_int = NULL,
  matB = NULL
)
combinatorial_round(
  design,
  n,
  criterion = NULL,
  model = NULL,
  parameters = NULL,
  par_values = NULL,
  weight_fun = function(x) 1,
  par_int = NULL,
  reg_int = NULL,
  matB = NULL
)

Arguments

`design`	either a dataframe with the design to round, or an object of class "optdes". If the former, the criterion, model and parameters must be specified. The dataframe should have two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`n`	integer with the desired number of points of the resulting design.
`criterion`	character variable with the chosen optimality criterion. Can be one of the following: 'D-Optimality' 'Ds-Optimality' 'A-Optimality' 'I-Optimality' 'L-Optimality'
`model`	formula describing the model. Must use x as the variable.
`parameters`	character vector with the parameters of the models, as written in the `formula`.
`par_values`	numeric vector with the parameters nominal values, in the same order as given in `parameters`.
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response.
`par_int`	optional numeric vector with the index of the `parameters` of interest for Ds-optimality.
`matB`	optional matrix of dimensions k x k, for L-optimality.

Value

A data.frame with the rounded design to n number of points

Examples

aprox_design <- opt_des("D-Optimality", y ~ a * exp(-b / x), c("a", "b"), c(1, 1500), c(212, 422))
combinatorial_round(aprox_design, 27)
aprox_design <- opt_des("D-Optimality", y ~ a * exp(-b / x), c("a", "b"), c(1, 1500), c(212, 422))
combinatorial_round(aprox_design, 27)

Master function for the criterion function

Description

Depending on the criterion input, the function returns the output of the corresponding criterion function given the information matrix.

Usage

crit(criterion, M, k = 0, par_int = c(1), matB = NA)
crit(criterion, M, k = 0, par_int = c(1), matB = NA)

Arguments

`criterion`	character variable with the chosen optimality criterion. Can be one of the following: 'D-Optimality' 'Ds-Optimality' 'A-Optimality' 'I-Optimality' 'L-Optimality'
`M`	information matrix for which the criterion value wants to be calculated.
`k`	numeric variable with the number of parameters of the model. Taken from the number of rows of the matrix if omitted.
`par_int`	numeric vector with the index of the parameters of interest of the model. Only for "Ds-Optimality".
`matB`	optional matrix of dimensions k x k, for I- and L-optimality.

Value

Numeric value of the optimality criterion for the information matrix.

Calculate crosspoints

Description

Given the parameters for augmenting a design, this function calculates the crosspoints in the efficiency function that delimit the candidate points region

Usage

crosspoints(val, sens, gridlength, tol, xmin, xmax)
crosspoints(val, sens, gridlength, tol, xmin, xmax)

Arguments

`val`	Efficiency value to solve in the curve relationing the space of the design and efficiency of new design
`sens`	Sensitivity function of the design for the model
`gridlength`	Number of points in the grid to find the crosspoints
`tol`	Tolerance that establishes how close two points close to one another are considered the same
`xmin`	Minimum of the space of the design
`xmax`	Maximum of the space of the design

Value

A numeric vector of crosspoints that define the candidate points region

D-Augment Design

Description

D-Augments a design. The user gives an initial design for which he would like to add points and specifies the weight of the new points. Then he is prompted to choose a minimum efficiency. After that, the candidate points region is calculated and the user can choose the points and weights to add.

Usage

daugment_design(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  weight_fun = function(x) 1
)
daugment_design(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  weight_fun = function(x) 1
)

Arguments

`init_design`	dataframe with "Point" and "Weight" columns that represents the initial design to augment
`alpha`	combined weight of the new points
`model`	formula that represents the model with x as the independent variable
`parameters`	character vector with the unknown parameters of the model to estimate
`par_values`	numeric vector with the initial values of the unknown parameters
`design_space`	numeric vector with the limits of the space of the design
`calc_optimal_design`	boolean parameter, if TRUE, the optimal design is calculated and efficiencies of the initial and augmented design are given
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A dataframe that represents the D-augmented design

Examples

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
augment_design("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
augment_design("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)
init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
augment_design("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
augment_design("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)

Criterion function for D-Optimality

Description

Calculates the value of the D-Optimality criterion function, which follows the expression:

$\phi_D = \left(\frac{1}{|M|}\right)^{1/k}$

Usage

dcrit(M, k)
dcrit(M, k)

Arguments

`M`	information matrix for which the criterion value wants to be calculated.
`k`	numeric variable with the number of parameters of the model. Taken from the number of rows of the matrix if omitted.

Value

numeric value of the D-optimality criterion for the information matrix.

Remove low weight points

Description

Removes the points of a design with a weight lower than a threshold, delta, and distributes that weights proportionally to the rest of the points.

Usage

delete_points(design, delta)
delete_points(design, delta)

Arguments

design

The design from which to remove points as a dataframe with two columns:

Point contains the support points of the design.
Weight contains the corresponding weights of the Points.

delta

The threshold from which the points with such a weight or lower will be removed.

Value

The design without the removed points.

Efficiency between optimal design and a user given design

Description

Takes an optimal design provided from the function opt_des and a user given design and compares their efficiency

Usage

design_efficiency(opt_des_obj, design)
design_efficiency(opt_des_obj, design)

Arguments

opt_des_obj

an object given by the function opt_des.

design

dataframe that represents the design. Must have two columns:

Point contains the support points of the design.
Weight contains the corresponding weights of the Points.

Value

The efficiency as a value between 0 and 1

Examples

result <- opt_des("D-Optimality", y ~ a * exp(-b / x), c("a", "b"), c(1, 1500), c(212, 422))
design <- data.frame("Point" = c(220, 240, 400), "Weight" = c(1 / 3, 1 / 3, 1 / 3))
design_efficiency(result, design)
result <- opt_des("D-Optimality", y ~ a * exp(-b / x), c("a", "b"), c(1, 1500), c(212, 422))
design <- data.frame("Point" = c(220, 240, 400), "Weight" = c(1 / 3, 1 / 3, 1 / 3))
design_efficiency(result, design)

Ds-Augment Design

Description

Ds-Augments a design. The user gives an initial design for which he would like to add points and specifies the weight of the new points. Then he is prompted to choose a minimum efficiency. After that, the candidate points region is calculated and the user can choose the points and weights to add.

Usage

dsaugment_design(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  par_int,
  design_space,
  calc_optimal_design,
  weight_fun = function(x) 1
)
dsaugment_design(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  par_int,
  design_space,
  calc_optimal_design,
  weight_fun = function(x) 1
)

Arguments

`init_design`	dataframe with "Point" and "Weight" columns that represents the initial design to augment
`alpha`	combined weight of the new points
`model`	formula that represents the model with x as the independent variable
`parameters`	character vector with the unknown parameters of the model to estimate
`par_values`	numeric vector with the initial values of the unknown parameters
`par_int`	optional numeric vector with the index of the `parameters` of interest for Ds-optimality.
`design_space`	numeric vector with the limits of the space of the design
`calc_optimal_design`	boolean parameter, if TRUE, the optimal design is calculated and efficiencies of the initial and augmented design are given
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A dataframe that represents the Ds-augmented design

Examples

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
augment_design("Ds-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), par_int = c(1), TRUE)
augment_design("Ds-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), par_int = c(1), FALSE)

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
augment_design("Ds-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), par_int = c(1), TRUE)
augment_design("Ds-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), par_int = c(1), FALSE)

Criterion function for Ds-Optimality

Description

Calculates the value of the Ds-Optimality criterion function, which follows the expression:

$\phi_{Ds} = \left(\frac{|M_{22}|}{|M|}\right)^{1/s}$

Usage

dscrit(M, par_int)
dscrit(M, par_int)

Arguments

`M`	information matrix for which the criterion value wants to be calculated.
`par_int`	numeric vector with the index of the parameters of interest of the model.

Value

Numeric value of the Ds-optimality criterion for the information matrix.

Sensitivity function for D-Optimality

Description

Calculates the sensitivity function from the gradient vector and the Identity Matrix.

Usage

dsens(grad, M)
dsens(grad, M)

Arguments

`grad`	A function in a single variable that returns the partial derivatives vector of the model.
`M`	Information Matrix for the sensitivity function.

Value

The sensitivity function as a matrix of single variable.

Sensitivity function for Ds-Optimality

Description

Calculates the sensitivity function from the gradient vector, the Identity Matrix and the parameters of interest.

Usage

dssens(grad, M, par_int)
dssens(grad, M, par_int)

Arguments

`grad`	A function in a single variable that returns the partial derivatives vector of the model.
`M`	Information Matrix for the sensitivity function.
`par_int`	Numeric vector of the indexes of the parameters of interest for Ds-Optimality.

Value

The sensitivity function as a matrix of single variable.

Cocktail Algorithm implementation for Ds-Optimality

Description

Function that calculates the Ds-Optimal designs for the interest parameters given by intPar. The rest of the parameters can help the convergence of the algorithm.

Usage

DsWFMult(
  init_design,
  grad,
  par_int,
  min,
  max,
  grid.length,
  join_thresh,
  delete_thresh,
  delta_weights,
  tol,
  tol2
)
DsWFMult(
  init_design,
  grad,
  par_int,
  min,
  max,
  grid.length,
  join_thresh,
  delete_thresh,
  delta_weights,
  tol,
  tol2
)

Arguments

`init_design`	optional dataframe with the initial design for the algorithm. A dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`grad`	function of partial derivatives of the model.
`par_int`	numeric vector with the index of the `parameters` of interest. Only necessary when the `criterion` chosen is 'Ds-Optimality'.
`min`	numeric value with the inferior bound of the space of the design.
`max`	numeric value with the upper bound of the space of the design.
`grid.length`	numeric value that gives the grid to evaluate the sensitivity function when looking for a maximum.
`join_thresh`	numeric value that states how close, in real units, two points must be in order to be joined together by the join heuristic.
`delete_thresh`	numeric value with the minimum weight, over 1 total, that a point needs to have in order to not be deleted from the design.
`delta_weights`	numeric value in (0, 1), parameter of the algorithm.
`tol`	numeric value for the convergence of the weight optimizing algorithm.
`tol2`	numeric value for the stop condition of the algorithm.

Value

list correspondent to the output of the correspondent algorithm called, dependent on the criterion. A list of two objects:

optdes: a dataframe with the optimal design in two columns, Point and Weight.
sens: a plot with the sensitivity function to check for optimality of the design.

Cocktail Algorithm implementation for D-Optimality

Description

Function that calculates the DsOptimal design. The rest of the parameters can help the convergence of the algorithm.

Usage

DWFMult(
  init_design,
  grad,
  min,
  max,
  grid.length,
  join_thresh,
  delete_thresh,
  k,
  delta_weights,
  tol,
  tol2
)
DWFMult(
  init_design,
  grad,
  min,
  max,
  grid.length,
  join_thresh,
  delete_thresh,
  k,
  delta_weights,
  tol,
  tol2
)

Arguments

`init_design`	optional dataframe with the initial design for the algorithm. A dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`grad`	function of partial derivatives of the model.
`min`	numeric value with the inferior bound of the space of the design.
`max`	numeric value with the upper bound of the space of the design.
`grid.length`	numeric value that gives the grid to evaluate the sensitivity function when looking for a maximum.
`join_thresh`	numeric value that states how close, in real units, two points must be in order to be joined together by the join heuristic.
`delete_thresh`	numeric value with the minimum weight, over 1 total, that a point needs to have in order to not be deleted from the design.
`k`	number of unknown parameters of the model.
`delta_weights`	numeric value in (0, 1), parameter of the algorithm.
`tol`	numeric value for the convergence of the weight optimizing algorithm.
`tol2`	numeric value for the stop condition of the algorithm.

Value

list correspondent to the output of the correspondent algorithm called, dependent on the criterion. A list of two objects:

optdes: a dataframe with the optimal design in two columns, Point and Weight.
sens: a plot with the sensitivity function to check for optimality of the design.

Efficiency between two Information Matrices

Description

Efficiency between two Information Matrices

Usage

eff(criterion, mat1, mat2, k = 0, intPars = c(1), matB = NA)
eff(criterion, mat1, mat2, k = 0, intPars = c(1), matB = NA)

Arguments

`criterion`	character variable with the chosen optimality criterion. Can be one of the following: 'D-Optimality' 'Ds-Optimality' 'A-Optimality' 'I-Optimality' 'L-Optimality'
`mat1`	first information matrix, for the numerator.
`mat2`	second information matrix, for the denominator.
`k`	number of parameters of the model. Taken from the number of rows of the matrix if omitted.
`intPars`	numeric vector with the index of the parameters of interest of the model. Only for "Ds-Optimality".
`matB`	matrix of the integral of the information matrix over the interest region. Only for "I-Optimality".

Value

Efficiency of first design with respect to the second design, as a decimal number.

Efficient Round

Description

Takes an approximate design, and a number of points and converts the design to an approximate design. It uses the multiplier (n - l/2) and evens the total number of observations afterwards.

Usage

efficient_round(design, n, tol = 1e-05)
efficient_round(design, n, tol = 1e-05)

Arguments

`design`	a dataframe with columns "Point" and "Weight" that represents a design
`n`	an integer that represents the desired number of observations of the exact design
`tol`	optional parameter for the consideration of an integer in the rounding process

Value

a data.frame with columns "Point" and "Weight" representing an exact design with n observations

Examples

design_test <- data.frame("Point" = seq(1, 5, length.out = 7),
         "Weight" = c(0.1, 0.0001, 0.2, 0.134, 0.073, 0.2111, 0.2818))

efficient_round(design_test, 20)

exact_design <- efficient_round(design_test, 21)
aprox_design <- exact_design
aprox_design$Weight <- aprox_design$Weight/sum(aprox_design$Weight)
design_test <- data.frame("Point" = seq(1, 5, length.out = 7),
         "Weight" = c(0.1, 0.0001, 0.2, 0.134, 0.073, 0.2111, 0.2818))

efficient_round(design_test, 20)

exact_design <- efficient_round(design_test, 21)
aprox_design <- exact_design
aprox_design$Weight <- aprox_design$Weight/sum(aprox_design$Weight)

Find Maximum

Description

Searches the maximum of a function over a grid on a given interval.

Usage

findmax(sens, min, max, grid.length)
findmax(sens, min, max, grid.length)

Arguments

`sens`	A single variable numeric function to evaluate.
`min`	Minimum value of the search interval.
`max`	Maximum value of the search interval.
`grid.length`	Length of the search interval.

Value

The value at which the maximum is obtained

Find Maximum Value

Description

Searches the maximum of a function over a grid on a given interval.

Usage

findmaxval(sens, min, max, grid.length)
findmaxval(sens, min, max, grid.length)

Arguments

`sens`	A single variable numeric function to evaluate.
`min`	Minimum value of the search interval.
`max`	Maximum value of the search interval.
`grid.length`	Length of the search interval.

Value

The value of the maximum

Find Minimum Value

Description

Searches the maximum of a function over a grid on a given grid.

Usage

findminval(sens, min, max, grid.length)
findminval(sens, min, max, grid.length)

Arguments

`sens`	a single variable numeric function to evaluate.
`min`	minimum value of the search grid.
`max`	maximum value of the search grid.
`grid.length`	length of the search grid.

Value

The value of the minimum

Get Augment Regions

Description

Given a model and criterion, calculates the candidate points region. The user gives an initial design for which he would like to add points and specifies the weight of the new points. Then he is prompted to choose a minimum efficiency. After that, the candidate points region is calculated.

Usage

get_augment_region(
  criterion,
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  par_int = NA,
  matB = NA,
  distribution = NA,
  weight_fun = function(x) 1
)
get_augment_region(
  criterion,
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  par_int = NA,
  matB = NA,
  distribution = NA,
  weight_fun = function(x) 1
)

Arguments

`criterion`	character with the chosen optimality criterion. Can be one of the following: 'D-Optimality' 'Ds-Optimality' 'A-Optimality' 'I-Optimality' 'L-Optimality'
`init_design`	dataframe with "Point" and "Weight" columns that represents the initial design to augment
`alpha`	combined weight of the new points
`model`	formula that represent the model with x as the independent variable
`parameters`	character vector with the unknown parameters of the model to estimate
`par_values`	numeric vector with the initial values of the unknown parameters
`design_space`	numeric vector with the limits of the space of the design
`calc_optimal_design`	boolean parameter, if TRUE, the optimal design is calculated and efficiencies of the initial and augmented design are given
`par_int`	optional numeric vector with the index of the `parameters` of interest for Ds-optimality.
`matB`	optional matrix of dimensions k x k, for L-optimality.
`distribution`	character specifying the probability distribution of the response. Can be one of the following: 'Homoscedasticity' 'Gamma', which can be used for exponential or normal heteroscedastic with constant relative error 'Poisson' 'Logistic' 'Log-Normal' (work in progress)
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A vector of the points limiting the candidate points region

Examples

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)
init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)

Get D-augment region

Description

Given a model, calculates the candidate points region for D-Optimality. The user gives an initial design for which he would like to add points and specifies the weight of the new points. Then he is prompted to choose a minimum efficiency. After that, the candidate points region is calculated.

Usage

get_daugment_region(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  weight_fun = function(x) 1
)
get_daugment_region(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  weight_fun = function(x) 1
)

Arguments

`init_design`	dataframe with "Point" and "Weight" columns that represents the initial design to augment
`alpha`	combined weight of the new points
`model`	formula that represent the model with x as the independent variable
`parameters`	character vector with the unknown parameters of the model to estimate
`par_values`	numeric vector with the initial values of the unknown parameters
`design_space`	numeric vector with the limits of the space of the design
`calc_optimal_design`	boolean parameter, if TRUE, the optimal design is calculated and efficiencies of the initial and augmented design are given
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A vector of the points limiting the candidate points region

Examples

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)
init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)

Get Ds-augment region

Description

Given a model, calculates the candidate points region for Ds-Optimality. The user gives an initial design for which he would like to add points and specifies the weight of the new points. Then he is prompted to choose a minimum efficiency. After that, the candidate points region is calculated.

Usage

get_dsaugment_region(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  par_int,
  design_space,
  calc_optimal_design,
  weight_fun = function(x) 1
)
get_dsaugment_region(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  par_int,
  design_space,
  calc_optimal_design,
  weight_fun = function(x) 1
)

Arguments

`init_design`	dataframe with "Point" and "Weight" columns that represents the initial design to augment
`alpha`	combined weight of the new points
`model`	formula that represent the model with x as the independent variable
`parameters`	character vector with the unknown parameters of the model to estimate
`par_values`	numeric vector with the initial values of the unknown parameters
`par_int`	optional numeric vector with the index of the `parameters` of interest for Ds-optimality.
`design_space`	numeric vector with the limits of the space of the design
`calc_optimal_design`	boolean parameter, if TRUE, the optimal design is calculated and efficiencies of the initial and augmented design are given
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A vector of the points limiting the candidate points region

Examples

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)
init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)

Get L-augment region

Description

Given a model, calculates the candidate points region for L-Optimality. The user gives an initial design for which he would like to add points and specifies the weight of the new points. Then he is prompted to choose a minimum efficiency. After that, the candidate points region is calculated.

Usage

get_laugment_region(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  matB,
  weight_fun = function(x) 1
)
get_laugment_region(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  matB,
  weight_fun = function(x) 1
)

Arguments

`init_design`	dataframe with "Point" and "Weight" columns that represents the initial design to augment
`alpha`	combined weight of the new points
`model`	formula that represent the model with x as the independent variable
`parameters`	character vector with the unknown parameters of the model to estimate
`par_values`	numeric vector with the initial values of the unknown parameters
`design_space`	numeric vector with the limits of the space of the design
`calc_optimal_design`	boolean parameter, if TRUE, the optimal design is calculated and efficiencies of the initial and augmented design are given
`matB`	optional matrix of dimensions k x k, for L-optimality.
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A vector of the points limiting the candidate points region

Examples

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)
init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
get_augment_region("D-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)

Give effective limits to candidate points region

Description

Given the start of the candidates points region, the parity of the crosspoints and the boundaries of the space of the design returns the effective limits of the candidate points region. Those points, taken in pairs from the first to the last delimit the region.

Usage

getCross2(cross, min, max, start, par)
getCross2(cross, min, max, start, par)

Arguments

`cross`	Vector of crosspoints in the sensitivity function given an efficiency and weight
`min`	Minimum of the space of the design
`max`	Maximum of the space of the design
`start`	Boolean that gives the effective start of the candidate points region
`par`	Boolean with the parity of the region

Value

Vector of effective limits of the candidate points region. Taken in pairs from the beginning delimit the region.

Parity of the crosspoints

Description

Determines if the number of crosspoints is even or odd given the vector of crosspoints

Usage

getPar(cross)
getPar(cross)

Arguments

cross

Vector of crosspoints in the sensitivity function given an efficiency and weight

Value

True if the number of crosspoints is even, false otherwise

Find where the candidate points region starts

Description

Given the crosspoints and the sensitivity function, this function finds where the candidate points region starts, either on the extreme of the space of the design or the first crosspoints

Usage

getStart(cross, min, max, val, sens_opt)
getStart(cross, min, max, val, sens_opt)

Arguments

`cross`	Vector of crosspoints in the sensitivity function given an efficiency and weight
`min`	Minimum of the space of the design
`max`	Maximum of the space of the design
`val`	Value of the sensitivity function at the crosspoints
`sens_opt`	Sensitivity function

Value

True if the candidate points region starts on the minimum, False otherwise

Gradient function

Description

Calculates the gradient function of a model with respect to the parameters, char_vars, evaluates it at the provided values and returns the result as a function of the variable x.

Usage

gradient(model, char_vars, values, weight_fun = function(x) 1)
gradient(model, char_vars, values, weight_fun = function(x) 1)

Arguments

`model`	formula describing the model, which must contain only `x`, the parameters defined in `char_vars` and the numerical operators.
`char_vars`	character vector of the parameters of the model.
`values`	numeric vector with the nominal values of the parameters in `char_vars`.
`weight_fun`	optional function variable that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A function depending on x that's the gradient of the model with respect to char_vars

Gradient function for a subset of variables

Description

Calculates the gradient function of a model with respect to a subset of the parameters given in par_int, char_vars, evaluates it at the provided values and returns the result as a function of the variable x.

Usage

gradient22(model, char_vars, values, par_int, weight_fun = function(x) 1)
gradient22(model, char_vars, values, par_int, weight_fun = function(x) 1)

Arguments

`model`	formula describing the model, which must contain only `x`, the parameters defined in `char_vars` and the numerical operators.
`char_vars`	character vector of the parameters of the model.
`values`	numeric vector with the nominal values of the parameters in `char_vars`.
`par_int`	vector of indexes indicating the subset of variables to omit in the calculation of the gradient.
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A function depending on x that's the gradient of the model with respect to char_vars

Criterion function for I-Optimality and L-Optimality

Description

Calculates the value of the I-Optimality criterion function, which follows the expression:

$\phi_I = Tr(M^{-1} \cdot B)$

Usage

icrit(M, matB)
icrit(M, matB)

Arguments

`M`	information matrix for which the criterion value wants to be calculated.
`matB`	matrix of the integral of the information matrix over the interest region. Identity matrix for A-Optimality.

Value

Numeric value of the I-optimality criterion for the information matrix.

Information Matrix

Description

Given the gradient vector of a model in a single variable model and a design, calculates the information matrix.

Usage

inf_mat(grad, design)
inf_mat(grad, design)

Arguments

grad

A function in a single variable that returns the partial derivatives vector of the model.

design

A dataframe that represents the design. Must have two columns:

Point contains the support points of the design.
Weight contains the corresponding weights of the Points.

Value

The information matrix of the design, a $k\times k$ matrix where k is the length of the gradient.

Integrate IM

Description

Integrates the information matrix over the region of interest to calculate matrix B to be used in I-Optimality calculation.

Usage

integrate_reg_int(grad, k, reg_int)
integrate_reg_int(grad, k, reg_int)

Arguments

`grad`	function of partial derivatives of the model.
`k`	number of unknown parameters of the model.
`reg_int`	optional numeric vector of two components with the bounds of the interest region for I-Optimality.

Value

The integrated information matrix.

Sensitivity function for I-Optimality

Description

Calculates the sensitivity function from the gradient vector, the Information Matrix and the integral of the one-point Identity Matrix over the interest region. If instead the identity matrix is used, it can be used for A-Optimality.

Usage

isens(grad, M, matB)
isens(grad, M, matB)

Arguments

`grad`	A function in a single variable that returns the partial derivatives vector of the model.
`M`	Information Matrix for the sensitivity function.
`matB`	Matrix resulting from the integration of the one-point Information Matrix along the interest region or lineal matrix for L-Optimality.

Value

The sensitivity function as a matrix of single variable.

Cocktail Algorithm implementation for L-, I- and A-Optimality (with matB = diag(k))

Description

Function that calculates the I-Optimal designs given the matrix B (should be integral of the information matrix over the interest region), or A-Optimal if given diag(k). The rest of the parameters can help the convergence of the algorithm.

Usage

IWFMult(
  init_design,
  grad,
  matB,
  min,
  max,
  grid.length,
  join_thresh,
  delete_thresh,
  delta_weights,
  tol,
  tol2,
  crit_name
)
IWFMult(
  init_design,
  grad,
  matB,
  min,
  max,
  grid.length,
  join_thresh,
  delete_thresh,
  delta_weights,
  tol,
  tol2,
  crit_name
)

Arguments

`init_design`	optional dataframe with the initial design for the algorithm. A dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`grad`	function of partial derivatives of the model.
`matB`	optional matrix of dimensions k x k, for L-optimality.
`min`	numeric value with the inferior bound of the space of the design.
`max`	numeric value with the upper bound of the space of the design.
`grid.length`	numeric value that gives the grid to evaluate the sensitivity function when looking for a maximum.
`join_thresh`	numeric value that states how close, in real units, two points must be in order to be joined together by the join heuristic.
`delete_thresh`	numeric value with the minimum weight, over 1 total, that a point needs to have in order to not be deleted from the design.
`delta_weights`	numeric value in (0, 1), parameter of the algorithm.
`tol`	numeric value for the convergence of the weight optimizing algorithm.
`tol2`	numeric value for the stop condition of the algorithm.

Value

list correspondent to the output of the correspondent algorithm called, dependent on the criterion. A list of two objects:

optdes: a dataframe with the optimal design in two columns, Point and Weight.
sens: a plot with the sensitivity function to check for optimality of the design.

L-Augment Design

Description

L-Augments a design. The user gives an initial design for which he would like to add points and specifies the weight of the new points. Then he is prompted to choose a minimum efficiency. After that, the candidate points region is calculated and the user can choose the points and weights to add.

Usage

laugment_design(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  matB,
  weight_fun = function(x) 1
)
laugment_design(
  init_design,
  alpha,
  model,
  parameters,
  par_values,
  design_space,
  calc_optimal_design,
  matB,
  weight_fun = function(x) 1
)

Arguments

`init_design`	dataframe with "Point" and "Weight" columns that represents the initial design to augment
`alpha`	combined weight of the new points
`model`	formula that represents the model with x as the independent variable
`parameters`	character vector with the unknown parameters of the model to estimate
`par_values`	numeric vector with the initial values of the unknown parameters
`design_space`	numeric vector with the limits of the space of the design
`calc_optimal_design`	boolean parameter, if TRUE, the optimal design is calculated and efficiencies of the initial and augmented design are given
`matB`	optional matrix of dimensions k x k, for L-optimality.
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response

Value

A dataframe that represents the L-augmented design

Examples

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
augment_design("I-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
augment_design("I-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)

init_des <- data.frame("Point" = c(30, 60, 90), "Weight" = c(1/3, 1/3, 1/3))
augment_design("I-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), TRUE)
augment_design("I-Optimality", init_des, 0.25, y ~ 10^(a-b/(c+x)), c("a","b","c"),
  c(8.07131,  1730.63, 233.426), c(1, 100), FALSE)

Calculates the optimal design for a specified criterion

Description

The opt_des function calculates the optimal design for an optimality criterion and a model input from the user. The parameters allows for the user to customize the parameters for the cocktail algorithm in case the default set does not provide a satisfactory output. Depending on the criterion, additional details are necessary. For 'Ds-Optimality' the par_int parameter is necessary. For 'I-Optimality' either the matB or reg_int must be provided.

Usage

opt_des(
  criterion,
  model,
  parameters,
  par_values = c(1),
  design_space,
  init_design = NULL,
  join_thresh = -1,
  delete_thresh = 0.02,
  delta = 1/2,
  tol = 1e-05,
  tol2 = 1e-05,
  par_int = NULL,
  matB = NULL,
  reg_int = NULL,
  desired_output = c(1, 2),
  distribution = NA,
  weight_fun = function(x) 1
)
opt_des(
  criterion,
  model,
  parameters,
  par_values = c(1),
  design_space,
  init_design = NULL,
  join_thresh = -1,
  delete_thresh = 0.02,
  delta = 1/2,
  tol = 1e-05,
  tol2 = 1e-05,
  par_int = NULL,
  matB = NULL,
  reg_int = NULL,
  desired_output = c(1, 2),
  distribution = NA,
  weight_fun = function(x) 1
)

Arguments

`criterion`	character variable with the chosen optimality criterion. Can be one of the following: 'D-Optimality' 'Ds-Optimality' 'A-Optimality' 'I-Optimality' 'L-Optimality'
`model`	formula describing the model to calculate the optimal design. Must use x as the variable.
`parameters`	character vector with the parameters of the models, as written in the `formula`.
`par_values`	numeric vector with the parameters nominal values, in the same order as given in `parameters`.
`design_space`	numeric vector with the limits of the space of the design.
`init_design`	optional dataframe with the initial design for the algorithm. A dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`join_thresh`	optional numeric value that states how close, in real units, two points must be in order to be joined together by the join heuristic.
`delete_thresh`	optional numeric value with the minimum weight, over 1 total, that a point needs to have in order to not be deleted from the design.
`delta`	optional numeric value in (0, 1), parameter of the algorithm.
`tol`	optional numeric value for the convergence of the weight optimizing algorithm.
`tol2`	optional numeric value for the stop criterion: difference between maximum of sensitivity function and optimality criterion.
`par_int`	optional numeric vector with the index of the `parameters` of interest for Ds-optimality.
`matB`	optional matrix of dimensions k x k, for L-optimality.
`reg_int`	optional numeric vector of two components with the bounds of the interest region for I-Optimality.
`desired_output`	not functional yet: decide which kind of output you want.
`distribution`	character variable specifying the probability distribution of the response. Can be one of the following: 'Homoscedasticity' 'Gamma', which can be used for exponential or normal heteroscedastic with constant relative error 'Poisson' 'Logistic' 'Log-Normal' (work in progress)
`weight_fun`	optional one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response.

Value

a list of two objects:

optdes: a dataframe with the optimal design in two columns, Point and Weight.
sens: a plot with the sensitivity function to check for optimality of the design.

Examples

opt_des("D-Optimality", y ~ a * exp(-b / x), c("a", "b"), c(1, 1500), c(212, 422))
opt_des("D-Optimality", y ~ a * exp(-b / x), c("a", "b"), c(1, 1500), c(212, 422))

Plot Convergence of the algorithm

Description

Plots the criterion value on each of the steps of the algorithm, both for optimizing weights and points, against the total step number.

Usage

plot_convergence(convergence)
plot_convergence(convergence)

Arguments

convergence

A dataframe with two columns:

criteria contains value of the criterion on each step.
step contains number of the step.

Value

A ggplot object with the criteria in the y axis and step in the x axis.

Plot sensitivity function

Description

Plots the sensitivity function and the value of the Equivalence Theorem as an horizontal line, which helps assess the optimality of the design of the given sensitivity function.

Usage

plot_sens(min, max, sens_function, criterion_value)
plot_sens(min, max, sens_function, criterion_value)

Arguments

`min`	Minimum of the space of the design, used in the limits of the representation.
`max`	Maximum of the space of the design, used in the limits of the representation.
`sens_function`	A single variable function, the sensitivity function.
`criterion_value`	A numeric value representing the other side of the inequality of the Equivalence Theorem.

Value

A ggplot object that represents the sensitivity function

Plot function for optdes

Description

Plot function for optdes

Usage

## S3 method for class 'optdes'
plot(x, ...)
## S3 method for class 'optdes'
plot(x, ...)

Arguments

`x`	An object of class `optdes`.
`...`	Possible extra arguments for plotting dataframes

Examples

rri <- opt_des(Criterion = "I-Optimality", model = y ~ a * exp(-b / x),
  parameters = c("a", "b"), par_values = c(1, 1500), design_space = c(212, 422),
  reg_int = c(380, 422))
plot(rri)
rri <- opt_des(Criterion = "I-Optimality", model = y ~ a * exp(-b / x),
  parameters = c("a", "b"), par_values = c(1, 1500), design_space = c(212, 422),
  reg_int = c(380, 422))
plot(rri)

Print function for optdes

Description

Print function for optdes

Usage

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

Arguments

`x`	An object of class `optdes`.
`...`	Possible extra arguments for printing dataframes

Examples

rri <- opt_des(Criterion = "I-Optimality", model = y ~ a * exp(-b / x),
  parameters = c("a", "b"), par_values = c(1, 1500), design_space = c(212, 422),
  reg_int = c(380, 422))
print(rri)
rri <- opt_des(Criterion = "I-Optimality", model = y ~ a * exp(-b / x),
  parameters = c("a", "b"), par_values = c(1, 1500), design_space = c(212, 422),
  reg_int = c(380, 422))
print(rri)

Master function to calculate the sensitivity function

Description

Calculates the sensitivity function given the desired Criterion, an information matrix and other necessary values depending on the chosen criterion.

Usage

sens(Criterion, grad, M, par_int = c(1), matB = NA)
sens(Criterion, grad, M, par_int = c(1), matB = NA)

Arguments

`Criterion`	character variable with the chosen optimality criterion. Can be one of the following: 'D-Optimality' 'Ds-Optimality' 'A-Optimality' 'I-Optimality' 'L-Optimality'
`grad`	A function in a single variable that returns the partial derivatives vector of the model.
`M`	Information Matrix for the sensitivity function.
`par_int`	Numeric vector of the indexes of the parameters of interest for Ds-Optimality.
`matB`	Matrix resulting from the integration of the one-point Information Matrix along the interest region or lineal matrix for L-Optimality.

Value

The sensitivity function as a matrix of single variable.

Shiny D-augment

Description

Launches the demo shiny application to D-augment several prespecified models

Usage

shiny_augment()
shiny_augment()

Examples

shiny_augment()
shiny_augment()

Shiny Optimal

Description

Launches the demo shiny application to calculate optimal designs for Antoine's Equation

Usage

shiny_optimal()
shiny_optimal()

Examples

shiny_optimal()
shiny_optimal()

Summary function for optdes

Description

Summary function for optdes

Usage

## S3 method for class 'optdes'
summary(object, ...)
## S3 method for class 'optdes'
summary(object, ...)

Arguments

`object`	An object of class `optdes`.
`...`	Possible extra arguments for the summary

Examples

rri <- opt_des(Criterion = "I-Optimality", model = y ~ a * exp(-b / x),
  parameters = c("a", "b"), par_values = c(1, 1500), design_space = c(212, 422),
  reg_int = c(380, 422))
summary(rri)
rri <- opt_des(Criterion = "I-Optimality", model = y ~ a * exp(-b / x),
  parameters = c("a", "b"), par_values = c(1, 1500), design_space = c(212, 422),
  reg_int = c(380, 422))
summary(rri)

Trace

Description

Return the mathematical trace of a matrix, the sum of its diagonal elements.

Usage

tr(M)
tr(M)

Arguments

`M`	The matrix from which to calculate the trace.

Value

The trace of the matrix.

Update Design with new point

Description

Updates a design adding a new point to it. If the added point is closer than delta to an existing point of the design, the two points are merged together as their arithmetic average. Then updates the weights to be equal to all points of the design.

Usage

update_design(design, xmax, delta, new_weight)
update_design(design, xmax, delta, new_weight)

Arguments

`design`	Design to update. It's a dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`xmax`	The point to add as a numeric value.
`delta`	Threshold which defines how close the new point has to be to any of the existing ones in order to merge with them.
`new_weight`	Number with the weight for the new point.

Value

The updated design.

Merge close points of a design

Description

Takes a design and merge together all points that are closer between them than a certain threshold delta.

Usage

update_design_total(design, delta)
update_design_total(design, delta)

Arguments

design

The design to update. It's a dataframe with two columns:

Point contains the support points of the design.
Weight contains the corresponding weights of the Points.

delta

Threshold which defines how close two points have to be to any of the existing ones in order to merge with them.

Value

The updated design.

Deletes duplicates points

Description

Within a vector of points, deletes points that are close enough (less than the tol parameter). Returns the points without the "duplicates"

Usage

update_sequence(points, tol)
update_sequence(points, tol)

Arguments

`points`	Points to be updated
`tol`	Tolerance for which two points are considered the same

Value

The points without duplicates

Update weight D-Optimality

Description

Implementation of the weight update formula for D-Optimality used to optimize the weights of a design, which is to be applied iteratively until no sizable changes happen.

Usage

update_weights(design, sens, k, delta)
update_weights(design, sens, k, delta)

Arguments

`design`	Design to optimize the weights from. It's a dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`sens`	Sensibility function for the design and model.
`k`	Number of parameters of the model.
`delta`	A parameter of the algorithm that can be tuned. Must be $0< delta < 1$ .

Value

returns the new weights of the design after one iteration.

Update weight Ds-Optimality

Description

Implementation of the weight update formula for Ds-Optimality used to optimize the weights of a design, which is to be applied iteratively until no sizable changes happen.

Usage

update_weightsDS(design, sens, s, delta)
update_weightsDS(design, sens, s, delta)

Arguments

`design`	Design to optimize the weights from. It's a dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`sens`	Sensibility function for the design and model.
`s`	number of parameters of interest of the model
`delta`	A parameter of the algorithm that can be tuned. Must be $0< delta < 1$ .

Value

returns the new weights of the design after one iteration.

Update weight I-Optimality

Description

Implementation of the weight update formula for I-Optimality used to optimize the weights of a design, which is to be applied iteratively until no sizable changes happen. A-Optimality if instead of the integral matrix the identity function is used.

Usage

update_weightsI(design, sens, crit, delta)
update_weightsI(design, sens, crit, delta)

Arguments

`design`	Design to optimize the weights from. It's a dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`sens`	Sensibility function for the design and model.
`crit`	Value of the criterion function for I-Optimality.
`delta`	A parameter of the algorithm that can be tuned. Must be $0< delta < 1$ .

Value

returns the new weights of the design after one iteration.

Weight function per distribution

Description

Weight function per distribution

Usage

weight_function(model, char_vars, values, distribution = "Homoscedasticity")
weight_function(model, char_vars, values, distribution = "Homoscedasticity")

Arguments

`model`	formula describing the model to use. Must use x as the variable.
`char_vars`	character vector with the parameters of the models, as written in the `formula`
`values`	numeric vector with the parameters nominal values, in the same order as given in `parameters`.
`distribution`	character variable specifying the probability distribution of the response. Can be one of the following: 'Homoscedasticity' 'Gamma', which can be used for exponential or normal heteroscedastic with constant relative error 'Poisson' 'Logistic' 'Log-Normal' (work in progress)

Value

one variable function that represents the square of the structure of variance, in case of heteroscedastic variance of the response.

Master function for the cocktail algorithm, that calls the appropriate one given the criterion.

Description

Depending on the Criterion the cocktail algorithm for the chosen criterion is called, and the necessary parameters for the functions are given from the user input.

Usage

WFMult(
  init_design,
  grad,
  criterion,
  par_int = NA,
  matB = NA,
  min,
  max,
  grid.length,
  join_thresh,
  delete_thresh,
  k,
  delta_weights,
  tol,
  tol2
)
WFMult(
  init_design,
  grad,
  criterion,
  par_int = NA,
  matB = NA,
  min,
  max,
  grid.length,
  join_thresh,
  delete_thresh,
  k,
  delta_weights,
  tol,
  tol2
)

Arguments

`init_design`	optional dataframe with the initial design for the algorithm. A dataframe with two columns: `Point` contains the support points of the design. `Weight` contains the corresponding weights of the `Point`s.
`grad`	function of partial derivatives of the model.
`criterion`	character variable with the chosen optimality criterion. Can be one of the following: 'D-Optimality' 'Ds-Optimality' 'A-Optimality' 'I-Optimality' 'L-Optimality'
`par_int`	numeric vector with the index of the `parameters` of interest. Only necessary when the `criterion` chosen is 'Ds-Optimality'.
`matB`	optional matrix of dimensions k x k, for L-optimality.
`min`	numeric value with the inferior bound of the space of the design.
`max`	numeric value with the upper bound of the space of the design.
`grid.length`	numeric value that gives the grid to evaluate the sensitivity function when looking for a maximum.
`join_thresh`	numeric value that states how close, in real units, two points must be in order to be joined together by the join heuristic.
`delete_thresh`	numeric value with the minimum weight, over 1 total, that a point needs to have in order to not be deleted from the design.
`k`	number of unknown parameters of the model.
`delta_weights`	numeric value in (0, 1), parameter of the algorithm.
`tol`	numeric value for the convergence of the weight optimizing algorithm.
`tol2`	numeric value for the stop condition of the algorithm.

Value

list correspondent to the output of the correspondent algorithm called, dependent on the criterion. A list of two objects:

optdes: a dataframe with the optimal design in two columns, Point and Weight.
sens: a plot with the sensitivity function to check for optimality of the design.

Package 'optedr'

Help Index

Add two designs

Description

Usage

Arguments

Value

Update design given crosspoints and alpha

Description

Usage

Arguments

Value

Augment Design

Description

Usage

Arguments

Value

Examples

Check Inputs

Description

Usage

Arguments

Combinatorial round

Description

Usage

Arguments

Value

Examples

Master function for the criterion function

Description

Usage

Arguments

Value

Calculate crosspoints

Description

Usage

Arguments

Value

D-Augment Design

Description

Usage

Arguments

Value

See Also

Examples

Criterion function for D-Optimality

Description

Usage

Arguments

Value

Remove low weight points

Description

Usage

Arguments

Value

Efficiency between optimal design and a user given design

Description

Usage

Arguments

Value

See Also

Examples

Ds-Augment Design

Description

Usage

Arguments

Value

See Also

Examples

Criterion function for Ds-Optimality

Description

Usage

Arguments

Value

Sensitivity function for D-Optimality

Description

Usage

Arguments

Value

Sensitivity function for Ds-Optimality