ForLion (version 0.1.0)

EW_ForLion_MLM_Optimal: EW ForLion function for multinomial logit models

Description

EW ForLion function for multinomial logit models

Usage

EW_ForLion_MLM_Optimal(
  J,
  n.factor,
  factor.level,
  hfunc,
  h.prime,
  bvec_matrix,
  link = "continuation",
  EW_Fi.func = EW_Fi_MLM_func,
  delta = 1e-05,
  epsilon = 1e-12,
  reltol = 1e-05,
  rel.diff = 0,
  maxit = 100,
  random = FALSE,
  nram = 3,
  rowmax = NULL,
  Xini = NULL,
  random.initial = FALSE,
  nram.initial = 3,
  optim_grad = FALSE
)

Value

m the number of design points

x.factor matrix of experimental factors with rows indicating design point

p the reported EW D-optimal approximate allocation

det the determinant of the maximum Expectation of Fisher information

convergence TRUE or FALSE, whether converge

min.diff the minimum Euclidean distance between design points

x.close pair of design points with minimum distance

itmax iteration of the algorithm

Arguments

J

number of response levels in the multinomial logit model

n.factor

vector of numbers of distinct levels, "0" indicates continuous factors, "0"s always come first, "2" or above indicates discrete factor, "1" is not allowed

factor.level

list of distinct levels, (min, max) for continuous factor, continuous factors first, should be the same order as n.factor

hfunc

function for obtaining model matrix h(y) for given design point y, y has to follow the same order as n.factor

h.prime

function to obtain dX/dx

bvec_matrix

the matrix of the bootstrap parameter values of beta

link

link function, default "continuation", other choices "baseline", "cumulative", and "adjacent"

EW_Fi.func

function to calculate row-wise Expectation of Fisher information Fi, default is EW_Fi_MLM_func

delta

tuning parameter, the generated design pints distance threshold, || x_i(0) - x_j(0) || >= delta, default 1e-5

epsilon

determining f.det > 0 numerically, f.det <= epsilon will be considered as f.det <= 0, default 1e-12

reltol

the relative convergence tolerance, default value 1e-5

rel.diff

points with distance less than that will be merged, default value 0

maxit

the maximum number of iterations, default value 100

random

TRUE or FALSE, if TRUE then the function will run EW lift-one with additional "nram" number of random approximate allocation, default to be FALSE

nram

when random == TRUE, the function will run EW lift-one nram number of initial proportion p00, default is 3

rowmax

maximum number of points in the initial design, default NULL indicates no restriction

Xini

initial list of design points, default NULL will generate random initial design points

random.initial

TRUE or FALSE, if TRUE then the function will run EW ForLion with additional "nram.initial" number of random initial design points, default FALSE

nram.initial

when random.initial == TRUE, the function will run EW ForLion algorithm with nram.initial number of initial design points Xini, default is 3

optim_grad

TRUE or FALSE, default is FALSE, whether to use the analytical gradient function or numerical gradient for searching optimal new design point

Examples

J=3
p=5
hfunc.temp = function(y){
matrix(data=c(1,y,y*y,0,0,0,0,0,1,y,0,0,0,0,0), nrow=3, ncol=5, byrow=TRUE)
} #hfunc is a 3*5 matrix, transfer x design matrix to model matrix for emergence of flies example

hprime.temp = function(y){
matrix(data=c(0, 1, 2*y, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0), nrow=3, ncol=5, byrow=TRUE)
}

link.temp = "continuation"
n.factor.temp = c(0)  # 1 continuous factor no discrete factor in EW ForLion
factor.level.temp = list(c(80,200)) #boundary for continuous parameter in Forlion
bvec_bootstrap<-matrix(c(-0.2401, -1.9292, -2.7851, -1.614,-1.162,
                         -0.0535, -0.0274, -0.0096,-0.0291, -0.04,
                          0.0004,  0.0003,  0.0002,  0.0003,  0.1,
                         -9.2154, -9.7576, -9.6818, -8.5139, -8.56),nrow=4,byrow=TRUE)
EW_ForLion_MLM_Optimal(J=J, n.factor=n.factor.temp, factor.level=factor.level.temp,
         hfunc=hfunc.temp,h.prime=h.prime.temp, bvec_matrix=bvec_bootstrap,rel.diff=1,
         link=link.temp, optim_grad=FALSE)