ForLion (version 0.1.0)

EW_ForLion_GLM_Optimal: EW ForLion for generalized linear models

Description

EW ForLion algorithm to find EW D-optimal design for GLM models with mixed factors, reference: . Factors may include discrete factors with finite number of distinct levels and continuous factors with specified interval range (min, max), continuous factors, if any, must serve as main-effects only, allowing merging points that are close enough.Continuous factors first then discrete factors, model parameters should in the same order of factors.

Usage

EW_ForLion_GLM_Optimal(
  n.factor,
  factor.level,
  hfunc,
  joint_Func_b,
  Lowerbounds,
  Upperbounds,
  link,
  reltol = 1e-05,
  rel.diff = 0,
  optim_grad = TRUE,
  maxit = 100,
  random = FALSE,
  nram = 3,
  logscale = FALSE,
  rowmax = NULL,
  Xini = NULL
)

Value

m number of design points

x.factor matrix with rows indicating design point

p EW D-optimal approximate allocation

det Optimal determinant of Fisher information matrix

x.model model matrix X

E_w vector of E_w such that E_w=diag(p*E_w)

convergence TRUE or FALSE

min.diff the minimum Euclidean distance between design points

x.close a pair of design points with minimum distance

Arguments

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

joint_Func_b

The prior joint probability distribution of the parameters

Lowerbounds

The lower limit of the prior distribution for each parameter

Upperbounds

The upper limit of the prior distribution for each parameter

link

link function, default "logit", other links: "probit", "cloglog", "loglog", "cauchit", "log", "identity"

reltol

the relative convergence tolerance, default value 1e-5

rel.diff

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

optim_grad

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

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

logscale

TRUE or FALSE, if TRUE then the EW ForLion will run EW lift-one with logscale, which is EW_liftoneDoptimal_log_GLM_func(); if FALSE then ForLion will run EW lift-one without logscale, which is EW_liftoneDoptimal_GLM_func()

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

Examples

#Example  Crystallography Experiment
hfunc.temp = function(y) {c(y,1)}   # y -> h(y)=(y1,1)
n.factor.temp = c(0)  # 1 continuous factors
factor.level.temp = list(c(-1,1))
link.temp="logit"
paras_lowerbound<-c(4,-3)
paras_upperbound<-c(10,3)
 gjoint_b<- function(x) {
 Func_b<-1/(prod(paras_upperbound-paras_lowerbound))
 ##the prior distributions are follow uniform distribution
return(Func_b)
}
EW_ForLion_GLM_Optimal(n.factor=n.factor.temp, factor.level=factor.level.temp,
hfunc=hfunc.temp,joint_Func_b=gjoint_b, Lowerbounds=paras_lowerbound,
Upperbounds=paras_upperbound, link=link.temp, reltol=1e-2, rel.diff=0.01,
optim_grad=FALSE, maxit=500, random=FALSE, nram=3, logscale=FALSE,Xini=NULL)