ForLion_GLM_Optimal: ForLion for generalized linear models

In ForLion: 'ForLion' Algorithm to Find D-Optimal Designs for Experiments

ForLion for generalized linear models

Description

ForLion algorithm to find D-optimal design for GLM models with mixed factors, reference: Section 4 in Huang, Li, Mandal, Yang (2024). 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

ForLion_GLM_Optimal(
  n.factor,
  factor.level,
  hfunc,
  bvec,
  link,
  reltol = 1e-05,
  rel.diff = 0,
  maxit = 100,
  random = FALSE,
  nram = 3,
  logscale = FALSE,
  rowmax = NULL,
  Xini = NULL
)

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
bvec	assumed parameter values of model parameters beta, same length of h(y)
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
maxit	the maximum number of iterations, default value 100
random	TRUE or FALSE, if TRUE then the function will run lift-one with additional "nram" number of random approximate allocation, default to be FALSE
nram	when random == TRUE, the function will run lift-one nram number of initial proportion p00, default is 3
logscale	TRUE or FALSE, if TRUE then the ForLion will run lift-one with logscale, which is liftoneDoptimal_log_GLM_func(); if FALSE then ForLion will run lift-one without logscale, which is 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

Value

m number of design points

x.factor matrix with rows indicating design point

p D-optimal approximate allocation

det Optimal determinant of Fisher information matrix

convergence TRUE or FALSE

min.diff the minimum Euclidean distance between design points

x.close a pair of design points with minimum distance

itmax iteration of the algorithm

Examples

#Example 3 in Huang, Li, Mandal, Yang (2024), electrostatic discharge experiment
hfunc.temp = function(y) {c(y,y[4]*y[5],1);};   # y -> h(y)=(y1,y2,y3,y4,y5,y4*y5,1)
n.factor.temp = c(0, 2, 2, 2, 2)  # 1 continuous factor with 4 discrete factors
factor.level.temp = list(c(25,45),c(-1,1),c(-1,1),c(-1,1),c(-1,1))
link.temp="logit"
b.temp = c(0.3197169,  1.9740922, -0.1191797, -0.2518067,  0.1970956,  0.3981632, -7.6648090)
ForLion_GLM_Optimal(n.factor=n.factor.temp, factor.level=factor.level.temp, hfunc=hfunc.temp,
bvec=b.temp, link=link.temp, reltol=1e-2, rel.diff=0.03, maxit=500, random=FALSE,
nram=3, logscale=TRUE)

ForLion documentation built on April 11, 2025, 5:38 p.m.