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,
  var_names = NULL,
  xlist_fix = NULL,
  hfunc,
  bvec,
  link,
  reltol = 1e-05,
  delta = 0,
  maxit = 100,
  random = FALSE,
  nram = 3,
  logscale = FALSE,
  rowmax = NULL,
  Xini = NULL
)

Arguments

n.factor	vector of numbers of distinct levels, “0” indicating continuous factors that always come first, “2” or more for discrete factors, and “1” not allowed.
factor.level	list of distinct factor levels, “(min, max)” for continuous factors that always come first, finite sets for discrete factors.
var_names	Names for the design factors. Must have the same length asfactor.level. Defaults to "X1", "X2", ...
xlist_fix	list of discrete factor experimental settings under consideration, default NULL indicating a list of all possible discrete factor experimental settings will be used.
hfunc	function for generating the corresponding model matrix or predictor vector, given an experimental setting or design point.
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
delta	relative difference as merging threshold for the merging step, the distance of two points less than delta may be merged, default 0, can be different from delta0 for the initial design.
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, whether or not to run the lift-one step in log-scale, i.e., using liftoneDoptimal_log_GLM_func() or 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 indicating automatically generating an initial list of 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, xlist_fix=NULL,
hfunc=hfunc.temp, bvec=b.temp, link=link.temp, reltol=1e-2, delta=0.03, maxit=500,
random=FALSE,nram=3, logscale=TRUE)

ForLion documentation built on June 28, 2025, 1:09 a.m.