ForLion (version 0.3.0)

ForLion_MLM_Optimal: ForLion function for multinomial logit models

Description

Function for ForLion algorithm to find D-optimal design under multinomial logit models with mixed factors. Reference Section 3 of 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_MLM_Optimal(
  J,
  n.factor,
  factor.level,
  var_names = NULL,
  xlist_fix = NULL,
  hfunc,
  h.prime,
  bvec,
  link = "continuation",
  Fi.func = Fi_MLM_func,
  delta0 = 1e-05,
  epsilon = 1e-12,
  reltol = 1e-05,
  delta = 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 D-optimal approximate allocation

det the determinant of the maximum 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” 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.

h.prime

function to obtain dX/dx

bvec

assumed parameter values of model parameters beta, same length of h(y)

link

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

Fi.func

function to calculate row-wise Fisher information Fi, default is Fi_MLM_func

delta0

merging threshold for initial design, such that, || x_i(0) - x_j(0) || >= delta0, default 1e-5

epsilon

tuning parameter as converging threshold, such that, a nonnegative number is regarded as numerical zero if less than epsilon, default 1e-12.

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, whether or not to repeat the lift-one step multiple times with random initial allocations, default FALSE.

nram

number of times repeating the lift-one step with random initial allocations, valid only if random is TRUE, default 3.

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.

random.initial

TRUE or FALSE, whether or not to repeat the whole procedure multiple times with random initial designs, default FALSE.

nram.initial

number of times repeating the whole procedure with random initial designs, valid only if random.initial is TRUE, default 3.

optim_grad

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

Examples

m=5
p=10
J=5
link.temp = "cumulative"
n.factor.temp = c(0,0,0,0,0,2)  # 1 discrete factor w/ 2 levels + 5 continuous
## Note: Always put continuous factors ahead of discrete factors,
## pay attention to the order of coefficients paring with predictors
factor.level.temp = list(c(-25,25), c(-200,200),c(-150,0),c(-100,0),c(0,16),c(-1,1))
hfunc.temp = function(y){
if(length(y) != 6){stop("Input should have length 6");}
 model.mat = matrix(NA, nrow=5, ncol=10, byrow=TRUE)
 model.mat[5,]=0
 model.mat[1:4,1:4] = diag(4)
 model.mat[1:4, 5] =((-1)*y[6])
 model.mat[1:4, 6:10] = matrix(((-1)*y[1:5]), nrow=4, ncol=5, byrow=TRUE)
 return(model.mat)
 }
bvec.temp=c(-1.77994301, -0.05287782,  1.86852211, 2.76330779, -0.94437464, 0.18504420,
-0.01638597, -0.03543202, -0.07060306, 0.10347917)

h.prime.temp = NULL #use numerical gradient (optim_grad=FALSE)
ForLion_MLM_Optimal(J=J, n.factor=n.factor.temp, factor.level=factor.level.temp, xlist_fix=NULL,
hfunc=hfunc.temp,h.prime=h.prime.temp, bvec=bvec.temp, link=link.temp, optim_grad=FALSE)