liftone_MLM: Unconstrained lift-one algorithm to find D-optimal...

In CDsampling: 'CDsampling': Constraint Sampling in Paid Research Studies

Unconstrained lift-one algorithm to find D-optimal allocations for MLM

Description

Unconstrained lift-one algorithm to find D-optimal allocations for MLM

Usage

liftone_MLM(
  m,
  p,
  Xi,
  J,
  beta,
  link = "continuation",
  Fi.func = Fi_func_MLM,
  reltol = 1e-05,
  maxit = 500,
  w00 = NULL,
  random = TRUE,
  nram = 3
)

Arguments

m	The number of design points; it is usually the number of combinations of all the stratification factors
p	The number of parameters in the MLM model
Xi	Model matrix, a J by p by m 3D array of predictors for separate response category at all design points(input to determine ppo,npo,po)
J	The number of response levels
beta	A p*1 vector, parameter coefficients for MLM, the order of beta should be consistent with Xi
link	Link function of MLM, default to be "cumulative", options from "continuation", "cumulative", "adjacent", and "baseline"
Fi.func	A function for calculating Fisher information at a specific design point, default to be Fi_func_MLM function in the package
reltol	The relative convergence tolerance, default value 1e-5
maxit	The maximum number of iterations, default value 500
w00	Specified initial design proportion; default to be NULL, this will generate a random initial design
random	TRUE or FALSE, if TRUE then the function will run with additional "nram" number of random initial points, default to be TRUE
nram	When random == TRUE, the function will generate nram number of initial points, default is 3

Value

w is the approximate D-optimal design

w0 is the initial design used to get optimal design

Maximum is the maximized |F| value

itmax is the number of iterations

convergence is TRUE or FALSE, if TRUE means the reported design is converged

Examples

J = 5    # number of categories,  >= 3
p = 12    # number of parameters
m = 8    # number of design points
Xi=rep(0,J*p*m) #J*p*m=5*12*8
dim(Xi)=c(J,p,m)
#design matrix
Xi[,,1] = rbind(c( 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))

Xi[,,2] = rbind(c( 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))

Xi[,,3] = rbind(c( 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))

Xi[,,4] = rbind(c( 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))

Xi[,,5] = rbind(c( 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1),
               c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))

Xi[,,6] = rbind(c( 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))

Xi[,,7] = rbind(c( 1, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 1),
               c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))

Xi[,,8] = rbind(c( 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 1, 4, 1, 0, 0, 0),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 1),
                c( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))

thetavec = c(-4.047, -0.131, 4.214, -2.225, -0.376, 3.519,
-0.302, -0.237,  2.420, 1.386,  -0.120,  1.284)

liftone_MLM(m=m, p=p, Xi=Xi, J=J, beta=thetavec, link = "cumulative",
Fi.func=Fi_func_MLM, reltol=1e-5, maxit=500, w00=NULL, random=TRUE, nram=3)

CDsampling documentation built on Oct. 13, 2024, 9:07 a.m.