liftone_constrained_GLM: Find constrained D-optimal approximate design for generalized...

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

Find constrained D-optimal approximate design for generalized linear models (GLM)

Description

Find constrained D-optimal approximate design for generalized linear models (GLM)

Usage

liftone_constrained_GLM(
  X,
  W,
  g.con,
  g.dir,
  g.rhs,
  lower.bound,
  upper.bound,
  reltol = 1e-05,
  maxit = 500,
  random = TRUE,
  nram = 3,
  w00 = NULL,
  epsilon = 1e-12
)

Arguments

X	Model matrix, with nrow = num of design points and ncol = num of parameters
W	Diagonal of W matrix in Fisher information matrix, can be calculated from W_func_GLM in package
g.con	A matrix of numeric constraint coefficients, one row per constraint, on column per variable (to be used in as const.mat lp() and mat in Rglpk_solve_LP())
g.dir	Vector of character strings giving the direction of the constraint: each value should be one of "<," "<=," "=," "==," ">," or ">=". (In each pair the two values are identical.) to be used as const.dir in lp() and dir in Rglpk_solve_LP()
g.rhs	Vector of numeric values for the right-hand sides of the constraints. to be used as const.rhs in lp() and rhs in Rglpk_solve_LP().
lower.bound	A function to determine lower bound r_i1 in Step 3 of Constrained lift-one algorithm from Yifei, H., Liping, T., Yang, J. (2023) Constrained D-optimal design for paid research study
upper.bound	A function to determine upper bound r_i2 in Step 3 of Constrained lift-one algorithm from Yifei, H., Liping, T., Yang, J. (2023) Constrained D-optimal design for paid research study
reltol	The relative convergence tolerance, default value 1e-5
maxit	The maximum number of iterations, default value 500
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
w00	Specified initial design proportion; default to be NULL, this will generate a random initial design
epsilon	A very small number, for comparison of >0, <0, ==0, to reduce errors, default 1e-12

Value

w is the approximate D-optimal design

w0 is the initial design used to get optimal design w

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

deriv.ans is the derivative from step 6 of constrained lift-one algorithm

gmax is the maximum g function in step 8 of constrained lift-one algorithm

reason is the lift-one loops break reason, either "all derivatives <=0" or "gmax <=0"

Examples

#Example 6 in Section 3.4 of Yifei, H., Liping, T., Yang, J. (2025)
#Constrained D-optimal design for paid research study

#main effect model beta_0, beta_1, beta_21, beta_22
beta = c(0, -0.1, -0.5, -2)

#gives the 6 categories (0,0,0), (0,1,0),(0,0,1),(1,0,0),(1,1,0),(1,0,1)
X.liftone=matrix(data=c(1,0,0,0,1,0,1,0,1,0,0,1,1,1,0,0,1,1,1,0,1,1,0,1),
ncol=4, byrow=TRUE)

#calculate W matrix based on beta's under logit link
W_matrix=W_func_GLM(X= X.liftone, b=beta)

m=6 #number of categories
nsample = 200
rc = c(50, 40, 10, 200, 150, 50)/nsample
g.con = matrix(0,nrow=(2*m+1), ncol=m)
g.con[1,] = rep(1, m)
g.con[2:(m+1),] = diag(m)
g.con[(m+2):(2*m+1), ] = diag(m)
g.dir = c("==", rep("<=", m), rep(">=", m))
g.rhs = c(1, rc, rep(0, m))

lower.bound=function(i, w){
  nsample = 200
  rc = c(50, 40, 10, 200, 150, 50)/nsample
  m=length(w) #num of categories
  temp = rep(0,m)
  temp[w>0]=1-pmin(1,rc[w>0])*(1-w[i])/w[w>0];
  temp[i]=0;
  max(0,temp);
}
upper.bound=function(i, w){
  nsample = 200
  rc = c(50, 40, 10, 200, 150, 50)/nsample
  m=length(w) #num of categories
  rc[i];
  min(1,rc[i]);
}

approximate_design = liftone_constrained_GLM(X=X.liftone, W=W_matrix,
g.con=g.con, g.dir=g.dir, g.rhs=g.rhs, lower.bound=lower.bound,
upper.bound=upper.bound, reltol=1e-10, maxit=100, random=TRUE, nram=4,
w00=NULL, epsilon = 1e-8)

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