design {OWEA}

Design Generator for Three Models

Description

Construct optimal approximate designs as well as efficient exact designs for crossover model with subject dropout, crossover model with proportional residual effect, and interference model.

Usage

design(
  model = c("dropout", "proportional", "interference"),
  n,
  opt,
  t,
  p,
  ...,
  max_iter = 40
)

Arguments

model

an model indicator, must be one of 'dropout', 'proportional', or 'interference'.

n

Positive Integer, total number of observations needed.

opt

Integer. optimal criterion indicator, opt = 0 means D-opt, opt = 1 means A-opt

t

Positive interger,number or levels of treatment, the default coding is integer from 1 to t

p

Numeric, number of periods for crossover model or number of blocks for intereference model

...

other necessary control parameters required by specific model For crossover with dropout, drop, a numeric vector of dropout mechanism For crossover proportional, lambda,value of proportion cofficient in proportional model and sigma, assumed covariance matrix. For interference model, sigma, assumed covariance matrix.

max_iter

a positive integer. Controls maximum iteration time of exchange. Default is 40.

Value

A S3 object of one of classes 'dropout', 'proportional' or 'interference'.

model

the model name

n

total number of observations of exact design

opt

optimal criterion

t

number of levels of treaments

p

number of periods or plots in a block

...

other inputs

initial_design

a randomly chosen design as a starting point for newton's method

exact_design

an exact design rounded from approximate design

approx_design

optimal approximate design

verify_equivalence

result of general equivalence theorem, the last entry is the value of directional derivative

time

computing time for approximate design

See Also

eff, effLB, summary

Examples

# NOTE: max_iter is usually set to 40. 
# Here max_iter = 5 is for demenstration only.
# crossover dropout model
## D-optimal

example1 <- design('dropout',10,0,3,3,drop=c(0,0,0.5), max_iter = 5)
summary(example1)
eff(example1) # efficiency from rounding
effLB(example1) # obtain lower bound of efficiency

## A-optimal
design('dropout',10,1,3,3,drop=c(0,0,0.5), max_iter = 5)


# proportional model
## D-optimal
design('proportional',10,0,3,3, sigma = diag(1,3),tau = matrix(sqrt(1+3),
    nrow=3, ncol=1),lambda = 0.2, max_iter = 5)

## A-optimal
design('proportional',10,1,3,3, sigma = diag(1,3), tau = matrix(sqrt(1+3),
    nrow=3, ncol=1),lambda = 0.2, max_iter = 5)


# interference model
## D-optimal
design('interference',10,0,3,3, sigma = diag(1,3), max_iter = 5)

## A-optimal
design('interference',10,1,3,3, sigma = diag(1,3), max_iter = 5)