Boptbd {Boptbd}

Bayesain optimal block designs

Description

The function Boptbd is used to compute Bayesian A- or D-optimal block designs under the linear mixed effects model settings using array/block exchange algorithm of Debusho, Gemechu and Haines (2018).

Usage

Boptbd(trt.N, blk.N, alpha, beta, nrep, brep, itr.cvrgval, Optcrit = "", ...)

## Default S3 method:
Boptbd(trt.N, blk.N, alpha, beta, nrep, brep, itr.cvrgval, Optcrit = "", ...)
## S3 method for class 'Boptbd'
print(x, ...)
## S3 method for class 'Boptbd'
summary(object, ...)

Arguments

trt.N

integer, specifying number of treatments, v.

blk.N

integer, specifying number of blocks, b.

alpha

numeric, representing the shape parameter of beta distribution.

beta

numeric, representing the shape parameter of beta distribution.

nrep

integer, specifying number of replications of the optimization procedure.

brep

integer, specifying number of Monte Carlo samples from a prior beta distribution.

itr.cvrgval

integer, specifying number of iterations required for convergence during the block exchange procedure.

Optcrit

character, specifying the optimality criteria to be used. Optcrit takes the letter "A" and "D" for Bayesian A- and D-optimal block designs, respectively.

x

the object to be printed.

object

an object of class "Boptbd".

...

not used.

Details

Boptbd computes Bayesian optimal block designs where the interest is in a comparison of all possible elementary treatment contrasts. Under the linear mixed effects model setting, where the block effects are assumed to be random, the treatment information matrix (C-matrix) is dependent on the unknown parameter rho (ratio of unknown variance components of random error and block effects). A Bayesian optimal design extends the locally optimal approach by specifying a prior distribution for the parameter rho. Boptbd function computes Bayesian A- and D-optimal block designs via calling of two sub-functions Baoptbd and Bdoptbd, respectively. Each function requires an initial connected block designs generated using the function intcbd.

The minimum value of trt.N and blk.N is 3 and trt.N should be less than or equal to blk.N - 1.

Boptbd perform the block exchange procedure through deletion and addition of candidate block at a time and selects a design with best block exchange with respect to the optimality criterion value. It uses the steps of Bueno Filho and Gilmour (2007) for numerical evaluation of the Bayesian criterion values.

nrep takes a value of greater than or equal to 2. However, to ensure optimality of the resultant design, the nrep should be greater than or equal to 10 and in addition, as trt.N and blk.N increase, to ensure optimality of resultant design, it is advised to further increase the value of nrep up to greater than or equal to 100. brep takes a value of greater than or equal to 2. As brep value increase, the execution time to generate Bayesian optimal design increase.

itr.cvrgval number of iterations during exchange procedure. It takes a value between 2 and blk.N. It is used to speedup the computer search time by setting how long should the user should wait for the exchange process to obtain any different (if any) design than the one that was produced as the result of the preceding exchange of the current array in the initial design with candidate array. This is mainly effective if blk.N is very large. For example itr.cvrgval = 2, means the exchange procedure will jump to the next block test if the exchange of the two preceding blocks with candidate block results with the same efficient designs. The function will not give error message if the users set itr.cvrgval > blk.N and it will automatically set itr.cvrgval = blk.N. The smaller the itr.cvrgval means the faster the exchange procedure is, but this will reduce the chance of getting optimal block design and users are advised to set itr.cvrgval closer to blk.N.

Value

Returns the resultant Bayesian A- or D-optimal block design with its corresponding score value and parametric combination saved in excel file in a temporary directory. In addition, the function Boptbd displays the graphical layout of the resultant Bayesian optimal block designs. Specifically:

call

the method call.

v

number of treatments.

b

number of blocks

alpha

alpha value.

beta

beta value.

nrep

number of replications of the optimization procedure.

itr.cvrgval

number of iterations required for convergence during the exchange procedure.

Optcrit

optimality criteria.

brep

umber of Monte Carlo samples from a prior beta distribution.

OptdesF

a 2 x b obtained Bayesain optimal block design.

Optcrtsv

score value of the optimality criteria 'Optcrit' of the resultant Bayesian optimal block design 'OptdesF'.

file_loc, file_loc2

location where the summary of the resultant Bayesian optimal block design is saved in .csv format.

equireplicate

logical value indicating whether the resultant Bayesian optimal block design is equireplicate or not.

vtrtrep

vector of treatment replication of the resultant Bayesian optimal block design.

Cmat

the C-matrix or treatment information matrix of the Bayesian optimal block design.

The graphical layout of the resultant Bayesain optimal block design.

NB: The function "Boptbd" also saves the summary of the resultant Bayesian optimal block design in .csv format in a temporary directory. Furthermore, this function reports only one final optimal block design, however, there is a possibility of more than one optimal block designs for a given parametric combination. The function graphoptBbd can be used to view and rearrange the graphical layout of the resultant optimal block design on tcltk window. Alternative to the function Boptbd, a GUI tcltk window can be used to generate Bayesain optimal block designs, see mmenuBbd and fixparBbd.

Author(s)

Dibaba Bayisa Gemechu, Legesse Kassa Debusho, and Linda Haines

References

Bueno Filho, J. S. de S., Gilmour, S. G. and Rosa, G. J. M. (2006). Design of microarray experiments for genetical genomics studies. Genetics, 174, 945-957

Debusho, L. K., Gemechu, D. B. and Haines, L. (2018). Algorithmic construction of optimal block designs for two-colour cDNA microarray experiments using the linear mixed effects model. Communications in Statistics - Simulation and Computation, https://doi.org/10.1080/03610918.2018.1429617.

Gemechu D. B., Debusho L. K. and Haines L. M. (2014). A-optimal designs for two-colour cDNA microarray experiments using the linear mixed effects model. Peer-reviewed Proceedings of the Annual Conference of the South African Statistical Association for 2014 (SASA 2014), Rhodes University, Grahamstown, South Africa. pp 33-40, ISBN: 978-1-86822-659-7.

See Also

mmenuBbd, fixparBbd, intcbd

Examples

  ##To obtain Bayesian A-optimal block design for the following treatment combintions:
  trt.N <- 3 #Number of treatments
  blk.N <- 3 #Number of blocks
  alpha <- 0.1 #alpha value
  beta <- 0.1 #beta value
  nrep <- 5  #Number of replications
  brep <- 5  #Number of Monte Carlo samples from a prior beta distribution, Beta(0.1, 0.1) 
  itr.cvrgval <- 6 #Number of iterations required during the exchange procedure
  Optcrit <- "A"   #Optimality criteria
  
  Baoptbd_example <- Boptbd(trt.N = 3, blk.N = 3, alpha = 0.1, beta = 0.1, nrep = 5, brep = 5, 
                            itr.cvrgval = 6, Optcrit = "A")
  
  summary(Baoptbd_example)