Computes the treatment information matrix

Description

Computes the information matrix (C-matrix) for treatment effects under either the linear fixed effects model or the linear mixed effects model setting for a given block design of size 2.

Usage

cmatbd.mae(trt.N, blk.N, theta, des)

Arguments

Value

Returns a v x v treatment information matrix (C-matrix).

Author(s)

Dibaba Bayisa Gemechu, Legesse Kassa Debusho, and Linda Haines

References

Debusho, L. K., Gemechu, D. B., and Haines, L. M. (2016). Algorithmic construction of optimal block designs for two-colour cDNA microarray experiments using the linear mixed model. Under review.

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

optbdmaeAT, fixparbd.mae, intcbd.mae

Examples

##Information matrix

     trt.N <- 3 
     blk.N <- 3 
     theta <- 0.2 
     dsgn <- intcbd.mae(trt.N = 3, blk.N = 3)

     cmatbd.mae(trt.N = 3, blk.N = 3, theta = 0.2, des = dsgn)

Sets parametric values

Description

Creates a tcltk widow that allow the users to set or fix values for the parametric combinations to compute optimal or near-optimal block designs.

Usage

fixparbd.mae(Optcrit)

Arguments

Details

fixparbd.mae creates a pop-up tcltk window that allow the users to set the parametric combinations to compute optimal or near-optimal block designs. The parameters include the number of treatments trt.N, number arrays blk.N, theta value theta, number of replications of the optimization procedure nrep and number of iterations required during exchange procedure itr.cvrgval. Furthermore, on this window, the checkbox options that allow the users to choose whether or not they need to have the graphical layout of the resultant optimal or near-optimal block design, to make a choice between the two-alternative algorithms (treatment exchange and array exchange algorithms) and to print the summary of the resultant optimal or near-optimal block design on R-console directly are available.

After setting all the required parametric combinations and selecting the algorithm of interest, clicking on the search button on the set parametric combinations tcltk window, similar to the results that can be obtained when using the function optbdmaeAT, the summary of the resultant optimal or near-optimal block design will be saved in the current working directory in .csv format and it will also be displayed on R console with graphical layout of the resultant optimal or near-optimal block designs.

Value

The fixparbd.mae function creates a pop-up tcltk window that allow the users to set the parametric combinations to compute optimal or near-optimal block designs.

Author(s)

Dibaba Bayisa Gemechu, Legesse Kassa Debusho, and Linda Haines

See Also

optbdmaeAT, mmenubd.mae

Creates the graphical layout of resultant optimal design

Description

Creates the graphical layout of resultant A-, MV-, D- or E-optimal or near-optimal block design on a separate pop-up GUI tcltk window.

Usage

graphoptbd.mae(trt.N, blk.N, theta, OptdesF, Optcrit, cbVal2)

Arguments

Details

Detail discussions concerning the constructions of a graphs can be found in igraph R package.

Value

Returns the graphical layout of the resultant optimal or near-optimal block design 'OptdesF' on a separate pop-up window. Furthermore, the function graphoptbd.mae saves the graphical layout of the resultant optimal or near-optimal block design in .pdf format in a working subdirectory.

Note

When closing a pop-up window for graphical layout of the resultant designs (Graph plot), if the window is closed by clicking on the red button with "X" sign (top-right), the warning message "Warning message: In rm(list = cmd, envir = .tkplot.env): object 'tkp ...' not found" will occur in R console irrespective of what command is executed next. To resolve this warning message, click on "close" menu that is located at the top-left of the graph plot pop-up window when closing this window.

Author(s)

Dibaba Bayisa Gemechu, Legesse Kassa Debusho, and Linda Haines

Examples

    ##To create the graphical layout of the D-optimal block design
    ##obtained using the treatment exchange algorithm for 
    trt.N <- 10  #Number of treatments
    blk.N <- 10  #Number of blocks
    theta <- 0.2 #theta value 
    OptdesF <- rbind(1:10, c(2:10,1)) #D-optimal design (loop design)

    graphoptbd.mae(trt.N = 10, blk.N = 10, theta = 0.2, OptdesF, Optcrit = "D", cbVal2 = 0)

Generates initial connected block design

Description

Generates a random initial connected block design for a given number of blocks b of size k = 2 and the number of treatments v.

Usage

intcbd.mae(trt.N, blk.N)

Arguments

Value

Returns a 2 x b connected block design with b blocks of size k = 2 and number of treatments v.

Author(s)

Dibaba Bayisa Gemechu, Legesse Kassa Debusho, and Linda Haines

References

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

optbdmaeAT, cmatbd.mae

Examples

    #Initial connected block design for 
    trt.N <- 4 #Number of treatments
    blk.N <- 4 #Number of blocks

    intcbd.mae(trt.N = 4, blk.N = 4)

Creates the main menu tcltk window

Description

Alternative to directly using the function optbdmaeAT on the R console, the function mmenubd.mae creates the main menu tcltk window with the list of four optimality criteria (A, MV, D and E) for search of optimal or near-optimal block designs for two-colour cDNA microarray experiments.

Usage

mmenubd.mae()

Details

The main menu window created using the function mmenubd.mae contains the list of four optimality criteria (the A-, MV -, D- and E) for block designs that allows user to choose an optimality criterion of interest. The function will then call for a function fixpar.mae for further option regarding the setup of parametric combinations and output, see fixpar.mae documentation.

Author(s)

Dibaba B. Gemechu, Legesse K. Debusho, and Linda M. Haines

See Also

optbdmaeAT, fixparbd.mae

Optimal block designs for two-colour cDNA microarray experiments

Description

Used to compute A-, MV-, D- or E-optimal or near-optimal block designs for two-colour cDNA microarray experiments under either the linear fixed effects model or the linear mixed effects model settings using either the array exchange or treatment exchange algorithms of Debusho, Gemechu and Haines (2018) <doi.org/10.1080/03610918.2018.1429617>.

Usage

optbdmaeAT(trt.N, blk.N, theta, nrep, itr.cvrgval, Optcrit = "", Alg = "", ...)

## Default S3 method:
optbdmaeAT(trt.N, blk.N, theta, nrep, itr.cvrgval, Optcrit = "", Alg = "", ...)
## S3 method for class 'optbdmaeAT'
print(x, ...)
## S3 method for class 'optbdmaeAT'
summary(object, ...)

Arguments

Details

optbdmaeAT computes optimal or near-optimal block design for the two-colour cDNA microarray experiments where the interest is in a comparison of all possible elementary treatment contrasts. The function computes A-, MV-, D- and E-optimal or near optimal block designs via calling of eight sub-functions Aoptbd.maeT, Aoptbd.maeA, MVoptbd.maeT, MVoptbd.maeA, Doptbd.maeT, Doptbd.maeA, Eoptbd.maeT and Eoptbd.maeA, respectively. Each function requires an initial connected block designs, generated using the function intcbd.mae.

The minimum value of trt.N and blk.N is 3 and trt.N should be less than or equal to blk.N - 1. The linear fixed effects model results for given trt.N and blk.N are obtained by setting theta = 0.0.

Alg specifies the exchange algorithm of Debusho, Gemechu and Haines (2018). If Alg = "trtE", the function optbdmaeAT perform the treatment exchange procedure through deletion and addition of treatments at a time and selects a design with best treatment exchange with respect to the optimality criterion value. If Alg = "arrayE", the function optbdmaeAT perform the array exchange procedure through deletion and addition of candidate arrays at a time and selects a design with best array exchange with respect to the optimality criterion value.

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. However, it has to be noted that as trt.N or blk.N or nrep or all of them increses, computer time required to generate optimal or near-optimal block design increases.

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 array test if the exchange of the two preceding arrays with candidate arrays 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 A-, MV-, D- or E-optimal or near-optimal block design with its corresponding score value and parametric combination saved in excel file in a working directory. In addition, the function optbdmaeAT displays the graphical layout of the resultant optimal or near-optimal block designs. Specifically:

The graphical layout of the resultant optimal or near-optimal block design.

NB: The function optbdmaeAT also saves the summary of the resultant optimal or near-optimal block design in .csv format in the working directory. Furthermore, the function reports only one final optimal or near-optimal block design, however, there is a possibility of more than one optimal or near-optimal block designs for a given parametric combination. The function graphoptbd.mae can be used to view and rearrange the graphical layout of the resultant optimal or near-optimal block design on tcltk window. Alternative to the function optbdmaeAT, a GUI tcltk window can be used to generate optimal or near-optimal block designs, see mmenubd.mae and fixparbd.mae.

Author(s)

Dibaba Bayisa Gemechu, Legesse Kassa Debusho, and Linda Haines

References

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

mmenubd.mae, fixparbd.mae, intcbd.mae

Examples

  
  ##To obtain the A-optimal or near-optimal block design using treatment exchange algorithm, set
  trt.N <- 3 #Number of treatments
  blk.N <- 3 #Number of blocks
  theta <- 0 #theta value
  nrep <- 5  #Number of replications
  itr.cvrgval <- 6 #Number of iterations required during the exchange procedure
  Optcrit <- "A"   #Optimality criteria
  Alg <- "trtE"    #Algorithm
  
  Aoptexample <- optbdmaeAT(trt.N = 3, blk.N = 3, theta = 0, nrep = 5, 
                            itr.cvrgval = 6, Optcrit = "A", Alg = "trtE")
  
  summary(Aoptexample)

Internal functions

Description

Functions for internal usage only.

Usage

 
## Computes A-optimal or near-optimal block designs
## using array exchange algorithm
Aoptbd.maeA(trt.N, blk.N, theta, nrep, itr.cvrgval)
 
## Computes A-optimal or near-optimal block designs
## using treatment exchange algorithm
Aoptbd.maeT(trt.N, blk.N, theta, nrep, itr.cvrgval)
 
## Computes MV-optimal or near-optimal block designs
## using array exchange algorithm
MVoptbd.maeA(trt.N, blk.N, theta, nrep, itr.cvrgval)
 
## Computes MV-optimal or near-optimal block designs
## using treatment exchange algorithm
MVoptbd.maeT(trt.N, blk.N, theta, nrep, itr.cvrgval)
 
## Computes D-optimal or near-optimal block designs
## using array exchange algorithm
Doptbd.maeA(trt.N, blk.N, theta, nrep, itr.cvrgval)
 
## Computes D-optimal or near-optimal block designs
## using treatment exchange algorithm
Doptbd.maeT(trt.N, blk.N, theta, nrep, itr.cvrgval)
 
## Computes E-optimal or near-optimal block designs
## using array exchange algorithm
Eoptbd.maeA(trt.N, blk.N, theta, nrep, itr.cvrgval)
 
## Computes E-optimal or near-optimal block designs
## using treatment exchange algorithm
Eoptbd.maeT(trt.N, blk.N, theta, nrep, itr.cvrgval)

Arguments

Details

These functions are handled via a generic function optbdmaeAT. Please refer to the optbdmaeAT documentation for details.

Author(s)

Dibaba Bayisa Gemechu, Legesse Kassa Debusho, and Linda Haines

References

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

optbdmaeAT