A-efficiency of A Binary Incomplete Block Design

Description

Computes lower bound to A-efficiency of a binary incomplete block design. Treatment by block incidence matrix of the design is to be supplied as input to the function.

Usage

A_eff(N)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

N=matrix(c(1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0,
1,0,1,1,0,0),nrow=7,byrow=TRUE)
A_eff(N)

A-efficiency of A Proper Binary Incomplete Block Design

Description

This function computes lower bound to A-efficiency of a binary proper incomplete block design given the block size, number of blocks and concurrence matrix.

Usage

A_eff.NNP(b,k,NNP)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Information Matrix of a Block Design

Description

Gives the information matrix from a given treatment by block incidence matrix of a block design

Usage

Cmatrix(N)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

N = matrix(c(1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0
,1,0,1,1,0,0),nrow=7,byrow=TRUE)
Cmatrix(N)
Information.Matrix(N)

D-efficiency of a Binary Incomplete Block Design

Description

Computes lower bound to D-efficiency of a binary incomplete block design

Usage

D_eff(N)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

N=matrix(c(1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0
,1,0,1,1,0,0),nrow=7,byrow=TRUE)
D_eff(N)

Linear Integer Programming Formulation to Update Incidence Matrix

Description

Updates an incidence matrix by adding a row through linear integer programming formulation for given number of treatments, number of blocks, block sizes and concurrence matrix and the previous rows of incidence matrix

Usage

LIP(v,b,kvec,NNPo,N1,T,rownum,relaxed,binary=TRUE)

Arguments

Value

return the updated incidence matrix

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

An Alternative Approach to Obtain a Block Design with Specified Concurrence Matrix

Description

Generates a block design with specified parameters and concurrence matrix through an alternative linear integer programming approach

Usage

NLIP(v,b,k,NNPo)

Arguments

Value

Returns a design or a text saying that no design found

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

References

Mandal, B. N., Gupta, V. K., & Parsad, R. (2012). Generation of Binary Incomplete Block Design with a Specified Concurrence Matrix. Journal of Statistics & Applications, 7.

Block Design from Given Treatment by Block Incidence Matrix

Description

Generates the block contents from a given treatment by block incidence matrix

Usage

N_to_design(N)
design(N)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

N=matrix(c(1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,1,
1,1,0,0,0,1,0,0,1,0,1,1,0,0),nrow=7,byrow=TRUE)
N_to_design(N)
design(N)

Analysis of Variance, Estimated Marginal Means and Contrast Analysis of Data from An Incomplete Block Design

Description

Performs intrablock analysis of variance of data from experiments using a block design. It also computes estimated marginal means of the factor variables (e.g. treatments) and optionally estimates and tests the contrasts of factor variables (e.g treatments).

Usage

aov.ibd(formula,specs,data,contrast,joint=FALSE,details=FALSE,sort=TRUE,by=NULL,
alpha=0.05,Letters = "ABCDEFGHIJ",...)

Arguments

Details

The function makes use of lm() function in R and Anova() function in car package with specification of Type III sum of squares and emmeans(), contrast() functions in emmeans() package, cld() function in multcomp package and combines the results in a single place.

Value

Returns a list with following components

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

data(ibddata)
aov.ibd(y~factor(trt)+factor(blk),data=ibddata)
contrast=matrix(c(1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0),nrow=2,byrow=TRUE)
aov.ibd(y~factor(trt)+factor(blk),specs="trt",data=ibddata,contrast=contrast)

Balanced Incomplete Block Design for Given Parameters

Description

Generates a balanced incomplete block design with given number of treaments (v), number of blocks (b), number of replications (r), block size (k) and number of concurrences (lambda).

Usage

bibd(v,b,r,k,lambda,ntrial=5,pbar=FALSE)

Arguments

Value

Note

The function works best for values of number of treatments (v) up to 30 and block size (k) up to 10. However, for block size (k) up to 3, much larger values of number of treatments (v) may be used.

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

References

Mandal, B. N., Gupta, V. K. and Parsad, R. (2013). Application of optimization techniques for construction of incomplete block designs. Project report, IASRI, New Delhi.

Mandal, B. N., Gupta, V. K., & Parsad, R. (2014). Efficient Incomplete Block Designs Through Linear Integer Programming. American Journal of Mathematical and Management Sciences, 33(2), 110-124.

Mandal, B. N. (2015). Linear integer programming approach to construction of balanced incomplete block designs. Communications in Statistics-Simulation and Computation, 44:6, 1405-1411.

Examples

bibd(7,7,3,3,1)
bibd(9,12,4,3,1)

Balanced Treatment Incomplete Block Designs

Description

Generates a balanced treatment incomplete block design for specified parameters.

Usage

btib(v,b,r,r0,k,lambda,lambda0,ntrial=5,pbar=FALSE)

Arguments

Value

Note

The function works best for values of number of treatments (v) up to 30 and block size (k) up to 10. However, for block size (k) up to 3, much larger values of number of treatments (v) may be used.

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

References

Mandal, B. N., Gupta, V. K. and Parsad, R. (2013). Application of optimization techniques for construction of incomplete block designs. Project report, IASRI, New Delhi.

Mandal, B. N., Gupta, V. K., & Parsad, R. (2014). Balanced treatment incomplete block designs through integer programming, Communications in Statistics - Theory and Methods, 46:8, 3728-3737.

Examples

btib(4,6,3,6,3,1,3,10)

Balanced Treatment Incomplete Block Designs

Description

Generates a balanced treatment incomplete block design for specified parameters by searching all possible combinations.

Usage

btib1(v,b,r,r0,k,lambda,lambda0)

Arguments

Value

Note

The function works best for values of number of treatments (v) up to 30 and block size (k) up to 10. However, for block size (k) up to 3, much larger values of number of treatments (v) may be used.

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

References

Mandal, B. N., Gupta, V. K. and Parsad, R. (2013). Application of optimization techniques for construction of incomplete block designs. Project report, IASRI, New Delhi.

MANDAL, B. N., GUPTA, V. K. and PARSAD, R. (2012). Generation of Binary Incomplete Block Design with a Specified Concurrence Matrix. Journal of Statistics & Applications, 7.

Examples

btib(4,6,3,6,3,1,3)

Treatment by Block Incidence Matrix of a BTIB Design

Description

This function generate an incidence matrix of a BTIB design for given v,b,k and concurrence matrix

Usage

btibgen(v,b,k,NNPo,ntrial,pbar)

Arguments

Value

returns a v by b incidence matrix or a text that design was not found

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Concurrence Matrix for Given v, b and k

Description

Generates a nearly balanced concurrence matrix from given number of treatments (v), number of blocks (b) and block size (k) by trial and error.

Usage

ccmat(v,b,k)

Arguments

Value

A v by v matrix is returned if a desired concurrence matrix is found, else it returns a v by v matrix of zeros. If the parameters are infeasible for a nearly balanced concurrence matrix, the function returns the parameter values.

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Concurrence Matrix for Given v, b and k

Description

Generates the nearly balanced concurrence matrix from given number of treatments (v), number of blocks (b) and block size (k)

Usage

ccmat_LP(v,b,k)

Arguments

Value

A v by v matrix is returned if a desired concurrence matrix is found, else it returns 0.

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Orthogonality of Rows of a Given Matrix

Description

Checks whether rows of a given matrix are pairwise orthogonal or not. Returns a value 1 if the rows are pairwise orthogonal, else return 0.

Usage

check.orthogonality(M)

Arguments

Value

A value of 1 if rows of the matrix are pairwise orthogonal else 0.

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Whether a Given Matrix is Concurrence Matrix or Not

Description

Checks whether a v by v matrix is concurrence matrix or not. Mainly it checks whether the sum of off-diagonal elements of the matrix is (k-1) times the diagonal element for each row of the given matrix. Applicable for proper binary incomplete block design only. If the condition is satisfied, it returns a value of 1 else it returns 0.

Usage

check.validity.NNP(NNP,k)

Arguments

Value

A value of 1 for valid concurrence matrix or 0 for non valid matrix.

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Block Design to Treatment by Block Incidence Matrix

Description

Generates treatment by block incidence matrix from a given block design

Usage

design_to_N(design)
N(design)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

design = matrix(c(1,4,6,5,6,7,3,4,5,2,4,7,1,3,7,2,3,6,1,2,5),nrow=7,byrow=TRUE)
design_to_N(design)
# or alternatively
N(design)

Existence of A Nearly Balanced Incomplete Block Design Given The Parameters

Description

Checks whether a nearly balanced incomplete block design exists or not for given parameters

Usage

do.exist.NBIB(v,b,k)

Arguments

Value

Returns 1 if an NBIB design exists else return 0

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

g Function

Description

Computes value of g function for given v,b,k,x,z

Usage

g(v,b,k,x,z)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

gts Value

Description

Computes minimum value of g function for over permissible values of x,z for given v,b,k

Usage

gts(v,b,k)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Binary Incomplete Block Design for Given v, b and k and Optionally, with a Specified Concurrence Matrix

Description

Generates an A- and D- efficient binary incomplete block design with given number of treaments(v), number of blocks(b) and block size(k) and optionally with a specified concurrence matrix(NNP).

Usage

ibd(v,b,k,NNPo,ntrial=5,pbar=FALSE)

Arguments

Value

Note

This function works best for values of number of treatments (v) up to 30 and block size (k) up to 10. However, for block size (k) up to 3, much larger values of number of treatments (v) may be used.

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

References

Mandal, B. N., Gupta, V. K. and Parsad, R. (2013). Application of optimization techniques for construction of incomplete block designs. Project report, IASRI, New Delhi.

Mandal, B. N., Gupta, V. K., & Parsad, R. (2014). Efficient Incomplete Block Designs Through Linear Integer Programming. American Journal of Mathematical and Management Sciences, 33(2), 110-124.

Examples

ibd(v = 7,b = 7,k = 4, pbar=FALSE)

Data from an Experiment using Incomplete Block Design

Description

Data from an experiment using incomplete block design

Usage

data("ibddata")

Format

A data frame with 36 observations on the following 3 variables.

trt

Treatments

blk

Blocks

y

The response variable

Details

The experiment used a balanced incomplete block design.

References

Dey,A. (1986). Theory of block designs. Wiley Eastern Limited, New Delhi.

Examples

data(ibddata)

Generate a Treatment by Block Incidence Matrix for Given v,b,k, and Concurrence Matrix

Description

Generates an incidence matrix for given v,b,k and concurrence matrix

Usage

ibdgen(v,b,k,NNPo,ntrial,pbar)

Arguments

Value

returns a v by b incidence matrix or a text that design was not found

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Incomplete Block Design for Test vs Control(s) Comparions

Description

Generates an incomplete block design for test vs control(s) comparisons with specified parameters and concurrence matrix.

Usage

ibdtvc(v1,v2,b,k,NNPo,ntrial=5,pbar=FALSE)

Arguments

Value

v1=v1,v2=v2,b=b,k=k,design=design,N=N, NNP=NNP,Aeff=Aeff)

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

References

Mandal, B. N., Gupta, V.K. and Parsad, R. (2013). Binary Incomplete Block Designs with a Specified Concurrence Matrix through Integer Programming, to be submitted for publication

Examples

NNPo=matrix(c(7,3,3,3,3,3,3,3,3,7,3,3,3,3,3,3,3,3,7,3,3,3,3,3,3,3,3,7,3,3,3,3,3,3,3,3,7,
3,3,3,3,3,3,3,3,7,3,3,3,3,3,3,3,3,9,9,3,3,3,3,3,3,9,9),nrow=8,byrow=TRUE)
ibdtvc(6,2,15,4,NNPo)

Interchange the Elements of a Concurrence Matrix to Get Highest Possible Lower Bound to A-efficiency

Description

Interchanges the distinct off-diagonal elements of a given concurrence matrix and produces a concurrence matrix which has highest A-efficiency

Usage

interchange.NNP(b,k,NNP)

Arguments

Value

A v x v matrix

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Connctedness of a Binary Incomplete Block Design

Description

Checks whether an incomplete block design is connected or not. Treatment by block incidence matrix of the design is to be supplied as input to the function. If the design is connected, it returns a value of 1 else it returns 0.

Usage

is.connected(N)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

N=matrix(c(1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,
0,0,1,0,0,1,0,1,1,0,0),nrow=7,byrow=TRUE)
is.connected(N)

Equi-replicateness a Binary Incomplete Block Design

Description

Checks whether an incomplete block design is equi-replicated or not. Treatment by block incidence matrix of the design is to be supplied as input to the function. If the design is equir-eplicated, it returns a value of 1 else it returns 0.

Usage

is.equir(N)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

N=matrix(c(1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,
0,0,1,0,0,1,0,1,1,0,0),nrow=7,byrow=TRUE)
is.equir(N)

Orthogonality a Block Design

Description

Checks whether an incomplete block design is orthogonal or not. Treatment by block incidence matrix of the design is to be supplied as input to the function. If the design is orthogonal, it returns a value of 1 else it returns 0.

Usage

is.orthogonal(N)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

N=matrix(c(1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,
0,0,1,0,0,1,0,1,1,0,0),nrow=7,byrow=TRUE)
is.orthogonal(N)

Proper Binary Incomplete Block Design

Description

Checks whether an incomplete block design is proper or not. Treatment by block incidence matrix of the design is to be supplied as input to the function. If the design is proper, it returns a value of 1 else it returns 0.

Usage

is.proper(N)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

N=matrix(c(1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,
0,0,1,0,0,1,0,1,1,0,0),nrow=7,byrow=TRUE)
is.proper(N)

Variance Balancedness of a Binary Incomplete Block Design

Description

Checks whether an incomplete block design is variance balanced or not. Treatment by block incidence matrix of the design is to be supplied as input to the function. If the design is variance balanced, it returns a value of 1 else it returns 0.

Usage

is.vb(N)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

N=matrix(c(1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,
0,0,1,0,0,1,0,1,1,0,0),nrow=7,byrow=TRUE)
is.vb(N)

Whole Number or Not

Description

Checks whether a given number is whole number or not.

Usage

is.wholenumber(x, tol = .Machine$double.eps^0.5)

Arguments

Value

Returns TRUE or FALSE

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Randomize a block design

Description

Randomize a given block design

Usage

randomize(design)

Arguments

Value

Author(s)

Baidya Nath Mandal <mandal.stat@gmail.com>

Examples

design = matrix(c(1,4,6,5,6,7,3,4,5,2,4,7,1,3,7,2,3,6,1,2,5),nrow=7,byrow=TRUE)
randomize(design)