Information Decomposition of Two-phase Experiments

Description

he main purpose of this package is to generate the structure of the analysis of variance (ANOVA) table of the two-phase experiments. The user only need to input the design and the relationships of the random and fixed factors using the Wilkinson-Rogers' syntax, this package can then quickly generate the structure of the ANOVA table with the coefficients of the variance components for the expected mean squares. Thus, the balanced incomplete block design and provides the efficiency factors of the fixed effects can also be studied and compared much easily.

Details

Author(s)

Kevin Chang and Katya Ruggiero

Maintainer: Kevin Chang <k.chang@auckland.ac.nz>

Identity Matrix Minus Averaging Matrix

Description

Construct a square matrix which the identity matrix minus the averging matrix.

Usage

J(n)

Arguments

Value

This function return a square matrix which the identity matrix minus the averaging matrix.

Author(s)

Kevin Chang

Examples

J(10)

Averaging Matrix

Description

Construct a n-by-n averaging matrix.

Usage

K(n)

Arguments

Value

This function returns a n \times n square matrix with all elements equal 1/n.

Author(s)

Kevin Chang

References

John J, Williams E (1987). Cyclic and computer generated Designs. Second edition. Chapman & Hall.

Examples

K(10)

Adjust the Effects' Names

Description

Adjust for appropriate syntax describing the effects matching the structural formula.

Usage

adjustEffectNames(effectsMatrix, effectNames)

Arguments

Value

A vector of character containing the labels of the terms in the model with appropriate syntax describing the effects.

Author(s)

Kevin Chang

Examples

str.for = "A*(B/E/C)*D"
effectsMatrix= attr(terms(as.formula(paste("~", str.for)), keep.order = TRUE) , "factors")
effectNames =  attr(terms(as.formula(paste("~", str.for)), keep.order = TRUE) , "term.labels")

adjustEffectNames(effectsMatrix, effectNames) 

Adjust the Missing Levels

Description

Adjust for appropriate syntax describing the effects matching the structural formula.

Usage

adjustMissingLevels(design.df, str.for)

Arguments

Value

A list containing a data frame with the experimental design and a single string of characters containing the structural formula.

Author(s)

Kevin Chang

Examples

design.df = data.frame( Blk = factor(1:16),
                      	Ani = factor(c(	1,1,2,2,
                                      	1,1,2,2,
                                      	1,1,2,2,
                                      	1,1,2,2)),
                      	Trt = factor(c(	1,2,3,4,
                                      	1,2,3,4,
                                      	1,2,3,4,
                                     		1,2,3,4)), stringsAsFactors = TRUE )
 
adjustMissingLevels(design.df, str.for = "Ani/Trt") 

Randomised Block design consisted of 6 blocks and 3 plots.

Description

Randomised Block design consisted of 6 blocks and 3 plots.

Usage

chrisEx1

Format

A data frame with 18 rows and 5 variables:

Blocks

Block factor containing 6 levels

Plots

Plot factor containing 3 levels

A

Treatment factor A containing 3 levels

B

Treatment factor B containing 3 levels

C

Treatment factor C containing 9 levels

Examples

 data(chrisEx1)

summaryAovOnePhase(chrisEx1, "Blocks/Plots", "A*B*C")

Randomised Block design consisted of 8 blocks and 2 plots.

Description

Randomised Block design consisted of 8 blocks and 2 plots.

Usage

chrisEx2

Format

A data frame with 18 rows and 5 variables:

Blocks

Block factor containing 6 levels

Plots

Plot factor containing 3 levels

A

Treatment factor A containing 2 levels

B

Treatment factor B containing 2 levels

C

Treatment factor C containing 3 levels

Examples

 data(chrisEx2)

summaryAovOnePhase(chrisEx2, "Blocks/Plots", "A*B*C")

Randomised Block design consisted of 4 blocks and 2 plots.

Description

Randomised Block design consisted of 4 blocks and 2 plots.

Usage

chrisEx3

Format

A data frame with 8 rows and 5 variables:

Blocks

Block factor containing 4 levels

Plots

Plot factor containing 2 levels

A

Treatment factor A containing 2 levels

B

Treatment factor B containing 2 levels

C

Treatment factor C containing 4 levels

Examples

 data(chrisEx2)

summaryAovOnePhase(chrisEx2, "Blocks/Plots", "A*B*C") 

Get Variance Components' Coefficients and Mean Squares for Single-Phase or Two-Phase Experiments

Description

Compute the variance components' coefficients and corresponding to random effects in the expected mean squares of ANOVA table in single-phase or two-phase experiments. These coefficients are then inserted to a matrix where the rows correspond to each source of variation and column correspond to DF and every variance component. The mean squares is calculated if the response argument is used.

Usage

getCoefVC.onePhase(
  Pb,
  design.df,
  v.mat,
  response,
  table.legend,
  decimal,
  digits
)

Arguments

Details

The main purpose of this function is to combine the matrices presenting every source of variation of the ANOVA table and the variance matrix to compute the coefficients of the variance components.

The complication arise in giving the row names of the matrix for the source of variation in the ANOVA table.

Value

A matrix containing the characters.

Author(s)

Kevin Chang

Examples

design1 <- local({ 
  Ani <- as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt <- as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

blk.str <- "Ani"
    
rT <- terms(as.formula(paste("~", blk.str, sep = "")), keep.order = TRUE) 
blkTerm <- attr(rT,"term.labels")
     
Z <- makeBlkDesMat(design1, blkTerm)

trt.str <- "Trt"              
fT <- terms(as.formula(paste("~", trt.str, sep = "")), keep.order = TRUE)  #fixed terms

trtTerm <- attr(fT, "term.labels")
effectsMatrix <- attr(fT, "factor")        

T <- makeContrMat(design1, trtTerm, effectsMatrix, contr.vec = NA)

N =  makeOverDesMat(design1, trtTerm)

Replist = getTrtRep(design1, trtTerm)   
 
Rep <- Replist$Rep
trt.Sca <- Replist$Sca
    
effFactors = lapply(makeOrthProjectors(Z), function(z) 
      getEffFactor(z, T, N, Rep, trt.Sca))

#Now construct variance matrices
Pb <- effFactors[sort(1:length(effFactors), decreasing=TRUE)]

v.mat <- getVMat.onePhase(Z.Phase1 = Z, design.df = design.df, var.comp = NA)
    
getCoefVC.onePhase(Pb = Pb, design.df = design1, v.mat = v.mat, response = NA, 
    table.legend = FALSE, decimal = FALSE, digit = 2)

Get Variance Components' Coefficients and Mean Squares for Single-Phase or Two-Phase Experiments

Description

Compute the variance components' coefficients and corresponding to random effects in the expected mean squares of ANOVA table in single-phase or two-phase experiments. These coefficients are then inserted to a matrix where the rows correspond to each source of variation and column correspond to DF and every variance component. The mean squares is calculated if the response argument is used.

Usage

getCoefVC.twoPhase(
  Pb,
  design.df,
  v.mat,
  response,
  table.legend,
  decimal,
  digits
)

Arguments

Details

The main purpose of this function is to combine the matrices presenting every source of variation of the ANOVA table and the variance matrix to compute the coefficients of the variance components.

The complication arise in giving the row names of the matrix for the source of variation in the ANOVA table.

Value

A matrix containing the characters.

Author(s)

Kevin Chang

Construct the Matrix from Information Decomposition and Compute the Efficiency Factors of Treatment effects

Description

Perform the information decomposition for either the block or treatment effects within a single stratum and Compute the Efficiency Factors for every treatment effect within a single stratum.

Usage

getEffFactor(z, T, N, Rep, trt.Sca)

Arguments

Details

The main purpose of this function is to construct a list of resultant matrices associated with each source of variation after the information decomposition and to compute the canonical or average efficiency factors for each treatment effects in each stratum of ANOVA table.

The canonical efficiency factors are generated when the user input the treatment contrasts, otherwise the average efficiency factors, which is the harmonic mean of the canonical efficiency factors, are generated.

Value

A list of matrices and numeric vectors containing the efficiency factors of every treatment effect.

Author(s)

Kevin Chang

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

blk.str = "Ani"
    
rT = terms(as.formula(paste("~", blk.str, sep = "")), keep.order = TRUE) 
blkTerm = attr(rT,"term.labels")
     
Z = makeBlkDesMat(design1, blkTerm)

trt.str = "Trt"              
fT <- terms(as.formula(paste("~", trt.str, sep = "")), keep.order = TRUE)  #fixed terms

trtTerm <- attr(fT, "term.labels")
effectsMatrix <- attr(fT, "factor")        

T <- makeContrMat(design1, trtTerm, effectsMatrix, contr.vec = NA)

N =  makeOverDesMat(design1, trtTerm)

Replist = getTrtRep(design1, trtTerm)   
 
Rep <- Replist$Rep
trt.Sca <- Replist$Sca
    
effFactors = lapply(makeOrthProjectors(Z), function(z) 
      getEffFactor(z, T, N, Rep, trt.Sca))

Get the Fixed Components' coefficients and Efficiency Factors of Single-Phase Experiments.

Description

Calculate coefficients of fixed effects components of EMS and Treatment Efficiency Factors within each stratum in Single-Phase or two-phase experiment.

Usage

getFixedEF.onePhase(
  effFactors,
  trt.Sca,
  T,
  Rep,
  table.legend,
  decimal,
  digits,
  list.sep
)

Arguments

Details

Constructs a matrix containing the coefficients of the coefficients of fixed effects components of EMS within each stratum. Also calculates and the average efficiency factors of each treatment effect across all strata

Construct a matrix contain the coefficients of the fixed Components and the average efficiency factors of single-phase experiments.

The function uses the efficiency factors generated by getEffFactor to calculated the coefficients of fixed Effects components of EMS and insert the treatment efficiency factor within each stratum.

The complication arise in giving the row names of the matrix for the source of variation in the ANOVA table.

Value

A matrix.

Author(s)

Kevin Chang

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

blk.str <- "Ani"
    
rT <- terms(as.formula(paste("~", blk.str, sep = "")), keep.order = TRUE) 
blkTerm = attr(rT,"term.labels")
     
Z <- makeBlkDesMat(design1, blkTerm)

trt.str <- "Trt"              
fT <- terms(as.formula(paste("~", trt.str, sep = "")), keep.order = TRUE)  #fixed terms

trtTerm <- attr(fT, "term.labels")
effectsMatrix <- attr(fT, "factor")        

T <- makeContrMat(design1, trtTerm, effectsMatrix, contr.vec = NA)

N <- makeOverDesMat(design1, trtTerm)
		
Replist = getTrtRep(design1, trtTerm)   
 
Rep <- Replist$Rep
trt.Sca <- Replist$Sca
    
effFactors = lapply(makeOrthProjectors(Z), function(z) getEffFactor(z, T, N, Rep, trt.Sca))


effFactors <- effFactors[sort(1:length(effFactors), decreasing=TRUE)]

getFixedEF.onePhase(effFactors = effFactors, trt.Sca = trt.Sca,  T = T, Rep = Rep, 
			table.legend = FALSE, decimal = FALSE, digits = 2, list.sep = TRUE)

Get the Fixed Components' coefficients and Efficiency Factors of Two-Phase Experiments.

Description

Calculate coefficients of fixed effects components of EMS and Treatment Efficiency Factors within each stratum in Single-Phase or two-phase experiment.

Usage

getFixedEF.twoPhase(
  effFactors,
  trt.Sca,
  T,
  Rep,
  table.legend,
  decimal,
  digits,
  list.sep
)

Arguments

Details

Constructs a matrix containing the coefficients of the coefficients of fixed effects components of EMS within each stratum. Also calculates and the average efficiency factors of each treatment effect across all strata

Construct a matrix contain the coefficients of the fixed Components and the average efficiency factors of single-phase experiments.

The function uses the efficiency factors generated by getEffFactor to calculated the coefficients of fixed Effects components of EMS and insert the treatment efficiency factor within each stratum.

The complication arise in giving the row names of the matrix for the source of variation in the ANOVA table.

Value

A matrix.

Author(s)

Kevin Chang

Get the Treatment Coefficients

Description

Compute the overall coefficients every treatment term including the interaction.

Usage

getTrtCoef(design.df, trtTerm)

Arguments

Value

The numeric vector.

Author(s)

Kevin Chang

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

trt.str = "Trt"
  
fT = terms(as.formula(paste("~", trt.str, sep = "")), keep.order = TRUE)  #fixed terms

trtTerm = attr(fT,"term.labels")
effectsMatrix = attr(fT,"factor") 
		
trt.Coef = getTrtCoef(design1, trtTerm)

Calculate the Treatment Replication number

Description

Calculate the replication number of every treatment term including the interaction. This is used to compute the treatment efficiency factors.

Usage

getTrtRep(design.df, trtTerm)

Arguments

Value

A list containing two objects. The first object is a matrix called Rep which contains the replication numbers, where the rows correspond to each treatment combination and the columns correspond to the treatment factors, i.e. the replication number with respect to each treatment factor based on the treatment combination. The second object called Sca which is a numeric vector for computing a coefficients of the fixed effect parameter in EMS.

Author(s)

Kevin Chang

References

John J, Williams E (1987). Cyclic and computer generated Designs. Second edition. Chapman & Hall.

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

trt.str = "Trt"
  
fT = terms(as.formula(paste("~", trt.str, sep = "")), keep.order = TRUE)  #fixed terms

trtTerm = attr(fT,"term.labels")
effectsMatrix = attr(fT,"factor") 
		
getTrtRep(design1, trtTerm)   

Get the Variance Matrices for Single-Phase experiment

Description

Construct the matrix for each variance components for the single-phase or two-phase experiment.

Usage

getVMat.onePhase(Z.Phase1, design.df, var.comp = NA)

Arguments

Value

A list of matrices.

Author(s)

Kevin Chang

Examples

 design1 <- local({ 
    Ani = as.factor(LETTERS[c(1,2,3,4,
                              5,6,7,8)])
    Trt = as.factor(letters[c(1,1,1,1,
                              2,2,2,2)])
    data.frame(Ani, Trt, stringsAsFactors = TRUE )
  })

    blk.str = "Ani"
    
		rT = terms(as.formula(paste("~", blk.str, sep = "")), keep.order = TRUE) 

    blkTerm = attr(rT,"term.labels")
		Z = makeBlkDesMat(design1, rev(attr(rT,"term.labels")))

    V = getVMat.onePhase(Z, design1)
    

Get the Variance Matrices for Two-Phase experiment

Description

Construct the matrix for each variance components for the single-phase or two-phase experiment.

Usage

getVMat.twoPhase(Z.Phase1, Z.Phase2, design.df, var.comp = NA)

Arguments

Value

A list of matrices.

Author(s)

Kevin Chang

Examples

     design2 <- local({ 
  Run = as.factor(rep(1:4, each = 4))
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8,
                            3,4,1,2,
                            7,8,5,6)])
  Tag = as.factor(c(114,115,116,117)[rep(1:4, 4)])
  Trt = as.factor(letters[c(1,2,1,2,
                            2,1,2,1,
                            1,2,1,2,
                            2,1,2,1)])
  data.frame(Run, Ani, Tag, Trt, stringsAsFactors = TRUE )
})

    blk.str1 = "Ani"
    blk.str2 = "Run"
   
	rT1 = terms(as.formula(paste("~", blk.str1, sep = "")), keep.order = TRUE) 
	#random terms phase 1
	rT2 = terms(as.formula(paste("~", blk.str2, sep = "")), keep.order = TRUE) 
	#random terms phase 2

	blkTerm1 = attr(rT1,"term.labels")
	blkTerm2 = attr(rT2,"term.labels")

	Z1 = makeBlkDesMat(design2, rev(blkTerm1))
	Z2 = makeBlkDesMat(design2, rev(blkTerm2))

	V = getVMat.twoPhase(Z1, Z2, design2, var.comp = NA)

Identity Matrix

Description

Construct an identity matrix.

Usage

identityMat(n)

Arguments

Value

This function returns a matrix with the diagonal elements equal to one and the off-diagonal elements equal to zero.

Author(s)

Kevin

References

John J, Williams E (1987). Cyclic and computer generated Designs. Second edition. Chapman & Hall.

See Also

diag

Examples

identityMat(10)

Construct the Matrix from Information Decomposition

Description

Perform the information decomposition for either the block or treatment effects within a single stratum.

Usage

infoDecompMat(z, T, N)

Arguments

Details

The main purpose of this function is to construct a list of resultant matrices associated with each source of variation after the information decomposition.

This list of matrices are then used to compute the coefficient of the variance components in the expected mean squares.

Value

A list of matrices.

Author(s)

Kevin Chang

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

blk.str = "Ani"
    
rT = terms(as.formula(paste("~", blk.str, sep = "")), keep.order = TRUE) 
blkTerm = attr(rT,"term.labels")
     
Z = makeBlkDesMat(design1, blkTerm)
Pb = makeOrthProjectors(Z)

trt.str = "Trt"              
fT <- terms(as.formula(paste("~", trt.str, sep = "")), keep.order = TRUE)  #fixed terms

trtTerm <- attr(fT, "term.labels")
effectsMatrix <- attr(fT, "factors")        

T <- makeContrMat(design1, trtTerm, effectsMatrix, contr.vec = NA)

N =  makeOverDesMat(design1, trtTerm)


infoDecompMat(Pb[[1]], T, N)

Invert the Information Matrix

Description

Using the eigenvalue decomposition method to invert the information matrix.

Usage

invInfMat(C, N, T)

Arguments

Value

This function returns a matrix.

Author(s)

Kevin Chang

References

Nelder JA (1965b). "The Analysis of Randomized Experiments with Orthogonal Block Structure. II. Treatment Structure and the General Analysis of Variance." Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 283(1393), 163-178.

Examples

m <- matrix(rnorm(10), 10, 10)

invInfMat(m, identityMat(10), identityMat(10))
     

Construct Block Design Matrix

Description

Construct a binary matrix representing the block design. The rows are corresponding to the observations and the columns are corresponding to the blocks.

Usage

makeBlkDesMat(design.df, blkTerm)

Arguments

Value

A list of the binary matrices.

Author(s)

Kevin Chang

See Also

terms

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

blk.str = "Ani*Trt"
    
rT = terms(as.formula(paste("~", blk.str, sep = "")), keep.order = TRUE) 

blkTerm = attr(rT,"term.labels")
Z = makeBlkDesMat(design1, blkTerm)

Make Contrast Matrix

Description

Construct a list of contrast matrices for block for treatment effects.

Usage

makeContrMat(design.df, effectNames, effectsMatrix, contr.vec)

Arguments

Details

The main purpose of this function is to compute a list of C matrices described by John and Williams (1987). These C matrices are used for the information decomposition for every treatment effect in every stratum of the experiment.

If the user input their own defined contrasts for each treatment effects. This function will then transform the input contrasts to the C matrices for the treatment effects.

For the two-phase experiments, the same method of information decomposition is used for the block effects of Phase 1 experiment in the stratum defined from the block structure of the Phase 2 experiment. Hence, the C matrices for the block effects of Phase 1 experiment can also be constructed using this function.

Value

A list of contrast matrices.

Author(s)

Kevin Chang

References

John J, Williams E (1987). Cyclic and computer generated Designs. Second edition. Chapman & Hall.

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

trt.str = "Trt"              
fT <- terms(as.formula(paste("~", trt.str, sep = "")), keep.order = TRUE)  #fixed terms

trtTerm <- attr(fT, "term.labels")
effectsMatrix <- attr(fT, "factor")        

T <- makeContrMat(design1, trtTerm, effectsMatrix, contr.vec = NA)
		
#Fit each treatment contrasts as a vector seperately
Trt1 <- rep(c(1,-1), each = 4)
Trt2 <-  rep(c(1,-1), time = 4)
Trt3 <- Trt1*Trt2
  
T <- makeContrMat(design1, trtTerm, effectsMatrix, 
      contr.vec =list(Trt = list(Trt1 = Trt1, Trt2 = Trt2, Trt3 = Trt3)))

Construct Orthogonal Projector Matrices

Description

Construct a list of orthogonal projector matrices corresponding to all strata of the experiment.

Usage

makeOrthProjectors(BlkDesList)

Arguments

Details

The strata decomposition is performed within this function. The first step is to convert the list of block design matrices generated by makeBlkDesMat to projection matrices using projMat. The second step is to use these projection matrices to project the raw data vector from one stratum to next stratum of the experiment; the resulting matrix corresponds to each stratum is the orthogonal projector matrix of the given stratum.

Value

A list containing matrices.

Author(s)

Kevin Chang

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

blk.str = "Ani"
    
rT = terms(as.formula(paste("~", blk.str, sep = "")), keep.order = TRUE) 
blkTerm = attr(rT,"term.labels")
     
Z = makeBlkDesMat(design1, blkTerm)
Pb = makeOrthProjectors(Z)

Construct the Overall Treatment or Block design Matrix

Description

Construct the treatment or block matrix of the smallest unit based from the experimental design.

Usage

makeOverDesMat(design.df, effectNames)

Arguments

Details

The main purpose this matrix is used in information decomposition. For the factorial experiment, this matrix is typically the treatment design matrix associated with the interaction effects, because the interaction effects are the smallest unit for the treatment effects.

For the two-phase experiments, the same method of information decomposition is used for the block effects of Phase 1 experiment in the stratum defined from the block structure of the Phase 2 experiment. Hence, the block design matrix of the smallest unit for the block effects of Phase 1 experiment can also be constructed using this function.

Value

A matrix where the rows correspond to the observation and columns correspond to the overall combination of the treatment factors or the block factors of the Phase 1 experiment.

Author(s)

Kevin Chang

References

John J, Williams E (1987). Cyclic and computer generated Designs. Second edition. Chapman & Hall.

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

trt.str = "Trt"
  
fT = terms(as.formula(paste("~", trt.str, sep = "")), keep.order = TRUE) 

trtTerm = attr(fT,"term.labels")
effectsMatrix = attr(fT,"factor") 
    
makeOverDesMat(design1, trtTerm)
       

Construct a Projection Matrix

Description

Compute the projection matrix from a square matrix.

Usage

projMat(X)

Arguments

Value

A square matrix.

Author(s)

Kevin Chang

Examples

m = matrix(1, nrow = 10, ncol = 3)
projMat(m) 

Summarize an Theoretical Analysis of Variance Model of Single-Phase Experiments

Description

Computes the coefficients of the variance components for the expected mean squares for single-phase experiments. The function accepts a data frame of the experimental design with the structural formulae of the block and treatment factors. Two tables containing the variance components of the random effects and fixed effects are returned.

Usage

summaryAovOnePhase(
  design.df,
  blk.str,
  trt.str,
  var.comp = NA,
  trt.contr = NA,
  table.legend = FALSE,
  response = NA,
  latex = FALSE,
  fixed.names = NA,
  decimal = FALSE,
  digits = 2,
  list.sep = TRUE
)

Arguments

Value

The values returned depends on the value of the table.legend argument. If table.legend = FALSE, this function will return a list of two data frames. The first data frame contains the random effects and the second data frame contains the fixed effects. If the table.legend argument is TRUE, then it will return a list containing two lists. The first list consists of a data frame of random effects and a character string for the legend. The second list consists of a data frame of fixed effects and a character string for the legend. If response argument is used, the random effect table will have one extra column with of mean squares computed from the responses from the experiment.

Author(s)

Kevin Chang

References

John J, Williams E (1987). Cyclic and computer generated Designs. Second edition. Chapman & Hall.

Nelder JA (1965b). "The Analysis of Randomized Experiments with Orthogonal Block Structure. II. Treatment Structure and the General Analysis of Variance." Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 283(1393), 163-178.

Wilkinson GN, Rogers CE (1973). "Symbolic Description of Factorial Models for Analysis of Variance." Applied Statistics, 22(3), 392-399.

See Also

terms for more information on the structural formula.

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE)
})

summaryAovOnePhase(design1, blk.str = "Ani", trt.str = "Trt") 

summaryAovOnePhase(design1, blk.str = "Ani", trt.str = "Trt", 
latex = TRUE, fixed.names = c("\\tau"))

Summarize an Theoretical Analysis of Variance Model of Two-Phase Experiments

Description

Computes the coefficients of the variance components for the expected mean squares for two-phase experiments. The function accepts a data frame of the experimental design with the structural formulae of the block and treatment factors. Two tables containing the variance components of the random effects and fixed effects are returned.

Usage

summaryAovTwoPhase(
  design.df,
  blk.str1,
  blk.str2,
  trt.str,
  var.comp = NA,
  blk.contr = NA,
  trt.contr = NA,
  table.legend = FALSE,
  response = NA,
  latex = FALSE,
  fixed.names = NA,
  decimal = FALSE,
  digits = 2,
  list.sep = TRUE
)

Arguments

Value

The values returned depends on the value of the table.legend argument. If table.legend = FALSE, this function will return a list of two data frames. The first data frame contains the random effects and the second data frame contains the fixed effects. If the table.legend argument is TRUE, then it will return a list containing two lists. The first list consists of a data frame of random effects and a character string for the legend. The second list consists of a data frame of fixed effects and a character string for the legend. If response argument is used, the random effect table will have one extra column with of mean squares computed from the responses from the experiment.

Author(s)

Kevin Chang

References

John J, Williams E (1987). Cyclic and computer generated Designs. Second edition. Chapman & Hall.

Nelder JA (1965b). "The Analysis of Randomized Experiments with Orthogonal Block Structure. II. Treatment Structure and the General Analysis of Variance." Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 283(1393), 163-178.

Wilkinson GN, Rogers CE (1973). "Symbolic Description of Factorial Models for Analysis of Variance." Applied Statistics, 22(3), 392-399.

See Also

terms for more information on the structural formula.

Examples

#Phase 2 experiment  
design2 <- local({ 
  Run = as.factor(rep(1:4, each = 4))
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8,
                            3,4,1,2,
                            7,8,5,6)])
  Sam = as.factor(as.numeric(duplicated(Ani)) + 1)
  Tag = as.factor(c(114,115,116,117)[rep(1:4, 4)])
  Trt = as.factor(c("healthy", "diseased")[c(1,2,1,2,
                            2,1,2,1,
                            1,2,1,2,
                            2,1,2,1)])
  data.frame(Run, Ani, Sam, Tag, Trt, stringsAsFactors = TRUE)
})
design2
                                  
summaryAovTwoPhase(design2, blk.str1 = "Ani", blk.str2 = "Run", 
trt.str = "Tag + Trt")                                            
   
#Add the sample into the Phase 1 block structure                                           
summaryAovTwoPhase(design2, blk.str1 = "Ani/Sam", blk.str2 = "Run", 
trt.str = "Tag + Trt")                                            


#Assuming there is crossing between the animals and samples 
summaryAovTwoPhase(design2, blk.str1 = "Ani*Sam", blk.str2 = "Run", 
trt.str = "Tag + Trt")                                            

 
#Set Artificial stratum 
design2$AniSet = as.factor(c(2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1))
design2

summaryAovTwoPhase(design2, blk.str1 =  "Ani/Sam", blk.str2 = "AniSet/Run", 
trt.str = "Tag + Trt", var.comp = c("Ani:Sam", "Ani", "Run"))                                    

#Define traetment contrasts                                   
TagA = rep(c(1,1,-1,-1),time = 4)                
TagB = rep(c(1,-1,1,-1),time = 4)                
TagC = TagA * TagB
Tag = list(TagA = TagA, TagB = TagB, TagC = TagC)
Tag


Trt = as.numeric(design2$Trt)-1.5
Trt


summaryAovTwoPhase(design2, blk.str1 =  "Ani/Sam", blk.str2 = "Run", 
trt.str = "Tag + Trt", 
trt.contr = list(Tag = list(TagA = TagA, TagB = TagB, TagC = TagC), Trt = Trt),
table.legend = TRUE)                                

#Compute MS 
set.seed(527)
summaryAovTwoPhase(design2, blk.str1 = "Ani/Sam", blk.str2 = "Run", 
trt.str = "Tag + Trt", response = rnorm(16))$ANOVA                                            

#Generate Latex scripts
summaryAovTwoPhase(design2, blk.str1 = "Ani/Sam", blk.str2 = "Run", 
trt.str = "Tag + Trt", latex = TRUE, fixed.names = c("\\gamma", "\\tau"))  

#Generate Latex scripts with MS
set.seed(527)
summaryAovTwoPhase(design2, blk.str1 = "Ani/Sam", blk.str2 = "Run", 
trt.str = "Tag + Trt", response = rnorm(16), latex = TRUE, 
fixed.names = c("\\gamma", "\\tau") )                               

Convert the R output to Latex Table

Description

Print the Latex scripts on the screen for the user to output the table from the Latex output.

Usage

toLatexTable(ANOVA, EF, fixed.names)

Arguments

Details

Once the Latex script is generated, it requires the user to install and load two Latex packages: booktabs and bm to compile the Latex script.

Author(s)

Kevin Chang

Examples

design1 <- local({ 
  Ani = as.factor(LETTERS[c(1,2,3,4,
                            5,6,7,8)])
  Trt = as.factor(letters[c(1,1,1,1,
                            2,2,2,2)])
  data.frame(Ani, Trt, stringsAsFactors = TRUE )
})

blk.str <- "Ani"
    
rT <- terms(as.formula(paste("~", blk.str, sep = "")), keep.order = TRUE) 
blkTerm <- attr(rT,"term.labels")
     
Z <- makeBlkDesMat(design1, blkTerm)


trt.str = "Trt"              
fT <- terms(as.formula(paste("~", trt.str, sep = "")), keep.order = TRUE)  

trtTerm <- attr(fT, "term.labels")
effectsMatrix <- attr(fT, "factor")        

T <- makeContrMat(design1, trtTerm, effectsMatrix, contr.vec = NA)

N <- makeOverDesMat(design1, trtTerm)

Replist = getTrtRep(design1, trtTerm)   
 
Rep <- Replist$Rep
trt.Sca <- Replist$Sca
    
effFactors = lapply(makeOrthProjectors(Z), function(z) 
      getEffFactor(z, T, N, Rep, trt.Sca))

effFactors <- effFactors[sort(1:length(effFactors), decreasing=TRUE)]

v.mat <- getVMat.onePhase(Z.Phase1 = Z, design.df = design.df, var.comp = NA)
    
ANOVA <- getCoefVC.onePhase(Pb = effFactors, design.df = design1, v.mat = v.mat, 
    response = NA, table.legend = FALSE, decimal = FALSE, digits = 2)
		
EF <- getFixedEF.onePhase(effFactors = effFactors, trt.Sca = trt.Sca,  T = T, 
  Rep = Rep, 
	table.legend = FALSE, decimal = FALSE, digits = 2, list.sep = FALSE)

toLatexTable(ANOVA = ANOVA, EF = EF, fixed.names = c("\\tau"))

Trace of the Matrix

Description

Compute the trace of the square matrix.

Usage

tr(X)

Arguments

Value

A numeric value.

Author(s)

Kevin

References

John J, Williams E (1987). Cyclic and computer generated Designs. Second edition. Chapman & Hall.

See Also

diag

Examples

m = matrix(1, nrow = 10, ncol = 10)
tr(m)   

Construct a unity vector

Description

Construct a vector with all elements unity.

Usage

unity(n)

Arguments

Value

This function returns a n \\times 1 matrix will all elements unity.

Author(s)

Kevin Chang

References

John J, Williams E (1987). Cyclic and computer generated Designs. Second edition. Chapman & Hall.

Examples

unity(10)