summaryAovTwoPhase: Summarize an Theotrical 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 experimetnal 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,  contr.matrix = all(is.na(trt.contr)), table.legend = FALSE,  response = NA, latex = FALSE, fixed.names=NA)

Arguments

design.df

a data frame containing the design of the experiment. Every column must be factors.

blk.str1

a single string of characters containing the structural formula for the block factors of the first-phase experiment using the Wilkinson-Rogers' syntax.

blk.str2

a single string of characters containing the structural formula for the block factors of the second-phase experiment using the Wilkinson-Rogers' syntax.

trt.str

a single string of characters containing the structural formula for the treatment factors using the Wilkinson-Rogers' syntax.

var.comp

a vector of characters containing the variance components of interest this allows the user to specify the variance components to be shown on the ANOVA table. This also allows the user to specify artificial stratum to facilitate decomposition. Default is NA, which uses every random factor as the variance components with the first phase's variance components in random.terms1 appear before the second phase's variance components in random.terms2.

blk.contr

a list of first-phase block contrast vectors, this allows the user to specify the contrasts for each block factor in the first phase experiment. Note that if this arguement is used, it is necessary to specify the contrasts for every treatment factor with the same order as fixed.terms. Default is NA, which uses the C matrix described by John and Williams (1987).

trt.contr

a list of treatment contrast vectors, this allows the user to specify the contrasts for each treatment factor. Note that if this arguement is used, it is necessary to specify the contrasts for every treatment factor with the same order as fixed.terms. Default is NA, which uses the C matrix described by John and Williams (1987).

contr.matrix

a logical allows the users to use the contrast matrices or contrast vectors. If contr.matrix = FALSE, the outputs will use the contrast vectors each contributes one DF. If the contr.matrix arguement is TRUE the output will conbine the contrast vector for each treatment factors. The default depends on whether trt.contr has defined, if trt.contr has defined, then contr.matrix becomes FALSE.

table.legend

a logical allows the users to use the legend for the variance components of the ANOVA table for a large design. Default is FALSE, which uses the original names.

response

a numeric vector contains the responses from the experiment.

latex

a logical allows the users to output the Latex script to Latex table.

fixed.names

a vector of character allows the users to modify symbols for the fixed effects.

Value

The values returned depends on the value of the table.legend arguement. 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 arguement 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 arguement is used, the random effect table will have one extra column with of mean squares computed from the responses from the experiment.

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.

Examples

Run this code

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)
})

summaryAovTwoPhase(design2, blk.str1 = "Ani", blk.str2 = "Run", 
trt.str = "Trt + Tag")        


Tag1 = rep(c(1,-1), time = 4, each = 2)
Tag2 = rep(c(1,-1), time = 8)
Tag3 = Tag1 * Tag2

summaryAovTwoPhase(design2, blk.str1 = "Ani", blk.str2 = "Run", 
trt.str = "Trt + Tag", 
trt.contr = list(Trt = NA, Tag = list(Tag1 = Tag1, Tag2 = Tag2, Tag3 = Tag3)))        

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