robCompositions (version 2.1.0)

cubeCoord: Coordinate representation of a compositional cube and of a sample of compositional cubes

Description

cubeCoord computes a system of orthonormal coordinates of a compositional cube. Computation of either pivot coordinates or a coordinate system based on the given SBP is possible.

Wrapper (cubeCoordWrapper): For each compositional cube in the sample cubeCoordWrapper computes a system of orthonormal coordinates and provide a simple descriptive analysis. Computation of either pivot coordinates or a coordinate system based on the given SBP is possible.

Usage

cubeCoord(x, row.factor = NULL, col.factor = NULL,
  slice.factor = NULL, value = NULL, SBPr = NULL, SBPc = NULL,
  SBPs = NULL, pivot = FALSE, print.res = FALSE)
cubeCoordWrapper(X, obs.ID = NULL, row.factor = NULL,
  col.factor = NULL, slice.factor = NULL, value = NULL,
  SBPr = NULL, SBPc = NULL, SBPs = NULL, pivot = FALSE,
  test = FALSE, n.boot = 1000)

Arguments

x

a data frame containing variables representing row, column and slice factors of the respective compositional cube and variable with the values of the composition.

row.factor

name of the variable representing the row factor. Needs to be stated with the quotation marks.

col.factor

name of the variable representing the column factor. Needs to be stated with the quotation marks.

slice.factor

name of the variable representing the slice factor. Needs to be stated with the quotation marks.

value

name of the variable representing the values of the composition. Needs to be stated with the quotation marks.

SBPr

an \(I-1\times I\) array defining the sequential binary partition of the values of the row factor, where I is the number of the row factor levels. The values assigned in the given step to the + group are marked by 1, values from the - group by -1 and the rest by 0. If it is not provided, the pivot version of coordinates is constructed automatically.

SBPc

an \(J-1\times J\) array defining the sequential binary partition of the values of the column factor, where J is the number of the column factor levels. The values assigned in the given step to the + group are marked by 1, values from the - group by -1 and the rest by 0. If it is not provided, the pivot version of coordinates is constructed automatically.

SBPs

an \(K-1\times K\) array defining the sequential binary partition of the values of the slice factor, where K is the number of the slice factor levels. The values assigned in the given step to the + group are marked by 1, values from the - group by -1 and the rest by 0. If it is not provided, the pivot version of coordinates is constructed automatically.

pivot

logical, default is FALSE. If TRUE, or one of the SBPs is not defined, its pivot version is used.

print.res

logical, default is FALSE. If TRUE, the output is displayed in the Console.

X

a data frame containing variables representing row, column and slice factors of the respective compositional cubes, variable with the values of the composition and variable distinguishing the observations.

obs.ID

name of the variable distinguishing the observations. Needs to be stated with the quotation marks.

test

logical, default is FALSE. If TRUE, the bootstrap analysis of coordinates is provided.

n.boot

number of bootstrap samples.

Value

Coordinates

an array of orthonormal coordinates.

Grap.rep

graphical representation of the coordinates. Parts denoted by + form the groups in the numerator of the respective computational formula, parts - form the denominator and parts . are not involved in the given coordinate.

Row.balances

an array of row balances.

Column.balances

an array of column balances.

Slice.balances

an array of slice balances.

Row.column.OR

an array of row-column OR coordinates.

Row.slice.OR

an array of row-slice OR coordinates.

Column.slice.OR

an array of column-slice OR coordinates.

Row.col.slice.OR

an array of coordinates describing the mutual interaction between all three factors.

Contrast.matrix

contrast matrix.

Log.ratios

an array of pure log-ratios between groups of parts without the normalizing constant.

Coda.cube

cube form of the given composition.

Bootstrap

array of sample means, standard deviations and bootstrap confidence intervals.

Cubes

Cube form of the given compositions.

Details

cubeCoord

This transformation moves the IJK-part compositional cubes from the simplex into a (IJK-1)-dimensional real space isometrically with respect to its three-factorial nature.

Wrapper (cubeCoordWrapper): Each of n IJK-part compositional cubes from the sample is with respect to its three-factorial nature isometrically transformed from the simplex into a (IJK-1)-dimensional real space. Sample mean values and standard deviations are computed and using bootstrap an estimate of 95 % confidence interval is given.

References

Facevicova, K., Filzmoser, P. and K. Hron (2019) Compositional Cubes: Three-factorial Compositional Data. Under review.

See Also

tabCoord tabCoordWrapper

Examples

# NOT RUN {
###################
### Coordinate representation of a CoDa Cube

### example from Fa\v cevicov\'a (2019)
data(employment2)
CZE <- employment2[which(employment2$Country == 'CZE'), ]

# pivot coordinates
cubeCoord(CZE, "Sex", 'Contract', "Age", 'Value')

# coordinates with given SBP

r <- t(c(1,-1))
c <- t(c(1,-1))
s <- rbind(c(1,-1,-1), c(0,1,-1))

cubeCoord(CZE, "Sex", 'Contract', "Age", 'Value', r,c,s)

###################
### Analysis of a sample of CoDa Cubes

### example from Fa\v cevicov\'a (2019)
data(employment2)
### Compositional tables approach,
### analysis of the relative structure.
### An example from Facevi\v cov\'a (2019)

# pivot coordinates
cubeCoordWrapper(employment2, 'Country', 'Sex', 'Contract', 'Age', 'Value',  
test=TRUE)

# coordinates with given SBP (defined in the paper)

r <- t(c(1,-1))
c <- t(c(1,-1))
s <- rbind(c(1,-1,-1), c(0,1,-1))

res <- cubeCoordWrapper(employment2, 'Country', 'Sex', 'Contract', 
"Age", 'Value', r,c,s, test=TRUE)

### Classical approach,
### generalized linear mixed effect model.

# }
# NOT RUN {
library(lme4)
employment2$y <- round(employment2$Value*1000)
glmer(y~Sex*Age*Contract+(1|Country),data=employment2,family=poisson)
# }
# NOT RUN {
### other relations within cube (in the log-ratio form)
### e.g. ratio between women and man in the group FT, 15to24
### and ratio between age groups 15to24 and 55plus

# transformation matrix
T <- rbind(c(1,rep(0,5), -1, rep(0,5)), c(rep(c(1/4,0,-1/4), 4)))
T %*% t(res$Contrast.matrix) %*%res$Bootstrap[,1]
# }