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
)

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.

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.

Author

Kamila Facevicova

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.

Examples

Run this code

###################
### Coordinate representation of a CoDa Cube
if (FALSE) {
### 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
if (FALSE) {
### 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.

library(lme4)
employment2$y <- round(employment2$Value*1000)
glmer(y~Sex*Age*Contract+(1|Country),data=employment2,family=poisson)

### 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]
}

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