R: Coordinate representation of a compositional cube and of a...

cubeCoord {robCompositions} | R Documentation

## 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.

### 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.

### 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.

### Author(s)

Kamila Facevicova

### References

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

### See Also

`tabCoord` `tabCoordWrapper`

### Examples

    ###################
    ### Coordinate representation of a CoDa Cube
    ## Not run:
    ### 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)

    ## End(Not run)

    ###################
    ### Analysis of a sample of CoDa Cubes
    ## Not run:
    ### 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]

    ## End(Not run)

[Package robCompositions version 2.3.1 Index]