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

tabCoord {robCompositions} | R Documentation

## Coordinate representation of compositional tables and a sample of compositional tables

### Description

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

tabCoordWrapper: For each compositional table in the sample `tabCoordWrapper` 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

    tabCoord(
      x = NULL,
      row.factor = NULL,
      col.factor = NULL,
      value = NULL,
      SBPr = NULL,
      SBPc = NULL,
      pivot = FALSE,
      print.res = FALSE
    )

    tabCoordWrapper(
      X,
      obs.ID = NULL,
      row.factor = NULL,
      col.factor = NULL,
      value = NULL,
      SBPr = NULL,
      SBPc = NULL,
      pivot = FALSE,
      test = FALSE,
      n.boot = 1000
    )

### Arguments

`x` | a data frame containing variables representing row and column factors of the respective compositional table 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.
`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.
`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 and column factors of the respective compositional tables, 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

tabCoord

This transformation moves the IJ-part compositional tables from the simplex into a (IJ-1)-dimensional real space isometrically with respect to its two-factorial nature. The coordinate system is formed by two types of coordinates - balances and log odds-ratios.

tabCoordWrapper: Each of n IJ-part compositional tables from the sample is with respect to its two-factorial nature isometrically transformed from the simplex into a (IJ-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.
`Ind.coord` | an array of row and column balances. Coordinate representation of the independent part of the table.
`Int.coord` | an array of OR coordinates. Coordinate representation of the interactive part of the table.
`Contrast.matrix` | contrast matrix.
`Log.ratios` | an array of pure log-ratios between groups of parts without the normalizing constant.
`Coda.table` | table form of the given composition.
`Bootstrap` | array of sample means, standard deviations and bootstrap confidence intervals.
`Tables` | Table form of the given compositions.

### Author(s)

Kamila Facevicova

### References

Facevicova, K., Hron, K., Todorov, V. and M. Templ (2018) General approach to coordinate representation of compositional tables. Scandinavian Journal of Statistics, 45(4), 879–899.

### See Also

`cubeCoord` `cubeCoordWrapper`

### Examples

    ###################
    ### Coordinate representation of a CoDa Table

    # example from Fa\v cevicov\'a (2018):
    data(manu_abs)
    manu_USA <- manu_abs[which(manu_abs$country=='USA'),]
    manu_USA$output <- factor(manu_USA$output, levels=c('LAB', 'SUR', 'INP'))

    # pivot coordinates
    tabCoord(manu_USA, row.factor = 'output', col.factor = 'isic', value='value')

    # SBPs defined in paper
    r <- rbind(c(-1,-1,1), c(-1,1,0))
    c <- rbind(c(-1,-1,-1,-1,1), c(-1,-1,-1,1,0), c(-1,-1,1,0,0), c(-1,1,0,0,0))
    tabCoord(manu_USA, row.factor = 'output', col.factor = 'isic', value='value', SBPr=r, SBPc=c)

    ###################
    ### Analysis of a sample of CoDa Tables

    # example from Fa\v cevicov\'a (2018):
    data(manu_abs)

    ### Compositional tables approach,
    ### analysis of the relative structure.
    ### An example from Facevi\v cov\'a (2018)

    manu_abs$output <- factor(manu_abs$output, levels=c('LAB', 'SUR', 'INP'))

    # pivot coordinates
    tabCoordWrapper(manu_abs, obs.ID='country',
    row.factor = 'output', col.factor = 'isic', value='value')

    # SBPs defined in paper
    r <- rbind(c(-1,-1,1), c(-1,1,0))
    c <- rbind(c(-1,-1,-1,-1,1), c(-1,-1,-1,1,0),
    c(-1,-1,1,0,0), c(-1,1,0,0,0))
    tabCoordWrapper(manu_abs, obs.ID='country',row.factor = 'output',
    col.factor = 'isic', value='value', SBPr=r, SBPc=c, test=TRUE)

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

    ## Not run:
    library(lme4)
    glmer(value~output*as.factor(isic)+(1|country),data=manu_abs,family=poisson)

    ## End(Not run)

[Package robCompositions version 2.3.1 Index]