robCompositions (version 2.1.0)

tabCoord: 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.

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.

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.

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

# NOT RUN {
###################
### 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)
# }