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

In robCompositions: Compositional Data Analysis

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)

robCompositions documentation built on Aug. 25, 2023, 5:13 p.m.