ShareRatioElasticities {CoDaImpact}

Compute share ratio elasticities for CoDa models

Description

In CoDa models with compositional dependent variable (Y) share ratio elasticities (SRE) allow to interpret the influence of compositional explanatory variables (X). The interpretation is analogous to usual elasticities:

• When the share ratio of X increases by 1% the share ratio of Y increases by SRE%

• The main difference to usual elasticities that, since X is compositional the change of X musts be specified in terms of a direction in the simplex.

Usage

ShareRatioElasticities(object, Xvar, Xdir = NULL)

Arguments

object

an object of class "lmCoDa"

Xvar

a character indicating the name of the explanatory variable that changes

Xdir

a numeric vector, a single character, or NULL:

• if numeric Xdir is taken as a fixed direction in the simplex

• if character Xdir is interpreted as one summit of the X composition and converted to the fixed direction towards this summit

• if NULL the share ratio elasticities are computed for variable directions corresponding the example in Dargel and Thomas-Agnan (2024 Lukas Dargel & Christine Thomas-Agnan (2024) The link between multiplicative competitive interaction models and compositional data regression with a total, Journal of Applied Statistics, DOI: 10.1080/02664763.2024.2329923 )

Details

More details on this interpretation can be found in Dargel and Thomas-Agnan (2024) and in the accompanying vignette.

Value

a data.frame

Author(s)

Lukas Dargel

References

• Dargel, Lukas and Christine Thomas-Agnan, “Pairwise share ratio interpretations of compositional regression models”, Computational Statistics & Data Analysis 195 (2024), p. 107945

Examples

### XY-compositional model
res <- lmCoDa(
  ilr(cbind(left, right, extreme_right)) ~
  ilr(cbind(Educ_BeforeHighschool, Educ_Highschool, Educ_Higher)),
  data =  head(election, 20))

## Focus on changes in the education composition
educ_comp <- "cbind(Educ_BeforeHighschool, Educ_Highschool, Educ_Higher)"

## case 1
## changes towards the summit "Educ_Higher" as (fixed) direction
SRE1 <- ShareRatioElasticities(res, Xvar = educ_comp, Xdir = "Educ_Higher")

SRE1[1,]
# Result: SRE=Inf
# cannot be interpreted because, for this direction,
# the relative change in the share ratio of X (Highschool / BeforeHighschool) is zero
SRE1[7,]
# Result: SRE=0.9
# when the ratio of X (Higher / BeforeHighschool) increases by 1%
# the ratio of Y (right / left) increases by about 0.9%

## case 2
## numeric vector as (fixed) direction
SRE2 <- ShareRatioElasticities(res, Xvar = educ_comp, Xdir = exp(c(0,0,1)))
identical(SRE1,SRE2) # exp(c(0,0,1)) is the direction that points to the third summit

## case 3
## variable directions with Xdir = NULL
## In this case the direction depends components used for the share ratio of X
## In particular the component of X in the numerator grows
## by the same rate as the denominator decreases
SRE3 <- ShareRatioElasticities(res, Xvar = educ_comp, Xdir = NULL)
SRE3[1,]
# Result: SRE=-2.8
# when the ratio of X (Highschool / BeforeHighschool) increases by 1%
# the ratio of Y (right / left) decreases by about -2.8%