View source: R/ShareRatioElasticities.R
ShareRatioElasticities  R Documentation 
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.
ShareRatioElasticities(object, Xvar, Xdir = NULL)
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

More details on this interpretation can be found in Dargel and ThomasAgnan (2024) and in the accompanying vignette.
a data.frame
Lukas Dargel
Dargel, Lukas and Christine ThomasAgnan, “Pairwise share ratio interpretations of compositional regression models”, Computational Statistics & Data Analysis 195 (2024), p. 107945
### XYcompositional 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%
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