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Effects of infinitesimal changes in CoDa models

Source: R/VariationTable.R
VariationTable.Rd

This function allows to evaluate how a change in an explanatory variables impacts the response variable in a CoDa regression model. The changes are calculated based from the approximate formal presented in Dargel and Thomas-Agnan (2024). Changes in the response variables are provided as data.frame and the underlying changes in the explanatory variable are given as attributes.

Usage

VariationTable(
  object,
  Xvar,
  Xdir,
  obs = 1,
  inc_size = 0.1,
  inc_rate = NULL,
  Ytotal = 1,
  normalize_Xdir = TRUE
)

Arguments

object

an object of class "lmCoDa"

Xvar

a character indicating the name of the explanatory variable that changes

Xdir

either character or numeric, to indicate the direction in which Xvar should change

  • when character this should be one of the components of X, in which case the direction is the corresponding vertex of the simplex

  • when numeric this argument is coerced to a unit vector in the simplex

  • (when Xvar refers to a scalar variable this argument is ignored)

obs

a numeric indicating the observation used for the scenario

inc_size

a numeric indicating the distance between each point in the scenario of X

inc_rate

a numeric that can be used as a parameterization of the step size

Ytotal

a numeric indicating the total of Y

normalize_Xdir

a logical, if TRUE the direction Xdir scaled to have an Aitchison norm of 1, allowing to interpret inc_size as the Aitchison distance

Value

data.frame

References

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

Author

  • Lukas Dargel

  • Rodrigue Nasr

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)"

# ... changes towards a summit towards a summit (higher share of people with lower education)
VariationTable(res, educ_comp, Xdir = "Educ_BeforeHighschool")
#>                              left     right extreme_right
#> Initial parts           0.3395614 0.4066297     0.2538089
#> New parts               0.2519498 0.4203111     0.3277390
#> Elasticity             -2.5801405 0.3364601     2.9128277
#> Variation in %        -25.8014049 3.3646008    29.1282765
#> Variation in % points  -8.7611620 1.3681465     7.3930155

# ... same changes using a compositional vector as direction
VariationTable(res, educ_comp, Xdir = c(.5,.25,.25))
#>                              left     right extreme_right
#> Initial parts           0.3395614 0.4066297     0.2538089
#> New parts               0.2519498 0.4203111     0.3277390
#> Elasticity             -2.5801405 0.3364601     2.9128277
#> Variation in %        -25.8014049 3.3646008    29.1282765
#> Variation in % points  -8.7611620 1.3681465     7.3930155

# ... changes in a more general direction and for a different observation
VariationTable(res, educ_comp, Xdir = c(.35,.45,.10), obs = 2)
#>                             left      right extreme_right
#> Initial parts          0.3375668  0.4066003     0.2558329
#> New parts              0.3906038  0.3999548     0.2094415
#> Elasticity             1.5711531 -0.1634408    -1.8133484
#> Variation in %        15.7115308 -1.6344077   -18.1334837
#> Variation in % points  5.3036919 -0.6645506    -4.6391412