Interpreting CoDa Regression Models

Provides methods for interpreting CoDa (Compositional Data) regression models along the lines of "Pairwise share ratio interpretations of compositional regression models" (Dargel and Thomas-Agnan 2024) . The new methods include variation scenarios, elasticities, elasticity differences and share ratio elasticities. These tools are independent of log-ratio transformations and allow an interpretation in the original space of shares. 'CoDaImpact' is designed to be used with the 'compositions' package and its ecosystem.

CoDaImpact

CoDaImpact provides additional tools for the interpretation of regression CoDa models. It is conceived as an extension of the compositions package.

Installation

You can install the development version of CoDaImpact from GitHub with:

# install.packages("devtools")
devtools::install_github("LukeCe/CoDaImpact")

Example of a Y-compositional model

Below, we estimate a CoDa model that explains the market shares of five segments of the car market in France. To illustrate the influence of the HOUSEHOLD_EXPENDITURE on the market shares in each segment we use a VariationScenario(). In this scenario the HOUSEHOLD_EXPENDITURE is moved along a grid while all other variables are fixed to the values of the first observation.

library("CoDaImpact")
data("car_market")

model_car_segements <- lmCoDa(
  ilr(cbind(SEG_A, SEG_B, SEG_C, SEG_D, SEG_E)) ~
    GDP + HOUSEHOLD_EXPENDITURE + GAS_PRICE,
  data = car_market)

VS <- VariationScenario(
  model_car_segements,
  Xvar = "HOUSEHOLD_EXPENDITURE",
  obs = 1,
  inc_size = 100, 
  n_steps = 150,
  add_opposite = TRUE)


plot(x = VS$HOUSEHOLD_EXPENDITURE, y = VS$Y[,1],type = "l", col = "red",
     main = "Variation scenario of household expenditure",
     xlab = "Household expenditure", ylab = "Market share by segment")
lines(x = VS$HOUSEHOLD_EXPENDITURE, y = VS$Y[,2],type = "l", col = "blue" )
lines(x = VS$HOUSEHOLD_EXPENDITURE, y = VS$Y[,3],type = "l", col = "green")
lines(x = VS$HOUSEHOLD_EXPENDITURE, y = VS$Y[,4],type = "l", col = "orange")
lines(x = VS$HOUSEHOLD_EXPENDITURE, y = VS$Y[,5],type = "l", col = "black")
legend("topleft",
       legend = paste0("Segment ", LETTERS[1:5]),
       col = c("red", "blue", "green", "orange", "black"),
       lty = 1)