Contributions

Product contributions

It’s often convenient to decompose an index into the (additive) contribution of each price relative, also known as the percent-change contribution. This can be done with the same work flow used in vignette("piar"), specifying contrib = TRUE when calling elemental_index().

library(piar)

# Make an aggregation structure.
ms_weights[c("level1", "level2")] <- 
  expand_classification(ms_weights$classification)

pias <- ms_weights[c("level1", "level2", "business", "weight")] |>
  as_aggregation_structure()

# Make elemental index with contributions.
elementals <- ms_prices |>
  transform(
    relative = price_relative(price, period = period, product = product)
  ) |>
  elemental_index(
    relative ~ period + business,
    product = product,
    na.rm = TRUE,
    contrib = TRUE
  )

As with index values, percent-change contributions for a given level of the index can be extracted as a matrix.

contrib(elementals, level = "B1")

##   202001     202002     202003 202004
## 1      0  0.0000000  0.0000000      0
## 2     NA         NA -0.6657061      0
## 3      0 -0.1050903         NA     NA

Or as a data frame.

contrib2DF(elementals, level = "B1")

##   period level product      value
## 1 202001    B1       1  0.0000000
## 2 202001    B1       2         NA
## 3 202001    B1       3  0.0000000
## 4 202002    B1       2         NA
## 5 202002    B1       3 -0.1050903
## 6 202003    B1       2 -0.6657061
## 7 202003    B1       3         NA
## 8 202004    B1       3         NA

Aggregating the elemental indexes automatically aggregates percent-change contributions, so no extra steps are needed after the elemental indexes are made.

index <- aggregate(elementals, pias, na.rm = TRUE)

contrib(index)

##    202001      202002     202003       202004
## 1       0  0.00000000  0.0000000  0.000000000
## 10      0 -0.08782076  0.2731949 -0.078173579
## 11      0  0.00000000         NA  0.059392635
## 12      0  0.00000000         NA  1.322915301
## 2      NA          NA -0.2928098  0.000000000
## 3       0 -0.06718490         NA           NA
## 4       0          NA         NA -0.018209690
## 5       0          NA         NA  0.094562963
## 6       0          NA         NA  0.427935081
## 7       0  0.51646606 -0.2054665 -0.011177530
## 8       0  0.01906845  0.1755868 -0.003784845
## 9       0 -0.07980493  0.1125689 -0.058699008

Index contributions

After an index has been calculated, it’s often useful to compute the contribution of higher-level indexes towards the total index. The easiest way to do this with a collection of pre-computed index values is to simply coerce them into an index object with the index values as contributions and reaggregate with a restricted aggregation structure.

index <- as_index(as.matrix(index), contrib = TRUE)

If the index values are already an index object, it’s also possible to directly replace the contributions.

reset_contrib <- function(index) {
  contrib_matrix <- as.matrix(index) - 1
  for (l in levels(index)) {
    contrib(index, l) <- contrib_matrix[l, , drop = FALSE]
  }
  index
}

index <- reset_contrib(index)

We now cut the aggregation structure to keep only the top two levels and reaggregate to get the contribution of the second-level indexes to the top level index.

aggregate(index, cut(pias, 2)) |>
  contrib()

##    202001   202002     202003    202004
## 11      0 0.184488 0.03869481 0.3524534
## 12      0 0.116236 0.02437952 1.3823079

The same approach works with a fixed-base index as well.

chain(index) |>
  reset_contrib() |>
  aggregate(cut(pias, 2)) |>
  contrib()

##    202001   202002    202003    202004
## 11      0 0.184488 0.2348192 0.7221798
## 12      0 0.116236 0.1479470 2.0593557