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 elementary_index(). (See vignette("decomposing-indexes") for the underlying theory.)

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 elementary index with contributions.
elementals <- ms_prices |>
  transform(
    relative = price_relative(price, period = period, product = product)
  ) |>
  elementary_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
0.000	0.000	0.000	0.000
		-0.666	0.000
0.000	-0.105

Or as a data frame.

contrib2DF(elementals, level = "B1")

period	level	product	value
202001	B1	1	0.000
202001	B1	2
202001	B1	3	0.000
202002	B1	2
202002	B1	3	-0.105
202003	B1	2	-0.666
202003	B1	3
202004	B1	3

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

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

contrib(index)

202001	202002	202003	202004
0.000	0.000	0.000	0.000
0.000	-0.088	0.273	-0.078
0.000	0.000		0.059
0.000	0.000		1.323
		-0.293	0.000
⋮	⋮	⋮	⋮
0.000			0.095
0.000			0.428
0.000	0.516	-0.205	-0.011
0.000	0.019	0.176	-0.004
0.000	-0.080	0.113	-0.059

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 with the set_contrib_from_index() function. We can 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.

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

202001	202002	202003	202004
0.000	0.184	0.039	0.352
0.000	0.116	0.024	1.382

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

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

202001	202002	202003	202004
0.000	0.184	0.235	0.722
0.000	0.116	0.148	2.059