# 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