Price indexes are often aggregated over multiple dimensions. Matched sample indexes that use sequential Poisson sampling to draw a sample of businesses are a good example, as there are usually take-all and take-some strata in addition to, say, an industry classification.
Let’s extend vignette("piar") by adding another
dimension to the classification to say if a business belongs to the
take-all or take-some sampling stratum.
library(piar)
elementals <- ms_prices |>
transform(
relative = price_relative(price, period = period, product = product)
) |>
elemental_index(relative ~ period + business, na.rm = TRUE)## business classification weight level1 level2 stratum
## 1 B1 11 553 1 11 TS
## 2 B2 11 646 1 11 TA
## 3 B3 11 312 1 11 TS
## 4 B4 12 622 1 12 TS
## 5 B5 12 330 1 12 TSThe easiest way to deal with multiple digit-wise classifications is
to concatenate them into one classification. In this example the
“stratum” dimension comes before the “classification” dimension for the
purposes of parental imputation. This classification can be expanded
with the expand_classification() function as before, just
with an extra instruction to say that the last “digit” in the
classification is two characters wide, not one.
classification_sps <- paste0(ms_weights$classification, ms_weights$stratum) |>
expand_classification(width = c(1, 1, 2))
pias_sps <- aggregation_structure(
c(classification_sps, ms_weights["business"]),
ms_weights$weight
)
pias_sps## Aggregation structure for 5 elemental aggregates with 3 levels above the elemental aggregates
## level1 level2 level3 ea weight
## 1 1 11 11TS B1 553
## 2 1 11 11TA B2 646
## 3 1 11 11TS B3 312
## 4 1 12 12TS B4 622
## 5 1 12 12TS B5 330The elemental indexes can now be aggregated according to this new aggregation structure.
## Period-over-period price index for 11 levels over 4 time periods
## 202001 202002 202003 202004
## 1 1 1.3007239 1.0630743 2.684412
## 11 1 1.3007239 1.0630743 1.492443
## 12 1 1.3007239 1.0630743 4.576286
## 11TS 1 1.3007239 1.0630743 0.537996
## 11TA 1 1.3007239 1.0630743 2.770456
## 12TS 1 1.3007239 1.0630743 4.576286
## B1 1 0.8949097 0.3342939 0.537996
## B2 1 1.3007239 1.0630743 2.770456
## B3 1 2.0200036 1.6353355 0.537996
## B4 1 1.3007239 1.0630743 4.576286
## B5 1 1.3007239 1.0630743 4.576286When a price index has many dimensions (e.g., industry, sampling stratum, region), it can be useful to interact the classifications for these different dimensions to get all possible aggregation structures. The aggregated index can then be re-aggregated to get index values for all dimensions.
Continuing with the example, the industry and strata classifications
can be interacted to get two aggregation structures that can be used to
re-aggregate index_sps.
interacted_hierarchy <- interact_classifications(
expand_classification(ms_weights$classification),
expand_classification(ms_weights$stratum)
)
pias_sps2 <- lapply(
interacted_hierarchy,
\(x) aggregation_structure(c(x, ms_weights["business"]), ms_weights$weight)
)
index_sps2 <- lapply(pias_sps2, \(x) aggregate(index_sps, x, include_ea = FALSE))The resulting indexes can be merged together to give an index that includes all combinations of industry and sampling stratum.
## Period-over-period price index for 8 levels over 4 time periods
## 202001 202002 202003 202004
## 1:T 1 1.300724 1.063074 2.684412
## 1:TS 1 1.300724 1.063074 2.653820
## 1:TA 1 1.300724 1.063074 2.770456
## 11:T 1 1.300724 1.063074 1.492443
## 12:T 1 1.300724 1.063074 4.576286
## 11:TS 1 1.300724 1.063074 0.537996
## 11:TA 1 1.300724 1.063074 2.770456
## 12:TS 1 1.300724 1.063074 4.576286