---
title: "Aggregating across dimensions"
vignette: >
  %\VignetteIndexEntry{Aggregating across dimensions}
  %\VignetteEngine{quarto::html}
  %\VignetteEncoding{UTF-8}
knitr:
  opts_chunk: 
    collapse: true
    comment: '#>'
---

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.

```{r}
library(piar)

elementals <- ms_prices |>
  transform(
    relative = price_relative(price, period = period, product = product)
  ) |>
  elementary_index(relative ~ period + business, na.rm = TRUE)
```

```{r}
ms_weights$stratum <- c("TS", "TA", "TS", "TS", "TS")

ms_weights
```

The 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.

```{r}
classification_sps <- paste0(ms_weights$classification, ms_weights$stratum) |>
  expand_classification(width = c(1, 1, 2))

pias_sps <- aggregation_structure(
  c(classification_sps, list(ms_weights$business)),
  ms_weights$weight
)

pias_sps
```

The elementary indexes can now be aggregated according to this new
aggregation structure.

```{r}
index_sps <- aggregate(elementals, pias_sps, na.rm = TRUE)

index_sps
```

When 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`.

```{r}
interacted_hierarchy <- interact_classifications(
  expand_classification(ms_weights$classification),
  expand_classification(ms_weights$stratum)
)

pias_sps2 <- lapply(
  interacted_hierarchy,
  \(x) aggregation_structure(c(x, list(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.

```{r}
Reduce(merge, index_sps2)
```
