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

It is possible to rework the functions in this package to make a spatial, rather
than temporal, price index using a star model by simply replacing "time" with "space".
Although this is not a suitable
approach for making a system of purchasing power parities, is it useful for making indexes
that adjust pay for cost-of-living differences relative to a fixed location. These
sorts of indexes are made by the United Nations International Civil Service Commission, Eurostat, and various governments
and private-sector organizations for administering cost-of-living allowances.

The basic workflow is the same as with a temporal index, just treating each
country as a different "time period" in a fixed-based index.

```{r}
library(piar)

set.seed(12345)

# Make indexes for 6 basic headings for 4 countries.
bh_index <- matrix(
  c(rep(1, 6), runif(6 * 3, 0.8, 1.2)),
  nrow = 6,
  dimnames = list(
    paste0("BH", 1:6),
    paste("Country", 1:4)
  )
) |>
  as_index(chainable = FALSE)

head(bh_index)

# Make fixed aggregation weights.
#            1
#      |-----+-----|
#      11          12
#  |---+---|   |---+---|
#  B1  B2  B3  B4  B5  B6

weights <- data.frame(
  level1 = 1,
  level2 = rep(11:12, each = 3),
  bh = levels(bh_index),
  weights = runif(6, 100, 200)
)

head(weights)
```

The indexes at the basic-heading level can be aggregated as usual to get a
collection of indexes that give the difference in purchasing power relative to
the base country (country 1 in this example). Different choices for weights make
different assumptions about how people change their spending patterns between
each country and the base country.

```{r}
index <- aggregate(bh_index, weights)
```

As it can be costly to collect price data from various countries on a regular
basis, these sorts of indexes are often updated over time by changes in exchange
rates and inflation rates for each country.

```{r}
as.matrix(index[1, -1])

update_factors <- runif(3, 0.8, 1.2)

as.matrix(index[1, -1]) * update_factors
```

