vcov.aggregate_piar_index {piar}

Bootstrap variance for a price index with replicate weights

Description

Estimate the sampling variance for an aggregate price index when using a sample of elemental aggregates.

Usage

## S3 method for class 'aggregate_piar_index'
vcov(object, repweights, ..., mse = TRUE, sparse = FALSE)

Arguments

object

An aggregate price index, as made by aggregate().

repweights

A matrix, or something that can be coerced into one, of bootstrap replicate weights with a row for each elemental aggregate and a column for each replicate.

...

Not currently used.

mse

Should variance be centered off the value of the index in object (the default), or the mean of the replicates?

sparse

Use sparse matrices from Matrix when aggregating the index. Faster for indexes with large aggregation structures. The default uses regular dense matrices.

Details

This function is a simple wrapper that reaggregates the elemental indexes in object using the bootstrap replicate weights in repweights to get a collection of aggregate indexes from which the variance is calculated.

This approach is usually applicable when elemental aggregates are sampled with a stratified design that follows the aggregation structure, so that there is no correlation between the index values for different levels of the index. It ignores any variation from the elemental indexes (which often use judgmental sampling), and ultimately depends on the method of generating replicate weights. (Chapters 3 and 4 of Selvanathan and Rao (1994), especially section 4.7, provide analytic variance estimators for some common price indexes that are applicable with simple random sampling.)

Note that any missing elemental indexes need to be explicitly imputed prior to using this method, otherwise they will propagate throughout the variance calculation.

Value

A matrix of variances with a row for each upper-level index and a column for each time period.

Source

The vcov() method was influenced by a SAS routine by Justin Francis that was first ported to R by Ambuj Dewan, and subsequently rewritten by Steve Martin.

References

Selvanathan, E. A., and Rao, D. S. P. (1994). Index Numbers: A Stochastic Approach. MacMillan.

See Also

The sps_repweights() function in the sps package to generate replicates weights when elemental aggregates are sampled using sequential Poisson sampling.

Other index methods: [.piar_index(), aggregate.piar_index(), as.data.frame.piar_index(), chain(), contrib(), head.piar_index(), is.na.piar_index(), levels.piar_index(), mean.piar_index(), merge.piar_index(), split.piar_index(), stack.piar_index(), time.piar_index()

Examples

prices <- data.frame(
  rel = 1:8,
  period = rep(1:2, each = 4),
  ea = rep(letters[1:2], 4)
)

# A two-level aggregation structure

pias <- aggregation_structure(
  list(c("top", "top", "top"), c("a", "b", "c")), 1:3
)

repweights <- matrix(c(0, 2, 3, 1, 2, 4, 2, 3, 3), 3)

# Calculate Jevons elemental indexes

elemental <- with(prices, elemental_index(rel, period, ea))

# Aggregate

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

# Calculate variance

vcov(index, repweights)