decomposition: Decompose a demographic array

In StatisticsNZ/demest: Bayesian Demographic Estimation and Forecasting

Decompose a demographic array

Description

Decompose a DemographicArray into terms made up of component dimensions, plus an error. decomposition is typically used to obtain initial estimates of main effects and interactions, as part of model building.

Usage

decomposition(object, max = NULL)

## S4 method for signature 'DemographicArray'
decomposition(object, max = NULL)

Arguments

object	An object of class DemographicArray.
max	An integer. Optional.

Details

When building a Poisson model, the decomposition is usually carried out on log-rates, and when building a binomial model, it is usually carried out on logit-proportions, though in both cases other transformations (or no transformation) may be appropriate if there are lots of zeros (and also lots of ones in the case of binomial models).

The final element in the return value is an 'error' array. This equals the observed value for object minus the sum of the terms in the decomposition.

The max argument controls the maximum order of the interactions included in decomposition. For instance, if max is 2, then only main effects and second-order interactions are included in the decomposition. By default, all interactions are included.

Internally, decomposition calls function pairToState on object, to cope with origin-destination or parent-child dimensions.

Value

A named list, the elements of which have class Values.

References

Chapter 12 of Bryant and Zhang, Bayesian Demographic Estimation and Forecasting.

Examples

deaths <- Counts(demdata::VADeaths2)
popn <- Counts(demdata::VAPopn)
rates <- deaths/popn
log.rates <- log(rates)
ans <- decomposition(log.rates)
names(ans)
ans[1:3]
ans[["age:residence"]]
mean(log.rates)
round(sapply(ans, sum), 5)
all.equal(Reduce("+", ans), log.rates)
## main effects only
decomposition(log.rates, max = 1)

StatisticsNZ/demest documentation built on Nov. 2, 2023, 7:56 p.m.