Bayesian hierarchical models for demographic small area estimation

John Bryant

Statistics New Zealand

September 2013

Examples of demographic small area estimation

Birth rates by age of mother by ‘area unit’• 39 age groups• 70+ territorial authorities• 61,000 births

Maori deaths by age and sex• 101 age groups• 2 sexes• 3,000 deaths

2

Characteristics of demographic data

Cross-classified counts• Not records × variables

Often ‘complete’ counts rather than survey

Time-varying

Strong regularities

3

Deaths, Maori males

4

Bayesian hierarchical models an attractive approach

Demographic data are hierarchical

Shrinkage

Flexibility

Forecasting, probabilistic statements

Recent surge in number of papers

5

Packages Demographic and DemographicEstimation

Under development

Originally only ‘Demographic accounts’• later realized more general application

Demographicdata structures and basic manipulation functions

DemographicEstimationBayesian hierarchical models, customised for demographic problems

6

Application: Births rates by small area

7

Region 13, 1996 = 11 births; Region 2, 2006 = 1490 births; 10% of cells missing

A model, three ways

8

res <- estimateModel(Model(y ~ Poisson(mean ~ age * region + year), region ~ Exch(mean ~ income + propn.maori, data = data.reg)), y = births, exposure = deaths, file = "fertility.res")

(1) (2)

(3)

Results: All regions and years

9

theta <- fetch(res, where = c("model", "likelihood", "mean"))p <- dplot(~ age | region + factor(year), data = theta, midpoints = "age")useOuterStrips(p)

Results, with unsmoothed rates

10

Results: Change over time

11

regions <- paste("Reg", c(2, 5, 8, 13))p <- dplot(~ year | factor(age) * region, data = theta, subarray = region %in% regions, weights = females, overlay = list(values = subarray(births/females, region %in% regions), pch = 19, col = "black"))useOuterStrips(p)

Results: Covariates

12

covariate <- fetch(res, where = c("model", "hyper", "region", "covariates"))dplot(~ covariate, data = covariate)

Other features

Normal and binomial models

Diagnostics• Convergence• Replicate data

Manipulation of (voluminous) output

13

Future work

More priors

Survey data

Forecasting

Lots more testing• Especially on big datasets

Eventually release on CRAN

14