bayesian hierarchical models for demographic small area estimation john bryant statistics new...
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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
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Characteristics of demographic data
Cross-classified counts• Not records × variables
Often ‘complete’ counts rather than survey
Time-varying
Strong regularities
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Deaths, Maori males
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Bayesian hierarchical models an attractive approach
Demographic data are hierarchical
Shrinkage
Flexibility
Forecasting, probabilistic statements
Recent surge in number of papers
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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
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Application: Births rates by small area
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Region 13, 1996 = 11 births; Region 2, 2006 = 1490 births; 10% of cells missing
A model, three ways
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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
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theta <- fetch(res, where = c("model", "likelihood", "mean"))p <- dplot(~ age | region + factor(year), data = theta, midpoints = "age")useOuterStrips(p)
Results, with unsmoothed rates
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Results: Change over time
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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
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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
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Future work
More priors
Survey data
Forecasting
Lots more testing• Especially on big datasets
Eventually release on CRAN
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