Estimating Cross-Classified Population Counts of Multidimensional Tables: An Application to Regional Australia to Obtain Pseudo-Census Counts
Open Access
- 18 November 2017
- journal article
- research article
- Published by Walter de Gruyter GmbH in Journal of Official Statistics
- Vol. 33 (4), 1021-1050
- https://doi.org/10.1515/jos-2017-0048
Abstract
Estimating population counts for multidimensional tables based on a representative sample subject to known marginal population counts is not only important in survey sampling but is also an integral part of standard methods for simulating area-specific synthetic populations. In this article several estimation methods are reviewed, with particular focus on the iterative proportional fitting procedure and the maximum likelihood method. The performance of these methods is investigated in a simulation study for multidimensional tables, as previous studies are limited to 2 by 2 tables. The data are generated under random sampling but also under misspecification models, for which sample and target populations differ systematically. The empirical results show that simple adjustments can lead to more efficient estimators, but generally, at the expense of increased bias. The adjustments also generally improve coverage of the confidence intervals. The methods discussed in this article along with standard error estimators, are made freely available in the R package mipfp. As an illustration, the methods are applied to the 2011 Australian census data available for the Illawarra Region in order to obtain estimates for the desired three-way table for age by sex by family type with known marginal tables for age by sex and for family type.Keywords
This publication has 32 references indexed in Scilit:
- An Iterative Approach for Generating Statistically Realistic Populations of HouseholdsPLOS ONE, 2010
- Bayesian inference for categorical data analysisStatistical Methods & Applications, 2005
- Multinomial-Poisson homogeneous models for contingency tablesThe Annals of Statistics, 2004
- Approximate is Better than “Exact” for Interval Estimation of Binomial ProportionsThe American Statistician, 1998
- Generating Multivariate Categorical Variates Using the Iterative Proportional Fitting AlgorithmThe American Statistician, 1995
- Simultaneously Modeling Joint and Marginal Distributions of Multivariate Categorical ResponsesJournal of the American Statistical Association, 1994
- Calibration Estimators in Survey SamplingJournal of the American Statistical Association, 1992
- Models for Contingency Tables with Known Margins when Target and Sampled Populations DifferJournal of the American Statistical Association, 1991
- Estimation of Linear Functions of Cell ProportionsThe Annals of Mathematical Statistics, 1947
- On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are KnownThe Annals of Mathematical Statistics, 1940