The Annals of Applied Statistics

Clustering South African households based on their asset status using latent variable models

Damien McParland, Isobel Claire Gormley, Tyler H. McCormick, Samuel J. Clark, Chodziwadziwa Whiteson Kabudula, and Mark A. Collinson

Full-text: Open access

Abstract

The Agincourt Health and Demographic Surveillance System has since 2001 conducted a biannual household asset survey in order to quantify household socio-economic status (SES) in a rural population living in northeast South Africa. The survey contains binary, ordinal and nominal items. In the absence of income or expenditure data, the SES landscape in the study population is explored and described by clustering the households into homogeneous groups based on their asset status.

A model-based approach to clustering the Agincourt households, based on latent variable models, is proposed. In the case of modeling binary or ordinal items, item response theory models are employed. For nominal survey items, a factor analysis model, similar in nature to a multinomial probit model, is used. Both model types have an underlying latent variable structure—this similarity is exploited and the models are combined to produce a hybrid model capable of handling mixed data types. Further, a mixture of the hybrid models is considered to provide clustering capabilities within the context of mixed binary, ordinal and nominal response data. The proposed model is termed a mixture of factor analyzers for mixed data (MFA-MD).

The MFA-MD model is applied to the survey data to cluster the Agincourt households into homogeneous groups. The model is estimated within the Bayesian paradigm, using a Markov chain Monte Carlo algorithm. Intuitive groupings result, providing insight to the different socio-economic strata within the Agincourt region.

Article information

Source
Ann. Appl. Stat. Volume 8, Number 2 (2014), 747-776.

Dates
First available in Project Euclid: 1 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1404229513

Digital Object Identifier
doi:10.1214/14-AOAS726

Mathematical Reviews number (MathSciNet)
MR3262533

Zentralblatt MATH identifier
06333775

Keywords
Clustering mixed data item response theory Metropolis-within-Gibbs

Citation

McParland, Damien; Gormley, Isobel Claire; McCormick, Tyler H.; Clark, Samuel J.; Kabudula, Chodziwadziwa Whiteson; Collinson, Mark A. Clustering South African households based on their asset status using latent variable models. Ann. Appl. Stat. 8 (2014), no. 2, 747--776. doi:10.1214/14-AOAS726. https://projecteuclid.org/euclid.aoas/1404229513


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