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The Agincourt Health and Demographic Surveillance System has since 2001conducted a biannual household asset survey in order to quantify householdsocio-economic status (SES) in a rural population living in northeast SouthAfrica. The survey contains binary, ordinal and nominal items. In the absenceof income or expenditure data, the SES landscape in the study population isexplored and described by clustering the households into homogeneous groupsbased on their asset status. A model-based approach to clustering the Agincourthouseholds, based on latent variable models, is proposed. In the case ofmodeling binary or ordinal items, item response theory models are employed. Fornominal survey items, a factor analysis model, similar in nature to amultinomial probit model, is used. Both model types have an underlying latentvariable structure - this similarity is exploited and the models are combinedto produce a hybrid model capable of handling mixed data types. Further, amixture of the hybrid models is considered to provide clustering capabilitieswithin the context of mixed binary, ordinal and nominal response data. Theproposed 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 Agincourthouseholds into homogeneous groups. The model is estimated within the Bayesianparadigm, using a Markov chain Monte Carlo algorithm. Intuitive groupingsresult, providing insight to the different socio-economic strata within theAgincourt region.

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