Multinomial mixture for spatial data

The purpose of this paper is to extend standard finite mixture models in the context of multinomial mixtures for spatial data, in order to cluster geographical units according to demographic characteristics. The spatial information is incorporated into the model through the mixing probabilities of each component. To be more specific, a Gibbs distribution is assumed for prior probabilities. In this way, assignment of each observation is affected by neighbors' cluster and spatial dependence is included in the model. Estimation is based on a modified EM algorithm which is enriched by an extra, initial step for approximating the field. The simulated field algorithm is used in this initial step. Simulation studies are also provided to examine the ability of the methodology to properly cluster the data and reveal the true parameters, while focus is given in the performance of the approximated BIC on recovering the true number of clusters. The presented model will be used for clustering municipalities of Attica with respect to age distribution of residents. The results of the analysis have revealed eight distinct clusters. Each cluster includes municipalities with similar age structure of the population, as for example group of municipalities with excess of young adult people because of the universities in these regions.