One of the basic assumptions in spatial statistic is second-order stationarity, which implies homogeneity and isotropy. However, when using a spatial random field framework to model socio-economical or epidemiological data – just to mention two examples – it is often unreasonable to believe that the relationship between variables could be modelled as a realization of a unique stationary process. In order to provide a more realistic representation, we introduce a latent process which drives the value of the coefficients in a Cliff-Ord-type spatial autoregressive linear model identifying groups of observations with a similar behaviour. The latent process evolves as a Hidden Markov Random Field. This structure allows the topology of the problem to be taken into account when identifying groups. A simulation exercise is performed to investigate the influence of parameter values – estimated via a Markov chain Monte Carlo procedure – on the accuracy of the results. Criteria to perform model comparison in order to establish the optimal number of clusters are also provided. A case study referred to hedonic house prices in Boston illustrates the advantages of the proposed modelling strategy.

Modelling Nonstationary Spatial Lag Models with Hidden Markov Random Fields

Mira A.;
2021-01-01

Abstract

One of the basic assumptions in spatial statistic is second-order stationarity, which implies homogeneity and isotropy. However, when using a spatial random field framework to model socio-economical or epidemiological data – just to mention two examples – it is often unreasonable to believe that the relationship between variables could be modelled as a realization of a unique stationary process. In order to provide a more realistic representation, we introduce a latent process which drives the value of the coefficients in a Cliff-Ord-type spatial autoregressive linear model identifying groups of observations with a similar behaviour. The latent process evolves as a Hidden Markov Random Field. This structure allows the topology of the problem to be taken into account when identifying groups. A simulation exercise is performed to investigate the influence of parameter values – estimated via a Markov chain Monte Carlo procedure – on the accuracy of the results. Criteria to perform model comparison in order to establish the optimal number of clusters are also provided. A case study referred to hedonic house prices in Boston illustrates the advantages of the proposed modelling strategy.
2021
Hidden Markov Random Field; Latent process; Spatial clustering; Spatial nonstationarity
Ghiringhelli, C.; Bartolucci, F.; Mira, A.; Arbia, G.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2124118
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 4
social impact