In regional economics research, a problem of interest is to detect similarities between regions, and estimate their shared coefficients in economics models. In this article, we propose a mixture of finite mixtures clustered regression model with auxiliary covariates that account for similarities in demographic or economic characteristics over a spatial domain. Our Bayesian construction provides both inference for number of clusters and clustering configurations, and estimation for parameters for each cluster. Empirical performance of the proposed model is illustrated through simulation experiments, and further applied to a study of influential factors for monthly housing cost in Georgia.
BradleyJR, HolanSH and WikleCK. (2018). Computationally efficient multivariate Spatio-temporal models for high-dimen- sional count-valued data (with discussion). Bayesian Analysis, 13, 253–310.
2.
BrunsdonC, FotheringhamAS and CharltonME. (1996). Geographically weighted regres- sion: A method for exploring spatial non- stationarity. Geographical Analysis, 28, 281–98.
3.
CarlinBP, GelfandAE and BanerjeeS. (2014). Hierarchical Modeling and Analysis for Spatial Data. Boca Raton, FL: Chapman & Hall/CRC Press.
4.
ChenM-H, ShaoQ-M and IbrahimJG. (2012). Monte Carlo Methods in Bayesian computation. Berlin: Springer Science & Business Media.
5.
CressieN. (1992). Statistics for spatial data. Terra Nova, 4, 613–17.
6.
DahlDB. (2006). Model-based clustering for expression data via a Dirichlet process mixture model. Bayesian Inference for Gene Expression and Proteomics, 4, 201–18.
7.
de ValpineP, TurekD, PaciorekCJ, Anderson-BergmanC, LangDT and BodikR. (2017). Programming with models: Writing statistical algorithms for general model structures with NIMBLE. Journal of Computational and Graphical Statistics, 26, 403–13.
8.
DigglePJ, TawnJA and MoyeedR. (1998). Model-based geostatistics. Journal of the Royal Statistical Society: Series C (Applied Statistics), 47, 299–350.
9.
FergusonTS. (1973). A Bayesian analysis of some nonparametric problems. Annals of Statistics, 1, 209–30.
10.
FotheringhamAS, YangW and KangW. (2017). Multiscale geographically weighted regression (MGWR). Annals of the American Association of Geographers, 107, 1247–65.
11.
GaoH and BradleyJR. (2019). Bayesian analysis of areal data with unknown adjacencies using the stochastic edge mixed effects model. Spatial Statistics, 31, 100357.
12.
GelfandAE and SchliepEM. (2016). Spatial statistics and Gaussian processes: A beautiful marriage. Spatial Statistics, 18, 86–104.
13.
GelfandAE, KimH-J, SirmansC and BanerjeeS. (2003). Spatial modeling with spatially varying coeffcient processes. Journal of the American Statistical Association, 98, 387–96.
14.
GengL and HuG. (2021). Bayesian spatial homogeneity pursuit for survival data with an application to the SEER respiratory cancer data. Biometrics. doi: https://doi.org/10.1111/biom.13439
15.
HuG and BradleyJ. (2018). A Bayesian spatial-temporal model with latent multivariate log-gamma random effects with application to earthquake magnitudes. Stat, 7, e179.
16.
HuG and HufferF. (2020). Modified Kaplan -Meier estimator and Nelson -Aalen estimator with geographical weighting for survival data. Geographical Analysis, 52, 28–48.
17.
HuG, GengJ, XueY and SangH. (2020a). Bayesian spatial homogeneity pursuit of functional data: An application to the U.S.income distribution. arXiv preprint arXiv:2002.06663.
18.
HuG, XueY and HufferF. (2020b). A comparison of Bayesian accelerated failure time models with spatially varying coeffients. Sankhya B. URL https://arxiv.org/pdf/2002.03251.pdf (last accessed 21 September 2021).
19.
IbrahimJ. G, ChenM-H and SinhaD. (2013). Bayesian Survival Analysis. Berlin: Springer Science & Business Media.
20.
IshwaranH and JamesLF. (2001). Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association, 96, 161–73.
21.
IshwaranH and ZarepourM. (2002). Exact and approximate sum representations for the Dirichlet process. Canadian Journal of Statistics, 30, 269–83.
22.
KulldorffM and NagarwallaN. (1995). Spatial disease clusters: Detection and inference. Statistics in Medicine, 14, 799–810.
23.
LeeD, RushworthA and SahuSK. (2014). A Bayesian localized conditional autoregressive model for estimating the health effects of air pollution. Biometrics, 70, 419–29.
24.
LeeJ, GangnonR. E and ZhuJ. (2017). Cluster detection of spatial regression coefficients. Statistics in Medicine, 36, 1118–33.
25.
LeeJ, SunY and ChangHH. (2019). Spatial cluster detection of regression coefficients in a mixed-effects model. Environmetrics, 31, e2578.
26.
LiF and SangH. (2019). Spatial homogeneity pursuit of regression coefficients for large datasets. Journal of the American Statistical Association, 114, 1050–62.
27.
LiuJ, MaY and WangH. (2020). Semiparametric model for covariance regression analysis. Computational Statistics & Data Analysis, 142, 106815.
28.
MaZ, XueY and HuG. (2020a). Geographically weighted regression analysis for spatial economics data: A Bayesian recourse. International Regional Science Review. doi: https://doi.org/10.1177/0160017620959823
29.
MaZ, XueY and HuG. (2020b). Heterogeneous regression models for clusters of spatial dependent data. Spatial Economic Analysis, 1–17. doi: https://doi.org/10.1080/17421772.2020.1784989
30.
MillerJ. W and HarrisonMT. (2013). A simple example of Dirichlet process mixture inconsistency for the number of components. In Advances in Neural Information Processing Systems, pages 199–206.
31.
MillerJ. W and HarrisonMT. (2018). Mixture models with a prior on the number of components. Journal of the American Statistical Association, 113, 340–56.
32.
NakayaT, FotheringhamAS, BrunsdonC and CharltonM. (2005). Geographically weighted Poisson regression for disease association mapping. Statistics in Medicine, 24, 2695–2717.
33.
NealRM. (2000). Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics, 9, 249–65.
34.
PitmanJ. (1995). Exchangeable and partially exchangeable random partitions. Probability Theory and Related Fields, 102, 145–58.
35.
RafteryAE, MadiganD and HoetingJA. (1997). Bayesian model averaging for linear regression models. Journal of the American Statistical Association, 92, 179–91.
36.
RandWM. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66, 846–50.
37.
ReichB. J, FuentesM, HerringA. H and EvensonK. R. (2010). Bayesian variable selection for multivariate spatially varying coefficient regression. Biometrics, 66, 772–82.
38.
SethuramanJ. (1991). A constructive definition of Dirichlet priors. Statistics Sinica, 4, 639–50.
WhiteG and GhoshSK. (2009). A stochastic neighborhood conditional autoregressive model for spatial data. Computational Statistics & Data Analysis, 53, 3033–46.
41.
World Population Review (2020). The 200 largest cities in the United States by population 2021. URL https://worldpopulationreview.com/us-cities (last accessed 1 December 2020).
42.
XuZ, BradleyJR and SinhaD. (2019). Latent multivariate log-gamma models for high-dimensional multi-type responses with application to daily fine particulate matter and mortality counts. arXiv preprint arXiv:1909.02528.
43.
XueY, SchifanoED and HuG. (2020). Geographically weighted Cox regression for prostate cancer survival data in Louisiana. Geographical Analysis, 52, 570–87.
44.
YangH-C, HuG and ChenM-H. (2019). Bayesian variable selection for Pareto regression models with latent multivariate log gamma process with applications to earthquake magnitudes. Geosciences, 9, 169.
45.
ZhaoP, YangH-C, DeyDK and HuG. (2020). Bayesian spatial homogeneity pursuit regression for count value data. arXiv preprint arXiv:2002.06678.
46.
ZouT, LanW, WangH and TsaiC-L. (2017). Covariance regression analysis. Journal of the American Statistical Association, 112, 266–81.
