IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i8p3057-3069.html
   My bibliography  Save this article

Spatial latent class analysis model for spatially distributed multivariate binary data

Author

Listed:
  • Wall, Melanie M.
  • Liu, Xuan

Abstract

A spatial latent class analysis model that extends the classic latent class analysis model by adding spatial structure to the latent class distribution through the use of the multinomial probit model is introduced. Linear combinations of independent Gaussian spatial processes are used to develop multivariate spatial processes that are underlying the categorical latent classes. This allows the latent class membership to be correlated across spatially distributed sites and it allows correlation between the probabilities of particular types of classes at any one site. The number of latent classes is assumed to be fixed but is chosen by model comparison via cross-validation. An application of the spatial latent class analysis model is shown using soil pollution samples where 8 heavy metals were measured to be above or below government pollution limits across a 25 square kilometer region. Estimation is performed within a Bayesian framework using MCMC and is implemented using the OpenBUGS software.

Suggested Citation

  • Wall, Melanie M. & Liu, Xuan, 2009. "Spatial latent class analysis model for spatially distributed multivariate binary data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3057-3069, June.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3057-3069
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00375-7
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Denis Bolduc & Bernard Fortin & Stephen Gordon, 1997. "Multinomial Probit Estimation of Spatially Interdependent Choices: An Empirical Comparison of Two New Techniques," International Regional Science Review, , vol. 20(1-2), pages 77-101, April.
    2. Xiaoping Jin & Bradley P. Carlin & Sudipto Banerjee, 2005. "Generalized Hierarchical Multivariate CAR Models for Areal Data," Biometrics, The International Biometric Society, vol. 61(4), pages 950-961, December.
    3. Simon Cheng & J. Scott Long, 2007. "Testing for IIA in the Multinomial Logit Model," Sociological Methods & Research, , vol. 35(4), pages 583-600, May.
    4. Schmidheiny, Kurt, 2006. "Income segregation and local progressive taxation: Empirical evidence from Switzerland," Journal of Public Economics, Elsevier, vol. 90(3), pages 429-458, February.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Kurt J. Beron & Wim P. M. Vijverberg, 2004. "Probit in a Spatial Context: A Monte Carlo Analysis," Advances in Spatial Science, in: Luc Anselin & Raymond J. G. M. Florax & Sergio J. Rey (ed.), Advances in Spatial Econometrics, chapter 8, pages 169-195, Springer.
    7. Bunch, David S., 1991. "Estimability in the Multinomial Probit Model," University of California Transportation Center, Working Papers qt1gf1t128, University of California Transportation Center.
    8. Bolduc, Denis, 1999. "A practical technique to estimate multinomial probit models in transportation," Transportation Research Part B: Methodological, Elsevier, vol. 33(1), pages 63-79, February.
    9. Beth A. Reboussin & Kung-Yee Liang & David M. Reboussin, 1999. "Estimating Equations for a Latent Transit ion Model with Multiple Discrete Indicators," Biometrics, The International Biometric Society, vol. 55(3), pages 839-845, September.
    10. Holloway, Garth & Shankar, Bhavani & Rahman, Sanzidur, 2002. "Bayesian spatial probit estimation: a primer and an application to HYV rice adoption," Agricultural Economics, Blackwell, vol. 27(3), pages 383-402, November.
    11. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
    12. Bunch, David S., 1991. "Estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 1-12, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vidoli, Francesco & Pignataro, Giacomo & Benedetti, Roberto, 2022. "Identification of spatial regimes of the production function of Italian hospitals through spatially constrained cluster-wise regression," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    2. Solaiman Afroughi & Soghrat Faghihzadeh & Majid Jafari Khaledi & Mehdi Ghandehari Motlagh & Ebrahim Hajizadeh, 2011. "Analysis of clustered spatially correlated binary data using autologistic model and Bayesian method with an application to dental caries of 3--5-year-old children," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2763-2774, February.
    3. Jarno Vanhatalo & Scott D. Foster & Geoffrey R. Hosack, 2021. "Spatiotemporal clustering using Gaussian processes embedded in a mixture model," Environmetrics, John Wiley & Sons, Ltd., vol. 32(7), November.
    4. LeSage, James & Banerjee, Sudipto & Fischer, Manfred M. & Congdon, Peter, 2009. "Spatial statistics: Methods, models & computation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2781-2785, June.
    5. Lekkas, Peter & Paquet, Catherine & Howard, Natasha J. & Daniel, Mark, 2017. "Illuminating the lifecourse of place in the longitudinal study of neighbourhoods and health," Social Science & Medicine, Elsevier, vol. 177(C), pages 239-247.
    6. Jian Kang & Nanhua Zhang & Ran Shi, 2014. "A Bayesian nonparametric model for spatially distributed multivariate binary data with application to a multidrug-resistant tuberculosis (MDR-TB) study," Biometrics, The International Biometric Society, vol. 70(4), pages 981-992, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ziegler, Andreas, 2001. "Simulated z-tests in multinomial probit models," ZEW Discussion Papers 01-53, ZEW - Leibniz Centre for European Economic Research.
    2. Daziano, Ricardo A., 2015. "Inference on mode preferences, vehicle purchases, and the energy paradox using a Bayesian structural choice model," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 1-26.
    3. GRAMMIG, Joachim & HUJER, Reinhard & SCHEIDLER, Michael, 2001. "The econometrics of airline network management," LIDAM Discussion Papers CORE 2001055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Ziegler Andreas, 2010. "Z-Tests in Multinomial Probit Models under Simulated Maximum Likelihood Estimation: Some Small Sample Properties," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(5), pages 630-652, October.
    5. Yai, Tetsuo & Iwakura, Seiji & Morichi, Shigeru, 1997. "Multinomial probit with structured covariance for route choice behavior," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 195-207, June.
    6. repec:asg:wpaper:1048 is not listed on IDEAS
    7. David Roodman, 2009. "Estimating Fully Observed Recursive Mixed-Process Models with cmp," Working Papers 168, Center for Global Development.
    8. Joan L. Walker & Moshe Ben-Akiva & Denis Bolduc, 2007. "Identification of parameters in normal error component logit-mixture (NECLM) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1095-1125.
    9. Young, Gary & Valdez, Emiliano A. & Kohn, Robert, 2009. "Multivariate probit models for conditional claim-types," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 214-228, April.
    10. Joachim Grammig & Reinhard Hujer & Michael Scheidler, 2005. "Discrete choice modelling in airline network management," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 467-486, May.
    11. Garrido, Rodrigo A. & Leva, Mabel, 2004. "Port of destination and carrier selection for fruit exports: a multi-dimensional space-time multi-nomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 657-667, August.
    12. Victoria Prowse, 2012. "Modeling Employment Dynamics With State Dependence and Unobserved Heterogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 411-431, April.
    13. Bolduc, Denis & Khalaf, Lynda & Moyneur, Érick, 2008. "Identification-robust simulation-based inference in joint discrete/continuous models for energy markets," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3148-3161, February.
    14. Daziano, Ricardo A. & Achtnicht, Martin, 2012. "Forecasting adoption of ultra-low-emission vehicles using the GHK simulator and Bayes estimates of a multinomial probit model," ZEW Discussion Papers 12-017, ZEW - Leibniz Centre for European Economic Research.
    15. David Roodman, 2011. "Fitting fully observed recursive mixed-process models with cmp," Stata Journal, StataCorp LP, vol. 11(2), pages 159-206, June.
    16. Rub'en Loaiza-Maya & Didier Nibbering, 2022. "Fast variational Bayes methods for multinomial probit models," Papers 2202.12495, arXiv.org, revised Oct 2022.
    17. repec:rre:publsh:v:36:y:2006:i:2:p:140-62 is not listed on IDEAS
    18. Funashima, Yoshito & Ohtsuka, Yoshihiro, 2019. "Spatial crowding-out and crowding-in effects of government spending on the private sector in Japan," Regional Science and Urban Economics, Elsevier, vol. 75(C), pages 35-48.
    19. Friederike Paetz & Winfried J. Steiner, 2017. "The benefits of incorporating utility dependencies in finite mixture probit models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 793-819, July.
    20. Heng Z. Chen & Frank Lupi & John P. Hoehn, 1999. "An Empirical Assessment of Multinomial Probit and Logit Models for Recreation Demand," Chapters, in: Joseph A. Herriges & Catherine L. Kling (ed.), Valuing Recreation and the Environment, chapter 5, pages 141-162, Edward Elgar Publishing.
    21. Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-632, November.
    22. Michael Scheidler & Reinhard Hujer & Joachim Grammig, 2005. "Discrete choice modelling in airline network management," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 467-486.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3057-3069. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.