IDEAS home Printed from https://ideas.repec.org/a/vrs/stintr/v21y2020i3p1-19n5.html
   My bibliography  Save this article

A Bayesian Small Area Model with Dirichlet Processes on the Responses

Author

Listed:
  • Yin Jiani

    (Takeda Pharmaceuticals. Massachusetts, USA .)

  • Nandram Balgobin

    (Worcester Polytechnic Institute. Worcester, USA .)

Abstract

Typically survey data have responses with gaps, outliers and ties, and the distributions of the responses might be skewed. Usually, in small area estimation, predictive inference is done using a two-stage Bayesian model with normality at both levels (responses and area means). This is the Scott-Smith (S-S) model and it may not be robust against these features. Another model that can be used to provide a more robust structure is the two-stage Dirichlet process mixture (DPM) model, which has independent normal distributions on the responses and a single Dirichlet process on the area means. However, this model does not accommodate gaps, outliers and ties in the survey data directly. Because this DPM model has a normal distribution on the responses, it is unlikely to be realized in practice, and this is the problem we tackle in this paper. Therefore, we propose a two-stage non-parametric Bayesian model with several independent Dirichlet processes at the first stage that represents the data, thereby accommodating some of the difficulties with survey data and permitting a more robust predictive inference. This model has a Gaussian (normal) distribution on the area means, and so we call it the DPG model. Therefore, the DPM model and the DPG model are essentially the opposite of each other and they are both different from the S-S model. Among the three models, the DPG model gives us the best head-start to accommodate the features of the survey data. For Bayesian predictive inference, we need to integrate two data sets, one with the responses and other with area sizes. An application on body mass index, which is integrated with census data, and a simulation study are used to compare the three models (S-S, DPM, DPG); we show that the DPG model might be preferred.

Suggested Citation

  • Yin Jiani & Nandram Balgobin, 2020. "A Bayesian Small Area Model with Dirichlet Processes on the Responses," Statistics in Transition New Series, Statistics Poland, vol. 21(3), pages 1-19, September.
  • Handle: RePEc:vrs:stintr:v:21:y:2020:i:3:p:1-19:n:5
    DOI: 10.21307/stattrans-2020-041
    as

    Download full text from publisher

    File URL: https://doi.org/10.21307/stattrans-2020-041
    Download Restriction: no

    File URL: https://libkey.io/10.21307/stattrans-2020-041?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Nandram, Balgobin & Choi, Jai Won, 2010. "A Bayesian Analysis of Body Mass Index Data From Small Domains Under Nonignorable Nonresponse and Selection," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 120-135.
    Full references (including those not matched with items on IDEAS)

    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. Hamrick, Karen S., 2012. "Nonresponse Bias Analysis of Body Mass Index in the Eating and Health Module," Technical Bulletins 184303, United States Department of Agriculture, Economic Research Service.
    2. Jai Won Choi & Balgobin Nandram, 2021. "Large Sample Problems," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 1-81, March.
    3. Lu Chen & Balgobin Nandram, 2023. "Bayesian Logistic Regression Model for Sub-Areas," Stats, MDPI, vol. 6(1), pages 1-23, January.
    4. Balgobin Nandram, 2021. "A Bayesian Approach to Linking a Survey and a Census via Small Areas," Stats, MDPI, vol. 4(2), pages 1-20, June.
    5. Jiani Yin & Balgobin Nandram, 2020. "A Bayesian Small Area Model with Dirichlet Processes on the Responses," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 1-19, September.
    6. Zhang Nanhua & Chen Henian & Elliott Michael R., 2016. "Nonrespondent Subsample Multiple Imputation in Two-Phase Sampling for Nonresponse," Journal of Official Statistics, Sciendo, vol. 32(3), pages 769-785, September.

    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:vrs:stintr:v:21:y:2020:i:3:p:1-19:n:5. 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: Peter Golla (email available below). General contact details of provider: https://stat.gov.pl/en/ .

    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.