Bayesian Tree Models for Survey Sample Data

Daniell Toth, Scott H Holan and Diya Bhaduri

Journal of Survey Statistics and Methodology, 2025, vol. 13, issue 4, 445-464

Abstract: Tree models are a popular and effective nonparametric modeling tool for data that depend on many variables that exhibit complex dependence, including interaction effects. Consequently, there are many potential applications for these models when dealing with survey data, which often contain many variables that are not independent from one another. One drawback of these models is that the specification is not stable, in that a few observations could affect the number of nodes and the variables included in the model. Also, obtaining a measure of uncertainty associated with these models is extremely challenging. Using a Bayesian representation naturally alleviates some of these concerns, as it automatically implies a distribution over tree space given the data as well as a distribution for the estimates produced. Since survey data are usually collected using an informative sample design, it is necessary to have an algorithm for creating tree-based models that account for this design during model estimation. In this article, we propose an algorithm and associated prior distribution assumptions to obtain a Bayesian tree model using data collected under an informative sample design. We demonstrate this proposed method using the Consumer Expenditure Survey and the Academic Performance Index datasets. Using an empirical simulation study, we show that the design-based Bayesian algorithm is an extremely flexible and robust way to construct regression tree models with measures of uncertainty that provide prediction intervals with the correct nominal coverage rates.

Keywords: CART models; Domain estimation; Informative sample design; Machine learning; Official statistics; Semiparametric regression (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1093/jssam/smae050 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:jassam:v:13:y:2025:i:4:p:445-464.

Access Statistics for this article

Journal of Survey Statistics and Methodology is currently edited by Emily Berg and Brad Edwards

More articles in Journal of Survey Statistics and Methodology from American Association for Public Opinion Research and American Statistical Association
Bibliographic data for series maintained by Oxford University Press ().