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.2022 May 27;50(13):2701-2716.
doi: 10.1080/02664763.2022.2078289. eCollection 2023.

Bayesian models for spatial count data with informative finite populations with application to the American community survey

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Bayesian models for spatial count data with informative finite populations with application to the American community survey

Kai Qu et al. J Appl Stat..

Abstract

The American Community Survey (ACS) is an ongoing program conducted by the US Census Bureau that publishes estimates of important demographic statistics over pre-specified administrative areas. ACS provides spatially referenced count-valued outcomes that are paired with finite populations. For example, the number of people below the poverty line and the total population for each county are estimated by ACS. One common assumption is that the spatially referenced count-valued outcome given the finite population is binomial distributed. This conditionally specified (CS) model does not define the joint relationship between the count-valued outcome and the finite population. Thus, we consider a joint model for the count-valued outcome and the finite population. When cross-dependence in our joint model can be leveraged to 'improve spatial prediction' we say that the finite population is 'informative.' We model the count given the finite population as binomial and the finite population as negative binomial and use multivariate logit-beta prior distributions. This leads to closed-form expressions of the full-conditional distributions for an efficient Gibbs sampler. We illustrate our model through simulations and our motivating application of ACS poverty estimates. These empirical analyses show the benefits of using our proposed model over the more traditional CS binomial model.

Keywords: Bayesian statistics; conjugate; generalized linear models; official statistics; spatial statistics.

© 2022 Informa UK Limited, trading as Taylor & Francis Group.

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Conflict of interest statement

No potential conflict of interest was reported by the author(s).

Figures

Figure 1.
Figure 1.
ACS poverty count data: the observed families counts in poverty (left) and the total families number (right).
Figure 2.
Figure 2.
Simulated binomial and negative binomial counts and true proportions.
Figure 3.
Figure 3.
The first panel presents the true values and estimated values of{πi} by method withi on thex-axis. Similarly, the right panel presents the credible bands for{πi} by method.
Figure 4.
Figure 4.
MSPE versus prior specification for ACS binomial data mixed effects model.
Figure 5.
Figure 5.
Trace plots of the JBWBIN model for ACS binomial training data (898).
Figure 6.
Figure 6.
Testing (50) models for binomial data: the first row displays the predicted logit of poverty proportions and their associated MSPE (on the logit-scale for visualization purposes); the second row displays the estimated proportions versus the observed proportions; and the third row displays the 95% lower and upper credible limits for estimated proportions.
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References

    1. Ahlburg D.A., Population growth and poverty, in The Impact of Population Growth on Well-Being in Developing Countries, D.A. Ahlburg, A. C. Kelley, and K. O. Mason eds., Berlin-Heidelberg: Springer, 1996, pp. 219–258.
    1. Bradley J., Wikle C., and Holan S., Spatio-temporal change of support with application to American community survey multi-year period estimates, Statistics 4 (2015), pp. 255–270.
    1. Bradley J.R., Wikle C.K., and Holan S.H., Bayesian spatial change of support for count-valued survey data with application to the American community survey, J. Am. Stat. Assoc. 111 (2016), pp. 472–487.
    1. Bradley J.R., Wikle C.K., and Holan S.H., Spatio-temporal models for big multinomial data using the conditional multivariate logit-beta distribution, J. Time Ser. Anal. 40 (2019), pp. 363–382.
    1. Bradley J.R., Holan S.H., and Wikle C.K., Bayesian hierarchical models with conjugate full-conditional distributions for dependent data from the natural exponential family, J. Am. Stat. Assoc. 115 (2020), pp. 2037–2052.

Grants and funding

Jonathan R. Bradley's research was partially supported by the U.S. National Science Foundation (NSF) [NSF grant SES-1853099] and the National Institute of Health (NIH) [grant 1R03AG070669-01].

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