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

Area of Science:

• Statistics
• Demography
• Spatial Analysis

Background:

• The American Community Survey (ACS) provides crucial demographic estimates for administrative areas.
• Current models often assume a binomial distribution for count outcomes given finite populations, lacking a joint relationship definition.
• This limitation can impact the accuracy of spatial predictions.

Purpose of the Study:

• To develop and evaluate a joint statistical model for count-valued outcomes and finite populations within the ACS framework.
• To address the limitations of conditionally specified (CS) models by defining the joint relationship.
• To improve spatial prediction accuracy by leveraging cross-dependence between outcomes and populations.

Main Methods:

• A joint model was proposed, treating the count as binomial given the finite population and the finite population as negative binomial.
• Multivariate logit-beta prior distributions were employed.
• An efficient Gibbs sampler was developed using closed-form full-conditional distributions.

Main Results:

• Simulations and an application to ACS poverty estimates demonstrated the model's effectiveness.
• The proposed joint model showed benefits over the traditional CS binomial model.
• The finite population was shown to be 'informative' when cross-dependence improved spatial prediction.

Conclusions:

• The developed joint model offers improved spatial prediction for ACS data.
• This approach provides a more robust statistical framework than traditional CS models.
• The findings highlight the importance of modeling the joint distribution for accurate demographic estimations.