We present a Bayesian partial membership model that estimates the associations between an outcome, a small number of latent variables, and multiple observed exposures where the number of latent variables is specified a priori. We assign one observed exposure as the sentinel marker for each latent variable. The model allows non-sentinel exposures to have complete membership in one latent group, or partial membership across two or more latent groups. MCMC sampling is used to determine latent group partial memberships for the non-sentinel exposures, and estimate all model parameters. We compare the performance of our model to competing approaches in a simulation study and apply our model to inflammatory marker data measured in a large mother-child cohort of the Seychelles Child Development Study (SCDS). In simulations, our model estimated model parameters with little bias, adequate coverage, and tighter credible intervals compared to competing approaches. Under our partial membership model with two latent groups, SCDS inflammatory marker classifications generally aligned with the scientific literature. Incorporating additional SCDS inflammatory markers and more latent groups produced similar groupings of markers that also aligned with the literature. Associations between covariates and birth weight were similar across latent variable models and were consistent with earlier work in this SCDS cohort.
Spatio-temporal models can be used to analyze data collected at various spatial locations throughout multiple time points. However, even with a finite number of spatial locations, there may be a lack of resources to collect data from every spatial location at every time point. We develop a spatio-temporal finite-population block kriging (ST-FPBK) method to predict a quantity of interest, such as a mean or total, across a finite number of spatial locations. This ST-FPBK predictor incorporates an appropriate variance reduction for sampling from a finite population. Through an application to moose surveys in the east-central region of Alaska, we show that the predictor has a substantially smaller standard error compared to a predictor from the purely spatial model that is currently used to analyze moose surveys in the region. We also show how the model can be used to forecast a prediction for abundance in a time point for which spatial locations have not yet been surveyed. A separate simulation study shows that the spatio-temporal predictor is unbiased and that prediction intervals from the ST-FPBK predictor attain appropriate coverage. For ecological monitoring surveys completed with some regularity through time, use of ST-FPBK could improve precision. We also give an R package that ecologists and resource managers could use to incorporate data from past surveys in predicting a quantity from a current survey.
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