Descriptive inference using large, unrepresentative nonprobability samples: An introduction for ecologists

Biodiversity monitoring usually involves drawing inferences about some variable of interest across a defined landscape from observations made at a sample of locations within that landscape. If the variable of interest differs between sampled and nonsampled locations, and no mitigating action is taken, then the sample is unrepresentative and inferences drawn from it will be biased. It is possible to adjust unrepresentative samples so that they more closely resemble the wider landscape in terms of "auxiliary variables." A good auxiliary variable is a common cause of sample inclusion and the variable of interest, and if it explains an appreciable portion of the variance in both, then inferences drawn from the adjusted sample will be closer to the truth. We applied six types of survey sample adjustment-subsampling, quasirandomization, poststratification, superpopulation modeling, a "doubly robust" procedure, and multilevel regression and poststratification-to a simple two-part biodiversity monitoring problem. The first part was to estimate the mean occupancy of the plant Calluna vulgaris in Great Britain in two time periods (1987-1999 and 2010-2019); the second was to estimate the difference between the two (i.e., the trend). We estimated the means and trend using large, but (originally) unrepresentative, samples from a citizen science dataset. Compared with the unadjusted estimates, the means and trends estimated using most adjustment methods were more accurate, although standard uncertainty intervals generally did not cover the true values. Completely unbiased inference is not possible from an unrepresentative sample without knowing and having data on all relevant auxiliary variables. Adjustments can reduce the bias if auxiliary variables are available and selected carefully, but the potential for residual bias should be acknowledged and reported.

Assessing health insurance coverage in Florida using the behavioral risk factor surveillance system

We use data from the Behavioral Risk Factor Surveillance System, BRFSS, to investigate the important topic of health insurance coverage. Here, our investigation is about coverage in Florida at the county level and for important subpopulations defined by age, gender, and race. As large US government administered surveys are designed to provide reliable estimates of finite population characteristics for large geographical areas such as the entire US or for individual states, they are not designed to make direct inferences for small geographical regions and/or subpopulations. Given the importance of this topic, we use Bayesian predictive inference for the finite population quantities of interest, thus avoiding approximations necessary in other approaches. There are careful diagnostic checks of the model that we propose, including residual checks and cross-validation, together with formal tests of the concordance between the observed data and model. We check whether there is a selection bias investigating, in particular, the possible role of the conventional survey weights in correcting for selection bias and in improving inferences. We display our results in choropleth maps, together with displays of map variation. The latter maps can be used to assess the visual appearance of the "mean map", ie, the one usually presented, relative to a sequence of possible maps. Finally, we compare our county estimates of health insurance coverage with estimates from the BRFSS produced by the Centers for Disease Control and Prevention and from the US Census Bureau under their SAHIE program.