A hierarchical Bayesian approach for handling missing classification data

Abstract

Ecologists use classifications of individuals in categories to understand composition of populations and communities. These categories might be defined by demographics, functional traits, or species. Assignment of categories is often imperfect, but frequently treated as observations without error. When individuals are observed but not classified, these “partial” observations must be modified to include the missing data mechanism to avoid spurious inference. We developed two hierarchical Bayesian models to overcome the assumption of perfect assignment to mutually exclusive categories in the multinomial distribution of categorical counts, when classifications are missing. These models incorporate auxiliary information to adjust the posterior distributions of the proportions of membership in categories. In one model, we use an empirical Bayes approach, where a subset of data from one year serves as a prior for the missing data the next. In the other approach, we use a small random sample of data within a year to inform the distribution of the missing data. We performed a simulation to show the bias that occurs when partial observations were ignored and demonstrated the altered inference for the estimation of demographic ratios. We applied our models to demographic classifications of elk (Cervus elaphus nelsoni) to demonstrate improved inference for the proportions of sex and stage classes. We developed multiple modeling approaches using a generalizable nested multinomial structure to account for partially observed data that were missing not at random for classification counts. Accounting for classification uncertainty is important to accurately understand the composition of populations and communities in ecological studies.

Pathogen‐mediated selection and management implications for white‐tailed deer exposed to chronic wasting disease

“…Our model results for age correction were consistent with the results from Samuel and Storm (2016). The pattern of age bias in adult females is consistent with known classification bias where adult females are over-placed in younger age classes (Ketz, Johnson, et al, 2019;Smith & McDonald, 2002). We also found that CWD status was the most important predictor of PRNP genotype for deer whose genotype was unknown (Table S6; Figure S5), and predictions were consistent with those from .…”

“…Moreover, under moderate antlered harvest, the proportion of 96GS/SS male fawns produced under high antlerless harvest was 4% higher than under low antlerless harvest, indicative of increased breeding success of 96GS/SS males. Correct age classification of wildlife species is notoriously difficult (Conn & Diefenbach, 2007;Ketz, Johnson, et al, 2019;Storm et al, 2014) and can affect epidemiological parameters (Lachish & Murray, 2018;Samuel & Storm, 2016;Storm et al, 2014). Our model results for age correction were consistent with the results from Samuel and Storm (2016).…”

“…In the Wisconsin core area, Grear et al (2006) and Heisey et al (2010) found that CWD status did not influence hunting mortality, at least during the early phase of the epizootic. We are not aware of any study evaluating differential harvest of deer with different PRNP genotypes; however, a number of deer studies evaluating genotypic differences in CWD status have also assumed harvest was not based on PRNP genotype (see Ketz, Johnson, et al, 2019;. PRNP genotype distributions have consistently demonstrated that the frequency of least susceptible PRNP alleles are uncommon (LaCava et al, 2021;Monello et al, 2017;Robinson, Samuel, O'Rourke, et al, 2012).…”

“…Alternatively, cross-sectional age-prevalence data are increasingly used to estimate disease parameters for free-ranging animals (Heisey et al, 2006(Heisey et al, , 2010Samuel & Storm, 2016;Samuel et al, 2015). However, potential biases arise for wildlife populations because ages of individuals are uncertain (Conn & Diefenbach, 2007;Ketz, Johnson, et al, 2019;Storm et al, 2014). Methods to account for age misclassification must be considered to avoid spurious inference on force of infection and disease-associated mortality (Samuel & Storm, 2016).…”

A spatial capture–recapture model with attractions between individuals

“…In a seminal article on closed population modeling, Otis, Burnham, White, and Anderson (1978) allowed capture probability to vary by time, individual capture response (i.e., fear or attraction to trapping devices) and individual heterogeneity (individual covariates such as age or sex) and greatly motivated following closed population modeling efforts to date (for a good quick overview of parameter estimation approaches for these models see table 1 in Chao (2001)). More recent models have been developed to handle intricacies which can arise in CR studies such as missing classification data (Ketz, Johnson, Hooten, & Hobbs, 2019; Lasantha Premarathna, Schwarz, & Jones, 2018), individual mobility (Jensen, 1994), continuous time data (Becker, 1984; Wang & Yip, 2002; Yip, Xi, Chao, & Hwang, 2000), obtaining data from multiple sources or observers (El‐Khorazaty, 2000; Givens et al, 2015) as well as interesting examples outside of wildlife sciences (Bucholz & Laplante, 2009; Weller, Hoeting, & von Fischer, 2018).…”