Influence of prior distributions and random effects on count regression models: implications for estimating standing dead tree abundance

The presence and abundance of standing dead trees (SDTs) in forests is typically characterized by an excess number of zeros and high variation. The variability inherent in SDT data naturally leads to the assessment of novel quantitative methods to represent SDT populations and their role in contributing to forest ecosystem structure. This analysis assessed the performance of count regression methods fit with Bayesian mixed-effects models that estimate SDTs (all dead trees with a diameter at breast height ≥ 12.7cm found on plots 0.07-ha in size) on over 17,000 forest inventory plots across the US Lake States (Michigan, Minnesota, and Wisconsin). Random effects models that used the independent variables basal area, mean annual temperature, and plot ownership (i.e., publicly- or privately-owned) as fixed effects and forest type as a random effect outperformed a method which used fixed-effects, alone. Standard and zero-inflated negative binomial models were effective in accounting for overdispersion present in the data (variance/mean ratio for SDT counts was 72.6), whereas Poisson count models were not. Random effects were calibrated on a new population of SDTs. Employing informative prior distributions from the developed model led to improved estimates of SDT abundance by reducing root mean square error by seven percent. This analysis highlights an approach that uses existing models for representing population averages while calibrating their local random effects with new data to arrive at improved estimates of SDTs across the region.