A comparison of models for interval-censored plant cover data, with applications to monitoring schemes

Plant cover data collected by monitoring schemes are often expressed on interval-censored scales to reduce field effort. Existing statistical approaches to such data may not make full use of available information, or may both induce bias and assume more precision than may be warranted, e.g. by analysing mid-points and disregarding the spread of observations within a class.

We compare four approaches to modelling such data: two established methods (the proportional odds model and generalised linear mixed models) and two novel methods that explicitly accommodate the interval-censored nature of much data on plant cover. Of the latter, the first is a maximum likelihood (ML) approach that incorporates knowledge of the metric interval in which each datum lies. The second uses a Bayesian approach to incorporate interval-censoring and random effects to account for variation in annual changes between sites. All four methods are compared using data simulated with parameter values derived from analysis of a long-term monitoring dataset.

We demonstrate that model choice can influence the quality of statistical inference, particularly between models that make simplifications for convenience of fitting, and those which combine realistic distributional assumptions with accommodation of imprecise observations. A comparison of three of the methods demonstrated that all provide good accuracy and increasing precision over time. A comparison of power across the three frequentist approaches showed higher power for the novel ML approach. This is likely to be due to this non-hierarchical method underestimating residual variance. The Bayesian model is not directly comparable, but the measure of belief in a negative trend considered here was generally high, providing gradual increases in the believability of a decline with increasing time, number of sites, initial abundance, and larger effect sizes.

Our results suggest that the use of hierarchical models for plant monitoring schemes, conveniently applied in a Bayesian context, will help to bring greater realism and sensitivity to assessments of population change, and allow the use of more of the underlying information contained within cover data. Interval-censored methods will also allow for the integration of long-term plant datasets collected according to different cover scales, as well as presence/absence data.