A comparison of observation-level random effect and Beta-Binomial models for modelling overdispersion in Binomial data in ecology & evolution

By X. Harrison. PeerJ, 2015

387 citations recorded by the source corpus.

Overdispersion is a common feature of models of biological data, but researchers often fail to model the excess variation driving the overdispersion, resulting in biased parameter estimates and standard errors. Quantifying and modeling overdispersion when it is present is therefore critical for robust biological inference. One means to account for overdispersion is to add an observation-level random effect (OLRE) to a model, where each data point receives a unique level of a random effect that can absorb the extra-parametric variation in the data. Although some studies have investigated the utility of OLRE to model overdispersion in Poisson count data, studies doing so for Binomial proportion data are scarce. Here I use a simulation approach to investigate the ability of both OLRE models and Beta-Binomial models to recover unbiased parameter estimates in mixed effects models of Binomial data under various degrees of overdispersion. In addition, as ecologists often fit random intercept terms to models when the random effect sample size is low (<5 levels), I investigate the performance of both model types under a range of random effect sample sizes when overdispersion is present. Simulation results revealed that the efficacy of OLRE depends on the process that generated the overdispersion; OLRE failed to cope with overdispersion generated from a Beta-Binomial mixture model, leading to biased slope and intercept estimates, but performed well for overdispersion generated by adding random noise to the linear predictor. Comparison of parameter estimates from an OLRE model with those from its corresponding Beta-Binomial model readily identified when OLRE were performing poorly due to disagreement between effect sizes, and this strategy should be employed whenever OLRE are used for Binomial data to assess their reliability. Beta-Binomial models performed well across all contexts, but showed a tendency to underestimate effect sizes when modelling non-Beta-Binomial data. Finally, both OLRE and Beta-Binomial models performed poorly when models contained <5 levels of the random intercept term, especially for estimating variance components, and this effect appeared independent of total sample size. These results suggest that OLRE are a useful tool for modelling overdispersion in Binomial data, but that they do not perform well in all circumstances and researchers should take care to verify the robustness of parameter estimates of OLRE models.

Subfields: Ecological Modeling, Ecology, Health, Toxicology and Mutagenesis

View Paper: https://www.semanticscholar.org/paper/f93b5d9cfd295cf6d0e6ea040fcfd2349ae5e627

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Citations in the corpus

Formidable females and the power trajectories of socially integrated male vervet monkeys (2017, methodology): “In models 3 and 4, we omitted time period and, to address model overdispersion, specified observation level as a crossed random effect (Harrison, 2015).”
Analysing continuous proportions in ecology and evolution: A practical introduction to beta and Dirichlet regression (2019, methodology): “A simulation study showed that in general a beta‐binomial is preferred and lead to least biased estimates (Harrison, 2015).”
glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling (2017, background): “Overdispersion can also be addressed by adding a random effect with one level for each observation, i.e., a log-normal Poisson distribution (Elston et al., 2001; Hadﬁeld, 2010; Harrison, 2014, 2015).”
A brief introduction to mixed effects modelling and multi-model inference in ecology (2018, methodology): “In this case, the variance estimate will either collapse to zero, making the model equivalent to an ordinary GLM (Gelman & Hill 2007 p. 275) or be non-zero but incorrect if the small number of groups that were sampled are not representative of true distribution of means (Harrison 2015).”
The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded (2016, neutral): “Here, overdispersion 84 represents the excess variation relative to what is expected from a certain distribution and can be 85 estimated by fitting an observation-level random effect (OLRE; see, [12, 13]).”