Using observation-level random effects to model overdispersion in count data in ecology and evolution

PeerJ. 2014 Oct 9;2:e616. doi: 10.7717/peerj.616. eCollection 2014.

Abstract

Overdispersion is common in models of count data in ecology and evolutionary biology, and can occur due to missing covariates, non-independent (aggregated) data, or an excess frequency of zeroes (zero-inflation). Accounting for overdispersion in such models is vital, as failing to do so can lead to biased parameter estimates, and false conclusions regarding hypotheses of interest. Observation-level random effects (OLRE), where each data point receives a unique level of a random effect that models the extra-Poisson variation present in the data, are commonly employed to cope with overdispersion in count data. However studies investigating the efficacy of observation-level random effects as a means to deal with overdispersion are scarce. Here I use simulations to show that in cases where overdispersion is caused by random extra-Poisson noise, or aggregation in the count data, observation-level random effects yield more accurate parameter estimates compared to when overdispersion is simply ignored. Conversely, OLRE fail to reduce bias in zero-inflated data, and in some cases increase bias at high levels of overdispersion. There was a positive relationship between the magnitude of overdispersion and the degree of bias in parameter estimates. Critically, the simulations reveal that failing to account for overdispersion in mixed models can erroneously inflate measures of explained variance (r (2)), which may lead to researchers overestimating the predictive power of variables of interest. This work suggests use of observation-level random effects provides a simple and robust means to account for overdispersion in count data, but also that their ability to minimise bias is not uniform across all types of overdispersion and must be applied judiciously.

Keywords: Explained variance; Generalized linear mixed models; Observation-level random effect; Poisson-lognormal models; Quasi-Poisson; r-squared.

Grant support

This work was supported by a Research Fellowship awarded to XH by the Zoological Society of London and a British Ecological Society Research Grant awarded to XH. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.