Selecting the correct variance–covariance structure for longitudinal data in ecology: a comparison of the Akaike, quasi-information and deviance information criteria

Ecological data sets often use clustered sampling, or use repeated sampling in a longitudinal design. Choosing the correct covariance structure is an important step in the analysis of such data, as the covariance dictates the degree of similarity among repeated observations. Three methods for choosing the covariance are: Akaike’s information criterion (AIC), the quasi-information criterion (QIC), and the deviance information criterion (DIC). We first compared the methods using a simulation study. The overall success was 81.6% for the DIC, 80.6% for the AIC, and 29.4% for the QIC. We then compared the methods using an empirical data set that explored effects of forest fragmentation on avian species richness over 15 years. The AIC and DIC selected the unstructured covariance, whereas the QIC selected a simpler model. Graphical diagnostics suggested that the unstructured covariance was probably correct. We recommend using either the AIC or DIC for estimating the correct covariance structure. keywords covariance structure; longitudinal data; correlated data; information criteria; generalized estimating equation; Bayesian methods