Using information criteria to select the correct variance–covariance structure for longitudinal data in ecology

Abstract

1. Ecological data sets often use clustered measurements 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 describes the degree of similarity among the
repeated observations.
2. Three methods for choosing the covariance are: the Akaike
information criterion (AIC), the quasi-information criterion (QIC),
and the deviance information criterion (DIC). We compared the
methods using a simulation study and using a data set that explored
effects of forest fragmentation on avian species richness over 15 years.
3. The overall success was 80.6% for the AIC, 29.4% for the QIC
and 81.6% for the DIC. For the forest fragmentation study the AIC
and DIC selected the unstructured covariance, whereas the QIC
selected the simpler autoregressive covariance. Graphical diagnostics
suggested that the unstructured covariance was probably correct.
4. We recommend using DIC for selecting the correct covariance
structure.