• accuracy;
  • first-order autocorrelation;
  • generalized linear mixed models;
  • individual heterogeneity;
  • precision;
  • random intercept model


1. Autocorrelation and individual heterogeneity are now considered to reflect biological processes rather than simply being a nuisance requiring to be accounted for. Before using parameter estimates that represent autocorrelation and individual heterogeneity to infer biological processes, a statistical evaluation of their precision and accuracy is required to validate their use.

2. Using simulated data, we evaluated accuracy and precision of temporal autocorrelation and individual heterogeneity estimates provided by different statistical models. We compared estimates across different intensity of individual variation and life histories, and sampling effort. We focused on recurrent binary variables because statistical evaluations of models describing binary processes have often been overlooked although several evolutionary and ecological processes are expressed as binary variables (e.g. probability of annual reproduction, plant annual flowering and detection, seasonal migration decision).

3. Our results showed that autocorrelation and individual heterogeneity were generally better estimated using a ‘time series’ modelling approach, but that a ‘state dependence’ modelling approach also provided fair estimates in most cases. The latter method was even more robust when data sets included missing values. Data sets including missing values or consisting of very short times series resulted in important bias in some instances.

4. Models ignoring either individual heterogeneity or autocorrelation performed poorly, illustrating the fundamental association between these two processes, and demonstrating that the complex structure of autocorrelation and individual heterogeneity patterns is difficult to tackle using simple models.

5. Our work’s major finding is the demonstration that autocorrelation and individual heterogeneity need to be both accounted for to provide reliable estimates even in studies focusing on only one of these processes. Our study also offers a set of practical recommendations for helping researchers modelling these two processes depending on their scientific aims and the structure of their data. Finally, our results illustrate that more research is required for estimating individual heterogeneity when positive temporal autocorrelation is expected because none of the models evaluated provided suitable estimates.