A hitchhiker's guide to mixed models for randomized experiments

Designed experiments conducted by crop scientists often give rise to several random sources of variation. Pertinent examples are split-plot designs, series of experiments and repeated measurements taken on the same field plot. Data arising from such experiments may be conveniently analysed by mixed models. While the mixed model framework is by now very well developed theoretically, and good software is readily available, the technology is still under-utilized. The purpose of the present paper is, therefore, to encourage more widespread use of mixed models. We outline basic principles, which help in setting up mixed models appropriate in a given situation, the main task required from users of mixed model software. Several examples are considered to demonstrate key issues. The theoretical underpinnings are briefly sketched in so far as they are practically relevant for making informed use of mixed-model computer packages. Finally, a brief review is given of some recent methodological developments, which are of interest to the plant sciences. A German version of this paper is available from the corresponding author upon request.