Bayesian Ordinal Analysis of Cereal Growth Stage Data from Oat Trials in Western Australia

Growth stage in cereal field trials is usually scored on the Zadoks decimal scale. The score is ordinal, yet it is often analysed as if it were continuous, which can lead to misleading conclusions. Ordinal analysis of growth stage data has received little attention from biometricians or agronomists, and it is not straightforward when several plants are scored in each plot of a split-plot design. We analysed Zadoks scores recorded four weeks after sowing on ten plants per plot in two deep-sowing oat trials in Western Australia, using a Bayesian hierarchical ordinal model that carries the full split-plot structure and an AR1 x AR1 spatial covariance. The implementation was validated on simulated data, and the candidate models were compared by five-fold cross-validation over plots. Adding a random effect at the experimental-unit (plot) level changed the uncertainty of the sub-plot contrasts substantially, while the main-plot contrasts changed little. How that plot-level heterogeneity was modelled mattered much less. At either site, cross-validation could not separate the candidate models that carried a plot-level term, whether or not they included an AR1 x AR1 field or the blocking terms, and the autoregressive parameters were only weakly identified on this layout. Deeper sowing (80 and 120 mm against 30 mm) went with more advanced development at four weeks in both trials. Sowing at 120 mm rather than 30 mm raised the predicted probability of tillering from 0.04 to 0.24 at Wickepin and from 0.04 to 0.10 at Merredin. The depth effects were stable whether or not the spatial field was fitted, and under both the cumulative and the sequential ordinal family.