A hurdle model for ordinal scoring data with an underlying percentage scale

Abstract It is crucial to properly evaluate the traits that directly impact agricultural productivity. Some of these traits, such as soil erosion or crop diseases, are quantified with scoring systems. The resulting data are strictly ordinal and often have an underlying percentage scale. Deciding which model to use for this type of data is not straightforward. Ordinal scores do not meet the assumptions required for analysis of variance. Although multinomial ordinal models, particularly the threshold model, can be applied, they do not account for the underlying percentage scale of the data. To address this limitation, a hurdle model tailored for interval-censored percentage data is proposed. It is a two-part model that models the data according to their nature: In its first part, it models presence or absence of a disease (incidence), and in the second part it models severity or abundance. Individually modelling presence and absence in the first part allows to account for zero inflation. The second part implements theory from the threshold model and the Johnson S B system of distributions that involves a transformation of the percentage scale to a normal distribution. The model result also reflects the two components. They individually describe the degree of disease infestation, and the degree of disease spread. This improves interpretability and enables concrete, insightful conclusions. To illustrate the model, mildew scorings from an on-farm trial in grapevines were used. The model was found highly suitable for this dataset and superior to the threshold model.