A proportional odds transition model for ordinal responses with an application to pig behaviour

Categorical data are quite common in many fields of science including in behaviour studies in animal science. In this article, the data concern the degree of lesions in pigs, related to the behaviour of these animals. The experimental design corresponded to two levels of environmental enrichment and four levels of genetic lineages in a completely randomized $ 2 \times 4 $ 2×4 factorial with data collected longitudinally over four time occasions. The transition models used for the data analysis are based on stochastic processes and Generalized Linear Models. In general, these are not used for analysis of longitudinal data but they are useful in many situations as in this study. We present some aspects of this class of models for the stationary case. The proportional odds transition model is used to construct the matrix of transition probabilities and a function was developed in the R system to fit this model. The likelihood ratio test was used to verify the assumption of odds ratio proportionality and to select the structure of the linear predictor. The methodology used allowed for the choice of a model that can be used to explain the relationship between the severity of lesions in pigs and the use of the environmental enrichment.