Gradient test to assess homogeneity of probabilities in discrete-time transition models with application in agricultural science data

Longitudinal studies in discrete or continuous time involving categorical data are common in agricultural sciences. Transition models can be used as a means to analyse the resulting data, especially when the aim is to describe category changes over time, as well as to accommodate covariates due to experimental design. Here we focus on discrete-time models, for which it is critical to assess whether the underlying process is stationary or not. Tests based on likelihood procedures are very useful, and here we propose the Gradient test to assess stationary, or homogeneity of transition probabilities. We carried out simulation studies to evaluate the performance of the proposed test, which indicated a good performance regarding type-I error and power when compared to other classical tests available in the literature. As motivation we present two studies with agricultural data, the first one applied to entomology with nominal responses and the second application refers to the degree of injury in pigs. Using our proposed test, stationarity and non-stationarity were verified respectively in the applications. Since the gradient test to assess stationarity has a simplified structure when compared to other tests, it is therefore a useful alternative when carrying out inference in these types of models.