Transition models are an important framework that can be used to model longitudinal categorical data. They are particularly useful when the primary interest is in prediction. The available methods for this class of models are suitable for the cases in which responses are recorded individually over time. However, in many areas, it is common for categorical data to be recorded as groups, that is, different categories with a number of individuals in each. As motivation we consider a study in insect movement and another in pig behaviou. The first study was developed to understand the movement patterns of female adults of Diaphorina citri, a pest of citrus plantations. The second study investigated how hogs behaved under the influence of environmental enrichment. In both studies, the number of individuals in different response categories was observed over time. We propose a new framework for considering the time dependence in the linear predictor of a generalized logit transition model using a quantitative response, corresponding to the number of individuals in each category. We use maximum likelihood estimation and present the results of the fitted models under stationarity and non-stationarity assumptions, and use recently proposed tests to assess non-stationarity. We evaluated the performance of the proposed model using simulation studies under different scenarios, and concluded that our modeling framework represents a flexible alternative to analyze grouped longitudinal categorical data.

中文翻译：

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分组纵向分类数据的广义转换模型

转换模型是一个重要的框架，可用于对纵向分类数据进行建模。当主要兴趣在于预测时，它们特别有用。此类模型的可用方法适用于随着时间的推移单独记录响应的情况。然而，在许多领域，分类数据通常被记录为组，即不同的类别，每个类别中有多个个体。作为动机，我们考虑一项关于昆虫运动的研究和另一项关于猪行为的研究。第一项研究是为了了解柑橘园害虫柑橘木虱雌性成虫的运动模式。第二项研究调查了猪在环境丰富化的影响下的行为。在这两项研究中，随着时间的推移，观察了不同反应类别的个体数量。我们提出了一个新的框架，用于考虑广义 Logit 转换模型的线性预测器中的时间依赖性，该模型使用定量响应，对应于每个类别中的个体数量。我们使用最大似然估计并呈现平稳性和非平稳性假设下拟合模型的结果，并使用最近提出的检验来评估非平稳性。我们使用不同场景下的模拟研究评估了所提出模型的性能，并得出结论，我们的建模框架代表了分析分组纵向分类数据的灵活替代方案。