Intensive longitudinal (IL) data are increasingly prevalent in psychological science, coinciding with technological advancements that make it simple to deploy study designs such as daily diary and ecological momentary assessments. IL data are characterized by a rapid rate of data collection (1+ collections per day), over a period of time, allowing for the capture of the dynamics that underlie psychological and behavioral processes. One powerful framework for analyzing IL data is state-space modeling, where observed variables are considered measurements for underlying states (i.e., latent variables) that change together over time. However, state-space modeling has typically relied on continuous measurements, whereas psychological data often comes in the form of ordinal measurements such as Likert scale items. In this manuscript, we develop a general estimating approach for state-space models with ordinal measurements, specifically focusing on a graded response model for Likert scale items. We evaluate the performance of our model and estimator against that of the commonly used ``linear approximation'' model, which treats ordinal measurements as though they are continuous. We find that our model resulted in unbiased estimates of the state dynamics, while the linear approximation resulted in strongly biased estimates of the state dynamics

翻译：密集纵向数据在心理科学中日益普遍，这得益于技术进步使得日常日记和生态瞬时评估等研究设计易于实施。密集纵向数据以数据采集频率高（每天一次及以上）为特征，在持续时间内能够捕捉心理和行为过程的内在动态。分析密集纵向数据的一个强大框架是状态空间模型，其中观测变量被视为随时间共同变化的潜在状态（即潜变量）的测量。然而，状态空间模型通常依赖于连续测量，而心理数据常以顺序测量的形式出现，例如李克特量表题项。在本文中，我们开发了一种适用于顺序测量的状态空间模型通用估计方法，特别针对李克特量表题项聚焦于等级响应模型。我们评估了该模型及估计器与常用“线性近似”模型（该模型将顺序测量视为连续变量）的性能对比。结果表明，我们的模型能无偏估计状态动态，而线性近似则导致状态动态估计的严重偏倚。