Beyond Equidistant Assumptions: An Autoregressive Ordered Stereotype Model for Ordinal Time Series

Abstract

We propose an extension of the ordered stereotype model (OSM) for ordinal time series data, referred to as the Autoregressive OSM (AR-OSM). The model captures serial dependence by incorporating lagged values of the response as covariates in the systematic component. In contrast to existing regression models for ordinal time series, the AR-OSM does not assume equidistant categories, but instead allows the data to determine their relative spacing. This property makes the model particularly suitable for applications where the equidistance assumption is unrealistic. Such a case is illustrated through the analysis of infant sleep state data. Additionally, a comprehensive simulation study is conducted to assess the performance of the model under varying sample sizes and to investigate how parameter values influence the induced serial dependence structure.