Ordinal panel data are commonly analyzed by population-averaged or subject-specific approaches, which model the dependence of the outcome on the covariates that are observed at the same time. These approaches, although appropriate for assessing current covariates effect, can not be applied without loss of covariates information to the situation where covariates history is available. To use complete covariates information, we alternatively consider an approach which assumes a continuous time model underlying the ordinal panel data. The local equilibrium distribution (LED) model of Kosorok and Char [J. American Statist. Assoc. (1996):807-817] is chosen for our purpose because of its potential of capturing both the long term and short term covariates effects. A recurrence relation for parameter estimation in this model is developed to reduce the computational burden caused by possibly frequent covariates changes. Real data analysis and comparison analysis are performed to illustrate the utility of these LED models.