Logistic regression models for transition probabilities of higher order Markov models are developed for the sequence of chain dependent repeated observations. To identify the significance of these models and their parameters a test procedure for a likelihood ratio criterion is developed. A method of model selection is suggested on the basis of AIC and BIC procedures. The proposed models and test procedures are applied to analyze the occurrences of daily rainfall data for selected stations in Bangladesh. Based on results from these models, the transition probabilities of first order Markov model for temperature and humidity provided the most suitable option to model forecasts for daily rainfall occurrences for five selected stations in Bangladesh.