المستخلص: |
This study introduces the Mixture Transition Distribution model (MTD) as parsimonious alternative to the Markov model enabling the estimation of high -order markov chains and facilitating the interpretation by providing a much smaller transition matrix and lag parameters. And more, we introduce an iterative algorithm for the estimation of transition matrix for Markovian models. We consider two models derived from the basic homogeneous Markov chain: high- order markov chains and the Mixture Transition Distribution (MTD) model. We compare the estimated markov and MTD models using Bayesian Information Criterion (BIC), choosing the model which minimizes (BIC). The applied area of this study was stages of Chronic Kidney disease, where the stages of Chronic Kidney disease are five stages. The sample of study consists of 126 patients who were treated at Urology and Nephrology Center- Mansoura University, and we assessed renal function by measuring Serum Creatinine every 3 month (visit), calculated GFR and urine albumin which allow early detection of Chronic Kidney disease. Our results are in favor of the MTD model \
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