Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application

In this study, the use of the Markov chain to measure the change in time-dependent transitions is emphasized. Contingency tables were used to measure the time-dependent change of categorical data. Theoretically how to apply the Markov chain in the log-linear model with the help of one-step or higher-step transition matrices was demonstrated. In addition, the stationarity approach and the assessment of the order of the chain were given as the assumption of the model. In the real data application, 1217 undergraduate students, studying in Faculty of Political Science, Engineering, Science departments of Ankara University, were used. It was taken their cumulative average grades for 4 years, average grades for 8 semesters, beginning in the academic year 2013-2014.Whether the change in the success of the students is measurable in 8 semesters and 4 years, has been investigated. According to the results, before making any prediction: it concluded that one-step transition probabilities are not stationary and the three-step transition matrix is the second-order Markov Chain.

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A. Agresti, Categorical Data Analysis, Third Edition. John Wiley&Sons, Inc., Hoboken, New Jersey, 2012.

T.W. Anderson, Probability Model For Analyzing Time Changes in Attitudes.ss.17-66. P.F. Lazarsfeld, ed. 1954. In Mathematical Thinking in Social Science, Glencoe, III., The Free Pres., 1954.

T.W. Anderson, L. A., Goodman, Statistical Inference about Markov Chains. Ann. Math. Statistics, 28, 89-110, 1957.

M. M. Y. Bishop, E. S. Fienberg, W. P. Holland, Discrete Multivariate Analysis Theory and Practice. Springer, New York, 1974.

R. R. Bush, F. Mosteller, Stochastic Models for Learning. John Wiley&Sons, Inc., Hoboken, New Jersey, 1955.

F. Eskandar, M. R. Meslikani, Empirical Bayes analysis of log-linear models for a generalized finite stationary Markov chain. Metrika, 59, 173- 191, 2004.

L. A. Goodman, Statistical Methods for Analyzing Processes of Change. Amer. J. Sociol., 68, 57-78, 1962.

J. Hu, A. Joshi, V.E. Johnson, Log-Linear Models for Gene Association. J. Am. Stat Assoc., 104(486),597-607, 2009.

D. Knoke, P. J. Burke, Log-Linear Models. Sage Publications, Newbury Park, CA, 1980.

A. Madansky, Test of Homogeneity for Correlated Samples. Jour. American Statist. Assoc., 58, 97-119, 1963.

J. K. Vermunt, Log-linear Models for Event Histories., Sage, Thousand Oaks, CA, 1997.

A. von Eye, C. Spiel, Standart and nonstandard Log-Linear Symmetry Models for Measuring Change in Categorical Variables, The American Statistician, 50(4), 300-305, 1996.