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

Year 2019, Volume: 23 Issue: 4, 532 - 540, 01.08.2019

Nihan Potas , Cemal Atakan

https://doi.org/10.16984/saufenbilder.477181

Abstract

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.

Keywords

Contingency tables, Markov Chain, Log-Linear Analysis, Multinomial Distrubution

References

• 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.
• 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.