| | | |

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

#### Nihan Potas [1] , Cemal Atakan [2]

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.

Contingency tables, Markov Chain, Log-Linear Analysis, Multinomial Distrubution
• 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.
Primary Language en Mathematics August 2019 Research Articles Orcid: 0000-0002-0393-3135Author: Nihan Potas (Primary Author)Institution: ANKARA HACI BAYRAM VELI UNIVERSITY, FACULTY OF ECONOMICS AND ADMINISTRATIVE SCIENCES, DEPARTMENT OF HEALTH MANAGEMENTCountry: Turkey Orcid: 0000-0001-6943-1675Author: Cemal AtakanInstitution: ANKARA UNIVERSITY, FACULTY OF SCIENCE, DEPARTMENT OF STATISTICSCountry: Turkey Application Date : November 1, 2018 Acceptance Date : December 27, 2018 Publication Date : August 1, 2019
 Bibtex @research article { saufenbilder477181, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {}, publisher = {Sakarya University}, year = {2019}, volume = {23}, pages = {532 - 540}, doi = {10.16984/saufenbilder.477181}, title = {Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application}, key = {cite}, author = {Potas, Nihan and Atakan, Cemal} } APA Potas, N , Atakan, C . (2019). Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application. Sakarya University Journal of Science , 23 (4) , 532-540 . DOI: 10.16984/saufenbilder.477181 MLA Potas, N , Atakan, C . "Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application". Sakarya University Journal of Science 23 (2019 ): 532-540 Chicago Potas, N , Atakan, C . "Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application". Sakarya University Journal of Science 23 (2019 ): 532-540 RIS TY - JOUR T1 - Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application AU - Nihan Potas , Cemal Atakan Y1 - 2019 PY - 2019 N1 - doi: 10.16984/saufenbilder.477181 DO - 10.16984/saufenbilder.477181 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 532 EP - 540 VL - 23 IS - 4 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.477181 UR - https://doi.org/10.16984/saufenbilder.477181 Y2 - 2018 ER - EndNote %0 Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application %A Nihan Potas , Cemal Atakan %T Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application %D 2019 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 23 %N 4 %R doi: 10.16984/saufenbilder.477181 %U 10.16984/saufenbilder.477181 ISNAD Potas, Nihan , Atakan, Cemal . "Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application". Sakarya University Journal of Science 23 / 4 (August 2019): 532-540 . https://doi.org/10.16984/saufenbilder.477181 AMA Potas N , Atakan C . Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application. SAUJS. 2019; 23(4): 532-540. Vancouver Potas N , Atakan C . Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application. Sakarya University Journal of Science. 2019; 23(4): 540-532.