TY  - JOUR
T1  - Measuring the Change by Using Markov Chain Approach in Time-Dependent Transitions and a Real Data Application
AU  - Potas, Nihan
AU  - Atakan, Cemal
PY  - 2019
DA  - August
Y2  - 2018
DO  - 10.16984/saufenbilder.477181
JF  - Sakarya University Journal of Science
JO  - SAUJS
PB  - Sakarya University
WT  - DergiPark
SN  - 2147-835X
SP  - 532
EP  - 540
VL  - 23
IS  - 4
LA  - en
AB  - In this study, the use of the Markov chain to measure the change intime-dependent transitions is emphasized. Contingency tables were used tomeasure the time-dependent change of categorical data. Theoretically how toapply the Markov chain in the log-linear model with the help of one-step orhigher-step transition matrices was demonstrated. In addition, the stationarityapproach and the assessment of the order of the chain were given as theassumption of the model. In the real data application, 1217 undergraduatestudents, studying in Faculty of Political Science, Engineering, Sciencedepartments of Ankara University, were used. It was taken their cumulativeaverage grades for 4 years, average grades for 8 semesters, beginning in theacademic year 2013-2014.Whether the change in the success of the students ismeasurable in 8 semesters and 4 years, has been investigated. According to theresults, before making any prediction: it concluded that one-step transitionprobabilities are not stationary and the three-step transition matrix is thesecond-order Markov Chain.
KW  - Contingency tables
KW  - Markov Chain
KW  - Log-Linear Analysis
KW  - Multinomial Distrubution
CR  - A. Agresti, Categorical Data Analysis, Third Edition. John Wiley&Sons, Inc., Hoboken, New Jersey, 2012.
CR  - 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.
CR  - T.W. Anderson, L. A., Goodman, Statistical Inference about Markov Chains. Ann. Math. Statistics, 28, 89-110, 1957.
CR  - M. M. Y. Bishop, E. S. Fienberg, W. P. Holland, Discrete Multivariate Analysis Theory and Practice. Springer, New York, 1974.
CR  - R. R. Bush, F. Mosteller, Stochastic Models for Learning. John Wiley&Sons, Inc., Hoboken, New Jersey, 1955.
CR  - F. Eskandar, M. R. Meslikani, Empirical Bayes analysis of log-linear models for a generalized finite stationary Markov chain. Metrika, 59, 173-191, 2004.
CR  - L. A. Goodman, Statistical Methods for Analyzing Processes of Change. Amer. J. Sociol., 68, 57-78, 1962.
CR  - A. Madansky, Test of Homogeneity for   Correlated Samples. Jour. American Statist. Assoc., 58, 97-119, 1963.
CR  - J. K. Vermunt, Log-linear Models for Event Histories., Sage, Thousand Oaks, CA, 1997.
CR  - 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.
UR  - https://doi.org/10.16984/saufenbilder.477181
L1  - https://dergipark.org.tr/en/download/article-file/649082
ER  -