Doğrusal karma modellerde farklı algoritmaların uygulanması: TIMSS ile örnek olaylar

Mixed models are frequently used in longitudinal data types with time repetition over the same subject and clustered data types formed by observations gathered around certain groups. The modeling technique which models the dependency structure between repetitions and observations in the same cluster is required to use algorithms for parameter estimations. The same model can be solved with various algorithms arising from setup, inference and approach differences. In this study, several algorithms used for LMM, their development process and depending on what differences and similarities they can be resolved are explained with a data set related to an area that can contribute to society. In this sense, one of the sciences in which mixed models find application is education. The Trends in International Mathematics and Science Study (TIMSS) collects the most comprehensive and reliable information in the field of education internationally, and it is carried out every four years in 70 countries. With this data, several tests are prepared and applied to measure the success of students in science and mathematics in different countries, and demographic information about school, teacher, family and student is systematically collected with questionnaires that measure students' perspectives on lessons or parents' perspectives on schools. These results, beyond being a guide for policy makers, can also guide the steps that countries will take in these areas. In this study where a multi-layered approach is preferred, the variables that are effective in students' mathematics achievement are determined as the student's gender, birth status in Turkey, emotional thinking, mathematical tendency, socioeconomic status, and family's thoughts about school. In addition, while many parameters give the same value in the algorithm comparison results; the fast algorithm is faster than the ecme algorithm. In terms of model setup, while lme and lmer functions are easy to implement and similar to each other; there are some differences in ecmeml, fastml and fastmcmc algorithms. The analysis is implemented solely with Turkey and then with England and South Africa for comparisons. While the same variables are statistically significant for all countries, LMM proves the superiority of England over others in math score when all situations are constant.