Implementation of different algorithms in linear mixed models: case studies with TIMSS

Download

BurcuKoca_MSThesis.pdf

Date

2021-9-06

Author

Koca, Burcu

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

370
views

285
downloads

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.

Subject Keywords

TIMSS, Matematik başarısı, Doğrusal karma model, EM algoritması, Math achievement, Linear mixed model, EM algorithm

URI

https://hdl.handle.net/11511/93031

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Algorithm Overview and Design for Mixed Effects Models Koca, Burcu; Gökalp Yavuz, Fulya (2021-06-06) Linear Mixed Model (LMM) is an extended regression method that is used for longitudinal data which has repeated measures within the individual. It is natural to expect high correlation between these repeats over a period of time for the same individual. Since classical approaches may fail to cover these correlations, LMM handles this significant concern by introducing random effect terms in the model. Besides its flexible structure in terms of modeling, LMM has several application areas such as clinical tri...
Adapting a Robust Model into Hybrid Implementations of Machine Learning Algorithms and Statistical Methods for Longitudinal Data Erduran, İbrahim Hakkı; Gökalp Yavuz, Fulya; Ebegil, Meral; Department of Statistics (2021-9) Data structures in which the same characteristics are measured repeatedly at different time points are counted among the longitudinal data types. These datasets require the use of advanced modeling techniques because of the dependency structure amongst replicates. Linear mixed models (LMM) is an advanced regression method used in the analysis of such data sets. Although the LMM method provides many flexibility and advantages, the model setup is based on a number of assumptions that are challenging to provid...
ON FOUNDATIONS OF PARAMETER ESTIMATION FOR GENERALIZED PARTIAL LINEAR MODELS WITH B-SPLINES AND CONTINUOUS OPTIMIZATION TAYLAN, PAKİZE; Weber, Gerhard Wilhelm; Liu, Lian (2010-02-04) Generalized linear models are widely-used statistical techniques. As an extension, generalized partial linear models utilize semiparametric methods and augment the usual parametric terms by a single nonparametric component of a continuous covariate. In this paper, after a short introduction, we present our model in the generalized additive context with a focus on penalized maximum likelihood and on the penalized iteratively reweighted least squares (P-IRLS) problem based on B-splines which is attractive for...
Integrated nonlinear regression analysis of tracer and well test data Akın, Serhat (Elsevier BV, 2003-08-01) One frequent observation from conventional pressure transient test analysis is that field data match mathematical models derived for homogeneous systems. This observation suggests that pressure data as presently interpreted may not contain details concerning certain reservoir heterogeneities. On the other hand, tracer tests may be more sensitive to heterogeneous elements present in the reservoir because of the convective nature of the flow test. In this study, a possible improvement of conventional pressure...
Representation of Multiplicative Seasonal Vector Autoregressive Moving Average Models Yozgatlıgil, Ceylan (Informa UK Limited, 2009-11-01) Time series often contain observations of several variables and multivariate time series models are used to represent the relationship between these variables. There are many studies on vector autoregressive moving average (VARMA) models, but the representation of multiplicative seasonal VARMA models has not been seriously studied. In a multiplicative vector model, such as a seasonal VARMA model, the representation is not unique because of the noncommutative property of matrix multiplication. In this articl...

Citation Formats

B. Koca, “Implementation of different algorithms in linear mixed models: case studies with TIMSS,” M.S. - Master of Science, Middle East Technical University, 2021.