Students’ performance in mathematics has been an issue of great concern to most countries,
especially the developing nations. So many programmes have been put in place to improve performances and to
also encourage student to study the course in tertiary institution. In this study we investigate the relationship of
semester, department of a student, age and load unit on marginal mathematics performance o f undergraduate
students. A marginal model was formulated using four working correlation structure where the exchangeable
working correlation structure was selected as the best that models the dataset using quasi information criteria.
The semester, age and load unit were found to be related to the marginal performance in mathematics
An investigation of_factors_influencing_student_use_of_technology_in_k-12_cla...Cathy Cavanaugh
The purpose of this research was to examine the effects of teachers’ characteristics,
school characteristics, and contextual characteristics on classroom
technology integration and teacher use of technology as mediators of student
use of technology. A research-based path model was designed and tested
based on data gathered from 732 teachers from 17 school districts and 107
different schools in the state of Florida. Results show that a teacher’s level
of education and experience teaching with technology positively and significantly
influence his/her use of technology. Teacher use of technology
strongly and positively explains classroom technology integration and
student use of technology. Further, how a teacher integrates technology
into the classroom explains how frequently students use technology in a
school setting. The findings provided significant evidence that the path
model is useful in explaining factors affecting student use of technology
and the relationships among the factors.
Clustering analysis of learning style on anggana high school studentTELKOMNIKA JOURNAL
The inability of students to absorb the knowledge conveyed by the teacher is’nt caused by the inability of understanding and by the teacher which isn’t able to teach too, but because of the mismatch of learning styles between students and teachers, so that students feel uncomfortable in learning to a particular teacher. It also happens in senior high school (SHS/SMAN) 1 Anggana, so it is necessary to do this research, to analyze cluster (group) of student learning style by applying data mining method that is k-Means and Fuzzy C-Means. The purpose was to know the effectiveness of this learning style cluster on the development of absorptive power and improving student achievement. The method used to cluster the learning style with data mining process starts from the data cleaning stage, data selection, data transformation, data mining, pattern evolution, and knowledge development.
An investigation of_factors_influencing_student_use_of_technology_in_k-12_cla...Cathy Cavanaugh
The purpose of this research was to examine the effects of teachers’ characteristics,
school characteristics, and contextual characteristics on classroom
technology integration and teacher use of technology as mediators of student
use of technology. A research-based path model was designed and tested
based on data gathered from 732 teachers from 17 school districts and 107
different schools in the state of Florida. Results show that a teacher’s level
of education and experience teaching with technology positively and significantly
influence his/her use of technology. Teacher use of technology
strongly and positively explains classroom technology integration and
student use of technology. Further, how a teacher integrates technology
into the classroom explains how frequently students use technology in a
school setting. The findings provided significant evidence that the path
model is useful in explaining factors affecting student use of technology
and the relationships among the factors.
Clustering analysis of learning style on anggana high school studentTELKOMNIKA JOURNAL
The inability of students to absorb the knowledge conveyed by the teacher is’nt caused by the inability of understanding and by the teacher which isn’t able to teach too, but because of the mismatch of learning styles between students and teachers, so that students feel uncomfortable in learning to a particular teacher. It also happens in senior high school (SHS/SMAN) 1 Anggana, so it is necessary to do this research, to analyze cluster (group) of student learning style by applying data mining method that is k-Means and Fuzzy C-Means. The purpose was to know the effectiveness of this learning style cluster on the development of absorptive power and improving student achievement. The method used to cluster the learning style with data mining process starts from the data cleaning stage, data selection, data transformation, data mining, pattern evolution, and knowledge development.
International Journal of Humanities and Social Science Invention (IJHSSI)inventionjournals
International Journal of Humanities and Social Science Invention (IJHSSI) is an international journal intended for professionals and researchers in all fields of Humanities and Social Science. IJHSSI publishes research articles and reviews within the whole field Humanities and Social Science, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
The purpose of this research is to develop test questions of problem solving ability on work-energy material for high school students class X. This type of research is research and development. The model used in this study is ADDIE with the stages of analyzing, planning, developing, implementing, and evaluating, but this study only up to the implementation stage. The test developed in this research consists of three items of problem solving ability description that is multi context. Validation of item was done by content validation and empirical validation. The results of content validation indicate that the average score of test items is 3,125 with good category. The results of empirical validation indicate that there are two valid questions and one invalid question. Two valid questions have a Cronbach Alpha coefficient of 0.807. The results of the implementation of the test showed that the average student problem solving abilities in Question 1 is 17.41 of a maximum score of 25, the lowest score is 10 and the highest is 23. The results of students in the question number 2 by 16.60 of a maximum score of 25, with the lowest score is 10 and the highest is 22. These results indicate that the test instrument is feasible to use to assess students' problem solving abilities.
RESEARCH TRENDS İN EDUCATIONAL TECHNOLOGY İN TURKEY: 2010-2018 YEAR THESIS AN...ijcax
The purpose of this research is the analysis using meta-analysis of studies in the field of Educational
Technology in Turkey and in the field is to demonstrate how to get to that trend. For this purpose, a total of
263 studies were analyzed including 98 theses and 165 articles published between 2010-2018. Purpose
sampling method was used when selecting publications. In the research, while selecting articles and theses;
Turkey addressed; YOK Tez Tarama Database, Journal of Hacettepe University Faculty of Education,
Educational Sciences : Theory & Practice Journal, Education and Science Journal, Elementary Education
Online Journal, The Turkish Online Journal of Education and The Turkish Online Journal of Educational
Technology used in journals. Publications have been reviewed under 11 criteria. Index, year of
publication, research scope, method, education level, sample, number of samples, data collection methods,
analysis techniques, and research tendency, research topics in Educational Technology Research in Turkey
has revealed. The data is interpreted based on percentage and frequency and the results are shown using
the table.
This study was a survey conducted to determine the influence of stake holders on student career choice particularly amongst undergraduate students in school of science education Federal College of Education, (Technical) Bichi Kano.
A Model for Predicting Students’ Academic Performance using a Hybrid of K-mea...Editor IJCATR
Higher learning institutions nowadays operate in a more complex and competitive due to a high demand from prospective
students and an emerging increase of universities both public and private. Management of Universities face challenges and concerns of
predicting students’ academic performance in to put mechanisms in place prior enough for their improvement. This research aims at
employing Decision tree and K-means data mining algorithms to model an approach to predict the performance of students in advance
so as to devise mechanisms of alleviating student dropout rates and improve on performance. In Kenya for example, there has been
witnessed an increase student enrolling in universities since the Government started free primary education. Therefore the Government
expects an increased workforce of professionals from these institutions without compromising quality so as to achieve its millennium
development and vision 2030. Backlog of students not finishing their studies in stipulated time due to poor performance is another
issue that can be addressed from the results of this research since predicting student performance in advance will enable University
management to devise ways of assisting weak students and even make more decisions on how to select students for particular courses.
Previous studies have been done Educational Data Mining mostly focusing on factors affecting students’ performance and also used
different algorithms in predicting students’ performance. In all these researches, accuracy of prediction is key and what researchers
look forward to try and improve.
Predicting Success : An Application of Data Mining Techniques to Student Outc...IJDKP
This project examines the effectiveness of applying machine learning techniques to the realm of college
student success, specifically with the intent of discovering and identifying those student characteristics and
factors that show the strongest predictive capability with regards to successful graduation. The student
data examined consists of first time freshmen and transfer students who matriculated at California State
University San Marcos in the period of Fall 2000 through Fall 2010 and who either graduated successfully
or discontinued their education. Operating on over 30,000 student observations, random forests are used
to determine the relative importance of the student characteristics with genetic algorithms to perform
feature selection and pruning. To improve the machine learning algorithm cross validated hyperparameter
tuning was also implemented. Overall predictive strength is relatively high as measured by the
Matthews Correlation Coefficient, and both intuitive and novel features which provide support for the
learning model are explored.
PREDICTING ACADEMIC MAJOR OF STUDENTS USING BAYESIAN NETWORKS TO THE CASE OF ...ijcax
In this study, which took place current year in the city of Maragheh in IRAN. Number of high school students in the fields of study: mathematics, Experimental Sciences, humanities, vocational, business and science were studied and compared. The purpose of this research is to predict the academic major of high school students using Bayesian networks. The effective factors have been used in academic major selection for the first time as an effective indicator of Bayesian networks. Evaluation of Impacts of indicators on each other, discretization data and processing them was performed by GeNIe. The proper course would be advised for students to continue their education.
Data Mining Application in Advertisement Management of Higher Educational Ins...ijcax
In recent years, Indian higher educational institute’s competition grows rapidly for attracting students to get enrollment in their institutes. To attract students educational institutes select a best advertisement method. There are different advertisements available in the market but a selection of them is very difficult
for institutes. This paper is helpful for institutes to select a best advertisement medium using some data mining methods.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Fuzzy Association Rule Mining based Model to Predict Students’ Performance IJECEIAES
The major intention of higher education institutions is to supply quality education to its students. One approach to get maximum level of quality in higher education system is by discovering knowledge for prediction regarding the internal assessment and end semester examination. The projected work intends to approach this objective by taking the advantage of fuzzy inference technique to classify student scores data according to the level of their performance. In this paper, student’s performance is evaluated using fuzzy association rule mining that describes Prediction of performance of the students at the end of the semester, on the basis of previous database like Attendance, Midsem Marks, Previous semester marks and Previous Academic Records were collected from the student’s previous database, to identify those students which needed individual attention to decrease fail ration and taking suitable action for the next semester examination.
This study was conducted in an undergraduate level
with the use of e-learning
particularly in analytic geometry to lessen the com
mon fear of Filipino students to
mathematics. Since teen age students used to engros
s themselves with the use of
technology specifically computers, this study maxim
ized the capability of computers
in reducing math anxiety by teaching mathematics su
bject using e-learning thus
improving student academic performance.
International Journal of Humanities and Social Science Invention (IJHSSI)inventionjournals
International Journal of Humanities and Social Science Invention (IJHSSI) is an international journal intended for professionals and researchers in all fields of Humanities and Social Science. IJHSSI publishes research articles and reviews within the whole field Humanities and Social Science, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
The purpose of this research is to develop test questions of problem solving ability on work-energy material for high school students class X. This type of research is research and development. The model used in this study is ADDIE with the stages of analyzing, planning, developing, implementing, and evaluating, but this study only up to the implementation stage. The test developed in this research consists of three items of problem solving ability description that is multi context. Validation of item was done by content validation and empirical validation. The results of content validation indicate that the average score of test items is 3,125 with good category. The results of empirical validation indicate that there are two valid questions and one invalid question. Two valid questions have a Cronbach Alpha coefficient of 0.807. The results of the implementation of the test showed that the average student problem solving abilities in Question 1 is 17.41 of a maximum score of 25, the lowest score is 10 and the highest is 23. The results of students in the question number 2 by 16.60 of a maximum score of 25, with the lowest score is 10 and the highest is 22. These results indicate that the test instrument is feasible to use to assess students' problem solving abilities.
RESEARCH TRENDS İN EDUCATIONAL TECHNOLOGY İN TURKEY: 2010-2018 YEAR THESIS AN...ijcax
The purpose of this research is the analysis using meta-analysis of studies in the field of Educational
Technology in Turkey and in the field is to demonstrate how to get to that trend. For this purpose, a total of
263 studies were analyzed including 98 theses and 165 articles published between 2010-2018. Purpose
sampling method was used when selecting publications. In the research, while selecting articles and theses;
Turkey addressed; YOK Tez Tarama Database, Journal of Hacettepe University Faculty of Education,
Educational Sciences : Theory & Practice Journal, Education and Science Journal, Elementary Education
Online Journal, The Turkish Online Journal of Education and The Turkish Online Journal of Educational
Technology used in journals. Publications have been reviewed under 11 criteria. Index, year of
publication, research scope, method, education level, sample, number of samples, data collection methods,
analysis techniques, and research tendency, research topics in Educational Technology Research in Turkey
has revealed. The data is interpreted based on percentage and frequency and the results are shown using
the table.
This study was a survey conducted to determine the influence of stake holders on student career choice particularly amongst undergraduate students in school of science education Federal College of Education, (Technical) Bichi Kano.
A Model for Predicting Students’ Academic Performance using a Hybrid of K-mea...Editor IJCATR
Higher learning institutions nowadays operate in a more complex and competitive due to a high demand from prospective
students and an emerging increase of universities both public and private. Management of Universities face challenges and concerns of
predicting students’ academic performance in to put mechanisms in place prior enough for their improvement. This research aims at
employing Decision tree and K-means data mining algorithms to model an approach to predict the performance of students in advance
so as to devise mechanisms of alleviating student dropout rates and improve on performance. In Kenya for example, there has been
witnessed an increase student enrolling in universities since the Government started free primary education. Therefore the Government
expects an increased workforce of professionals from these institutions without compromising quality so as to achieve its millennium
development and vision 2030. Backlog of students not finishing their studies in stipulated time due to poor performance is another
issue that can be addressed from the results of this research since predicting student performance in advance will enable University
management to devise ways of assisting weak students and even make more decisions on how to select students for particular courses.
Previous studies have been done Educational Data Mining mostly focusing on factors affecting students’ performance and also used
different algorithms in predicting students’ performance. In all these researches, accuracy of prediction is key and what researchers
look forward to try and improve.
Predicting Success : An Application of Data Mining Techniques to Student Outc...IJDKP
This project examines the effectiveness of applying machine learning techniques to the realm of college
student success, specifically with the intent of discovering and identifying those student characteristics and
factors that show the strongest predictive capability with regards to successful graduation. The student
data examined consists of first time freshmen and transfer students who matriculated at California State
University San Marcos in the period of Fall 2000 through Fall 2010 and who either graduated successfully
or discontinued their education. Operating on over 30,000 student observations, random forests are used
to determine the relative importance of the student characteristics with genetic algorithms to perform
feature selection and pruning. To improve the machine learning algorithm cross validated hyperparameter
tuning was also implemented. Overall predictive strength is relatively high as measured by the
Matthews Correlation Coefficient, and both intuitive and novel features which provide support for the
learning model are explored.
PREDICTING ACADEMIC MAJOR OF STUDENTS USING BAYESIAN NETWORKS TO THE CASE OF ...ijcax
In this study, which took place current year in the city of Maragheh in IRAN. Number of high school students in the fields of study: mathematics, Experimental Sciences, humanities, vocational, business and science were studied and compared. The purpose of this research is to predict the academic major of high school students using Bayesian networks. The effective factors have been used in academic major selection for the first time as an effective indicator of Bayesian networks. Evaluation of Impacts of indicators on each other, discretization data and processing them was performed by GeNIe. The proper course would be advised for students to continue their education.
Data Mining Application in Advertisement Management of Higher Educational Ins...ijcax
In recent years, Indian higher educational institute’s competition grows rapidly for attracting students to get enrollment in their institutes. To attract students educational institutes select a best advertisement method. There are different advertisements available in the market but a selection of them is very difficult
for institutes. This paper is helpful for institutes to select a best advertisement medium using some data mining methods.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Fuzzy Association Rule Mining based Model to Predict Students’ Performance IJECEIAES
The major intention of higher education institutions is to supply quality education to its students. One approach to get maximum level of quality in higher education system is by discovering knowledge for prediction regarding the internal assessment and end semester examination. The projected work intends to approach this objective by taking the advantage of fuzzy inference technique to classify student scores data according to the level of their performance. In this paper, student’s performance is evaluated using fuzzy association rule mining that describes Prediction of performance of the students at the end of the semester, on the basis of previous database like Attendance, Midsem Marks, Previous semester marks and Previous Academic Records were collected from the student’s previous database, to identify those students which needed individual attention to decrease fail ration and taking suitable action for the next semester examination.
This study was conducted in an undergraduate level
with the use of e-learning
particularly in analytic geometry to lessen the com
mon fear of Filipino students to
mathematics. Since teen age students used to engros
s themselves with the use of
technology specifically computers, this study maxim
ized the capability of computers
in reducing math anxiety by teaching mathematics su
bject using e-learning thus
improving student academic performance.
WMNs: The Design and Analysis of Fair Schedulingiosrjce
IOSR Journal of Computer Engineering (IOSR-JCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of computer engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in computer technology. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
PREDICTING ACADEMIC MAJOR OF STUDENTS USING BAYESIAN NETWORKS TO THE CASE OF ...ijcax
In this study, which took place current year in the city of Maragheh in IRAN. Number of high school students in the fields of study: mathematics, Experimental Sciences, humanities, vocational, business and science were studied and compared. The purpose of this research is to predict the academic major of high school students using Bayesian networks. The effective factors have been used in academic major selection
for the first time as an effective indicator of Bayesian networks. Evaluation of Impacts of indicators on each other, discretization data and processing them was performed by GeNIe. The proper course would be advised for students to continue their education.
PREDICTING ACADEMIC MAJOR OF STUDENTS USING BAYESIAN NETWORKS TO THE CASE OF ...ijcax
In this study, which took place current year in the city of Maragheh in IRAN. Number of high school
students in the fields of study: mathematics, Experimental Sciences, humanities, vocational, business and
science were studied and compared. The purpose of this research is to predict the academic major of high
school students using Bayesian networks. The effective factors have been used in academic major selection
for the first time as an effective indicator of Bayesian networks. Evaluation of Impacts of indicators on
each other, discretization data and processing them was performed by GeNIe. The proper course would be
advised for students to continue their education.
PREDICTING ACADEMIC MAJOR OF STUDENTS USING BAYESIAN NETWORKS TO THE CASE OF ...ijcax
In this study, which took place current year in the city of Maragheh in IRAN. Number of high school students in the fields of study: mathematics, Experimental Sciences, humanities, vocational, business and
science were studied and compared. The purpose of this research is to predict the academic major of high school students using Bayesian networks. The effective factors have been used in academic major selection for the first time as an effective indicator of Bayesian networks. Evaluation of Impacts of indicators on each other, discretization data and processing them was performed by GeNIe. The proper course would be
advised for students to continue their education.
Gender Participation and Performance of Pre-Service Teachers in Physics Educa...iosrjce
This study was carried out with a view to investigating the existence of gender imbalance in the
participation and performance of pre-service teachers in physics education program in College of Education,
Azare. Data used in the study were obtained from students’ personal records, examination score sheets and
final cumulative results. Simple percentage and chi-square test were used to analyze the data. Findings
revealed that there exists serious gender gap in favor of male students in the participation of pre-service
teachers in physics education program. However, findings also showed that the performance of pre-service
teachers in physics education is independent of gender. The study concludes that, although women are
underrepresented in physics education program in College of Education, Azare, both male and female students
have equal chances of performing well in physics. Suggestions on how to adjust the observed gender imbalance
in favor of the disadvantaged group were proffered.
This paper reveals the result of 322 distance learners’ perception towards e-learning program
conducted by UiTM. Generally the respondents rated above average for all aspects of distance
learning program irrespective of gender, program of studies, income and occupation. Students’
gender also did not show any difference in their perception. Similarly, semester of studies too, did
not indicate any significant difference except their perception towards lecturer. However
students’ semester of studies showed significant difference towards lecturer, module and
physical. Gender, income and semester of studies did not show any relationship to students’
perception towards all aspects of distance learning program. However students’ program of
studies showed significant relationship towards their perceptions of the program. Students’ CGPA
showed negative relationship with all aspects of distance learning program.
Data mining in higher education university student dropout case studyIJDKP
In this paper, we apply different data mining approaches for the purpose of examining and predicting students’ dropouts through their university programs. For the subject of the study we select a total of 1290 records of computer science students Graduated from ALAQSA University between 2005 and 2011. The
collected data included student study history and transcript for courses taught in the first two years of
computer science major in addition to student GPA , high school average , and class label of (yes ,No) to
indicate whether the student graduated from the chosen major or not. In order to classify and predict
dropout students, different classifiers have been trained on our data sets including Decision Tree (DT),
Naive Bayes (NB). These methods were tested using 10-fold cross validation. The accuracy of DT, and NlB
classifiers were 98.14% and 96.86% respectively. The study also includes discovering hidden relationships
between student dropout status and enrolment persistence by mining a frequent cases using FP-growth
algorithm.
EFFECT OF MIND MAPS ON STUDENTS’ INTEREST AND ACHIEVEMENT IN MEASURES OF CENT...Gabriel Ken
The purpose of this work was to investigate the effect of Mind Maps on students’ interest and achievement in measures of central tendency. To ascertain the effect of teaching method and gender on the learners’ interest and achievement, four research questions and six null hypotheses guided the study.
This study explored the trends in students’ achievement in Senior School Certificate Examination (SSCE) in Further Mathematics in Kwara State, Nigeria. The study adopted descriptive research design of ex-post factor type. The sample comprised all Further Mathematics students in 79 public senior secondary schools with 3 Local Government Areas in Kwara State. Two research questions were raised and answered in the study. Frequency count, Percentage and Autoregressive (AR) processes for modelling of time series analyses were used to analyse the data. The results revealed that the trend of students’ achievement in WASSCE Further Mathematics from 2007 to 2016 was stochastic with random walk steadily progressive and percentage of the students obtained credit ranged from 23.0 to 77.3; pass ranged from 18.2 to 72.2 and fail ranged from 0.0 to 25.8. It was recommended among others that stakeholders in education should improve the quest for scientific literacy particularly for science-based subjects and further Mathematics curriculum should be all inclusive and non-discriminating to allow development of problem solving ability.
Statistical Scoring Algorithm for Learning and Study Skillsertekg
İndirmek için Bağlantı > https://ertekprojects.com/gurdal-ertek-publications/blog/statistical-scoring-algorithm-for-learning-and-study-skills/
This study examines the study skills and the learning styles of university students by using scoring method. The study investigates whether the study skills can be summarized in a single universal score that measures how hard a student works. The sample consists of 418 undergraduate students of an international university. The presented scoring was method adapted from the domain of risk management. The proposed method computes an overall score that represents the study skills, using a linear weighted summation scheme. From among 50 questions regarding to learning and study skills, the 30 highest weighted questions are suggested to be used in the future studies as a learning and study skills inventor. The proposed scoring method and study yield results and insights that can guide educators regarding how they can improve their students’ study skills. The main point drawn from this study is that the students greatly value opportunities for interaction with instructors and peers, cooperative learning and active engagement in lectures.
A comparative study of machine learning algorithms for virtual learning envir...IAESIJAI
Virtual learning environment is becoming an increasingly popular study option for students from diverse cultural and socioeconomic backgrounds around the world. Although this learning environment is quite adaptable, improving student performance is difficult due to the online-only learning method. Therefore, it is essential to investigate students' participation and performance in virtual learning in order to improve their performance. Using a publicly available Open University learning analytics dataset, this study examines a variety of machine learning-based prediction algorithms to determine the best method for predicting students' academic success, hence providing additional alternatives for enhancing their academic achievement. Support vector machine, random forest, Nave Bayes, logical regression, and decision trees are employed for the purpose of prediction using machine learning methods. It is noticed that the random forest and logistic regression approach predict student performance with the highest average accuracy values compared to the alternatives. In a number of instances, the support vector machine has been seen to outperform the other methods.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
WHY DO LEARNERS CHOOSE ONLINE LEARNING THE LEARNERS’ VOI.docxmansonagnus
WHY DO LEARNERS CHOOSE ONLINE LEARNING:
THE LEARNERS’ VOICES
Hale Ilgaz and Yasemin Gulbahar
Ankara University, Distance Education Center, 06830 Golbasi, Ankara, Turkey
ABSTRACT
Offering many advantages to adult learners, e-Learning is now being recognized - and preferred - by more and more
people, resulting in an increased number of distance learners in recent years. Numerous research studies focus on learner
preferences for online learning, with most converging around the individual characteristics and differences, if not the
features of the technology and pedagogy used. For Turkey, the situation is also similar, with the number of adult learners
who prefer online learning increasing each year due to several reasons. The result of this is an increase in the number of
online programs offered by many universities. Hence, this research study has been conducted to reveal the prevailing
factors causing learners to choose online learning. Through this qualitative research regarding online learners in a state
university, it is found that having a full time job, accessibility and flexibility, individual responsibility, effective time
management, physical distance, institutional prestige, disability are the common factors for under graduate and graduate
learners in their preference for online learning. Awareness of these factors can support the stakeholders while designing
e-Learning from both technological and pedagogical points of view.
KEYWORDS
Online learning, preferences, expectations
1. INTRODUCTION
Offering many advantages to adult learners, e-Learning is now being recognized - and preferred - by more
and more people, resulting in an increased number of distance learners in recent years. Emphasizing that
distance education has a bright and promising future, Zawacki-Richter and Naidu (2016) stress that, “In fact,
there has never been a better time to be in the field of open, flexible, distance and online education than
now!” (p. 20).
The commonly discussed factors that make online learning attractive for adults are: independence from
time and place; accessibility, and; economic reasons. With the MOOC movement, extremely high quality
online courses are now being delivered to learners by many well-known universities. Moreover, many
universities are either providing online programs or courses as a support to traditional instruction, in the form
of blended learning, flipped classes, etc. Indeed, there are almost no universities left who don’t benefit from
these advantages of technology usage and its support in teaching-learning processes.
A variety of reasons might account for these learning preferences. Çağlar and Turgut (2014) attempted to
identify the effective factors for the e-learning preferences of university students; they concluded that,
“Efficient usage of time and reduced educational expenses were found to be on top of the list as the most
valued advantages of e-learning” (p. 46). ...
Similar to A Longitudinal Study of Undergraduate Performance in Mathematics, an Application of Generalized Estimating Equation (GEE) (20)
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A Longitudinal Study of Undergraduate Performance in Mathematics, an Application of Generalized Estimating Equation (GEE)
1. IOSR Journal of Research & Method in Education (IOSR-JRME)
e-ISSN: 2320–7388,p-ISSN: 2320–737X Volume 5, Issue 6 Ver. I (Nov. - Dec. 2015), PP 77-85
www.iosrjournals.org
DOI: 10.9790/7388-05617785 www.iosrjournals.org 77 | Page
A Longitudinal Study of Undergraduate Performance in
Mathematics, an Application of Generalized Estimating Equation
(GEE)
1
Olukanye-David Oluwagbenga*, 1
Alo Damilola Olatubosun.
abestine@yahoo.com
1
Department of statistics, Federal University of Technology Akure, Nigeria
Abstract: Students’ performance in mathematics has been an issue of great concern to most countries,
especially the developing nations. So many programmes have been put in place to improve performances and to
also encourage student to study the course in tertiary institution. In this study we investigate the relationship of
semester, department of a student, age and load unit on marginal mathematics performance o f undergraduate
students. A marginal model was formulated using four working correlation structure where the exchangeable
working correlation structure was selected as the best that models the dataset using quasi information criteria.
The semester, age and load unit were found to be related to the marginal performance in mathematics
Keywords: longitudinal analysis, Generalized Estimating Equation, Repeated measure, marginal model,
mathematics performance, marginal effect
1. Introduction
In this study, we investigate the effect of some selected variables (semester, department, age and load
unit) which is believed to affect students performance in mathematics using a repeated response. This research
was as a result of degradation in students’ performance in early university mathematics courses which affects
their grade right from their inception in Federal University of Technology (FUT Akure) Nigeria. This study aim
at answering the research question “Is students’ marginal performance in mathematics related to semester,
department, age and load unit?” understanding which of these variables that affect the marginal performance
will assist the institution in policy that will enhance the students’ marginal performance.
1.1 Background
Federal University of Technology Akure (FUTA) came into existence in September, 1981 but
academic activities did not begin formally until November, 1982 with an enrolment of 149 students in three
foundation schools, namely the School of Agriculture and Agricultural Technology (SAAT), the School of Pure
and Applied Sciences (SPAS) now School of Science (SOS) and the School of Earth and Mineral Sciences
(SEMS). Over the years, the number of schools has increased and the number of student increased to over
13,000. FUTA was adjudged the best University of Technology in Nigeria by the National University
Commission (NUC) in 2004; produced the Nigerian best Researcher of the year in 2007; emerged the fifth best
University in Nigeria in 2009 and was ranked among the best 50 Universities in Africa in 2011. FUTA became
the centre of excellence in food security – a feat that attracted a grant of $700 million fromWorld Bank.
In its quest to fulfil its vision and mission, it strives for academic excellence which birthed this paper.
The dataset used in this research is obtained both primarily and secondarily. The primary dataset is
made of students’ scores in mathematics in three consecutive semesters under study. The scores were monitored
for three departments (biochemistry, physics and computer science) due to similarity in academic calendar and
same mode of teach so as to reduce error that may arise as a result of disparity in activities which may lead to an
invalid statistic. This collected variable formed a repeated measure over three time frames, which is also
referred to as a longitudinal dataset.
The secondary part of the dataset comprises of students’ bio-data information obtained from the school
office. The information collected involves the age, gender of the student and the load unit for each semester was
obtain fromeach departmental hand book.
Due to the importance of mathematics which serves as the bed rock of any developed country, many
study has been channel towards looking into the cause of degradation in mathematics performance. Great deal of
research has been carried out to determine how interest in mathematics can be improved from among young
pupils, to do this several factors militating performance in mathematics at different level of studies have been
investigated.
Olukanye and Ajiboye (2014) investigated the effect of some selected covariate over time on the
performance of undergraduate student in mathematics. Their study was based on monitoring the performance of
2. A Longitudinal Study of Undergraduate Performance in Mathematics, an Application of ....
DOI: 10.9790/7388-05617785 www.iosrjournals.org 78 | Page
student from mathematics department for three consecutive semesters, where they discovered that load unit,
time and the load unit over time are significant factors that affect mathematic performance.
Udousoro (2011) investigated the effect of gender and mathematics ability on academic performance of
students in Chemistry. He studied the population of secondary school students and discovered that gender does
not have any significant effect on students’ performance in Chemistry. A similar research was conducted by
Adeneye (2011), he considered the effect of gender on secondary school students’ performance in Mathematics
and discovered that gender has a significant effect on Mathematics performance.
This study would afford students the opportunity to be aware of certain existing variables that may
have an impact on their performance in mathematics and hence improve themselves. Information gathered from
results would inform students about their academic performance based on certain factors. Authorities in FUTA
could also used the result to create a policy that will enhance the general performance in mathematics
The remaining sections in this paper are divided into four sections, section 2: Description of the Data
and the Research Question; section 3: Methodology; section 4: Results and Discussion section 5: Conclusion.
2. Description Of Data And The Research Question
2.1 Data Description
The dataset used in this research is a real life dataset, it involves the study and follow up of students in
three departments (Computer Science, Physics and Electronics and Biochemistry), from the duration of three
semesters consecutively. These departments are selected because they belong to the same faculty (science)
which brings about similarity in academic activities. The sample comprises of 92 students from computer
science (35.5%), 85 students from physics (32.85) and 82 students from biochemistry (31.7%) which sum up to
a total of 259 students. Three scores were obtained from each student which gives a longitudinal dataset of 777
observations measured in total.
The percentage composition of male and female in this study is as illustrated in table 2.1 below.
Table 2.1: Gender distribution
BIOCHEMISTRY (%) PHYSICS (%)
COMPUTER
SCIENCE (%)
TOTAL
MALE 76 (89) 49 (60) 68 (74) 193
FEMALE 9 (11) 33 (40) 24 (26) 66
TOTAL 85 (100) 82 (100) 92 (100) 259
Also a brief summary of the explained variable across each department is displayed both in numeric
representation and graphical representation to display hidden properties in the dataset. Table 2.2 below gives
average performances of each department across the three semesters, their maximum score, minimum score and
the standard deviation. From the table below, it can be seen that the students in computer science department
performed better than the rest department in the first semester and third semester, where student in biochemistry
department did well in the second semester. The least score was recorded in biochemistry department while the
highest score was recorded in computer science in the first semester.
Table 2.2 Summary of Student Performance
SEMESTER
BIOCHEMISTRY PHYSICS COMPUTER SCIENCE
Mean (SD) Min – Max Mean (SD) Min – Max Mean (SD) Min – Max
1 58.1 (13.2) 25 – 85 51.2 (14.2) 13 – 84 62.3 (14.2) 40 – 94
2 62 (12.1) 23 – 83 57.4 (15.1) 14 – 87 51 (12.1) 12 – 81
3 44.6 (15.6) 3 – 73 50.2 (13.7) 13 – 86 54.9 (11.7) 40 – 81
2.2 Variable usedin this analysis
This sub-section describe the variables used in this study;
Demographic: the demographic variable used in this study is the gender. The variable identifies gender to which
a particular student belongs. It is coded as (1) for male and (2) for female in this study.
Categorical variable: several categorical variables were also used, the semester is a categorical variable with 3
levels which is coded as (1) for the first semester, (2) for the second semester and (3) for the third semester. The
department was also categorized into computer science, coded as (1), physics coded as (2) and biochemistry
coded as (3).
Continuous variable: Two continuous variables were used which are the age and the load unit.
2.3 Marginal model
The specific objective of this research is the modelling of the marginal expectation of students’ score as
a function of these covariates: load unit, age, gender, department, semester and the interaction between load unit
and semester. The marginal model which describes how the mean score relates to the covariate is given below;
3. A Longitudinal Study of Undergraduate Performance in Mathematics, an Application of ....
DOI: 10.9790/7388-05617785 www.iosrjournals.org 79 | Page
𝐸 𝑌𝑖𝑡 = 𝜇 𝑖𝑡 = 𝛽0 + 𝛽1 𝑠𝑒𝑚𝑒𝑠𝑡𝑒𝑟 + 𝛽2 𝑑𝑒𝑝𝑡𝑗 + 𝛽3 𝑎𝑔𝑒 + 𝛽4 𝑙𝑜𝑎𝑑 𝑢𝑛𝑖𝑡 + 𝛽5 𝑔𝑒𝑛𝑑𝑒𝑟𝑗 + 𝛽6(𝑠𝑒𝑚𝑒𝑠𝑡𝑒𝑟
∗ 𝑙𝑜𝑎𝑑 𝑢𝑛𝑖𝑡 ) 2.1
The marginal performance for each department and gender was shown in a graphical representation to
examine the trend of performances across the time frame. Fig 2.1 reveals that the overall marginal performance
decrease as the semester increases. The departmental marginal performance varies from department to
department. The performances in biochemistry department tend to improve in the second semester which latter
drop drastically in the third semester. The performance in computer science department is the reverse of that
obtained in biochemistry department, while that of the physics department tend to be stationary between 50 and
60 marks.
Figure 2.1: Marginal Performances
3. Methodology
This research study is a descriptive study and the main design used was descriptive. However the
mathematical methodology that was employed for the study was Generalized Estimating Equation (GEE)
Model, i.e. a marginal model longitudinal (MML) data approach since the variable under study are multivariate
with two or more dependents and independents variables.
3.1 Notation
Using the notation in Olukanye and Ajiboye (2014), we consider a study which involves N subjects, on
which n observations are measured for each subject at T time points. Let 𝑦𝑖 = (yi1, . . . , yit )′ denote the outcome
measured for the 𝑖𝑡ℎ subject associated with a vector of r × 1 covariates denoted by 𝑋𝑖𝑇 . Such data, known as
longitudinal data, are found in different fields of life. This provides a means of studying the performance of any
variable of interest over a time frame and also reduces within-subject error as a result of repeated measure. Such
data exhibit a particular property (i.e. correlated) which needs to be accounted for in the course of analyses.
The variable of interest in this study is scores of students in mathematics, which is denoted by 𝑦𝑖 , a
(3 X 1) row vector. It comprises of students’ score in three consecutive semesters in Introductory Mathematics I
(MTS 101), Introductory Mathematics II (MTS 102) and Mathematical Methods I (MTS 201), which are all
mathematics courses taught under the same conditions to the three departments.
4. A Longitudinal Study of Undergraduate Performance in Mathematics, an Application of ....
DOI: 10.9790/7388-05617785 www.iosrjournals.org 80 | Page
The aim of this research was simplified into two specific research questions that can be answered, they are as
follows;
1. Does each of the covariates considered affect the marginal performance in mathematics?
2. Which of the assumed working correlation best models the dataset?
Longitudinal dataset has a particular attribute which must be considered with care in order to choose an
appropriate methodology in analysing. Considering the data structure in this study, the response variable
measured on each student is collected for three consecutive time frames. This forms a cluster of responses on
each student i.e. the responses are correlated. Hence the response measured in this study is a continuous
correlated response and as such need to be account for. Also the interest in this study is the modelling of the
expected response that is a marginal response as a function of some selected covariates. As a result of these two
attributes in the dataset, generalised estimating equation (GEE) as discovered by Liang and Zeger (1986) is
selected as a suitable methodology.
3.2 Generalised Estimating Equation
Generalized estimating equation was discovered by Liang and Zeger in 1986, in their quest to obtain a
unified method suitable for the analysis of correlated responses of nay form (normal, binomial, count). GEE is
an extension of Quasi-likelihood work of Wedderburn (1972). It is an extension of Generalized Linear model
which accounts for dependency within responses. GEE can be used in two different analytical approach;
subject-specific and population average (Liang and Zeger 1986). Population –Average also known as the
marginal model was used in this study, because the aim of this research is the examination of the effect of some
covariates on marginal response. This approach which measures the fixed effect of the covariates under study
allows for specifying a predefined unique correlation structure often referred to as the working correlation
structure which accounts for the dependency within subjects. The most often used working correlation structure
and their construct are given below (Olukanye and Ajiboye 2014).
Table 3.1: Correlation Structures
Correlation type Correlation formula Working correlation structure
Independence 𝐶𝑜𝑟 𝑌𝑖𝑗 𝑌𝑖𝑘 = 0 , 𝑗 ≠ 𝑘
𝑅 𝛼 =
1 0 ⋯ 0
0 1 ⋯ 0
⋮
0
⋮
0
⋱ ⋮
… 1
Exchangeable 𝐶𝑜𝑟 𝑌𝑖𝑗 𝑌𝑖𝑘 = 𝛼 ,𝑗 ≠ 𝑘
𝑅 𝛼 =
1 𝛼 ⋯ 𝛼
𝛼 1 ⋯ 𝛼
⋮
𝛼
⋮
𝛼
⋱ ⋮
⋯ 𝛼
AR(1) 𝐶𝑜𝑟 𝑌𝑖𝑗 𝑌𝑖𝑘 = 𝛼| 𝑗− 𝑘|
, 𝑗 ≠ 𝑘
𝑅 𝛼 =
1
𝛼
𝛼
1
⋯
⋯
𝛼 𝑗 −1
𝛼| 𝑗−2|
⋮ ⋮ ⋱ ⋮
𝛼 𝑗 −1
𝛼 𝑗 −2
⋯ 1
Unstructured 𝐶𝑜𝑟 𝑌𝑖𝑗 𝑌𝑖𝑘 = 𝛼𝑗𝑘 , 𝑗 ≠ 𝑘
𝑅 𝛼 =
1 𝛼12 ⋯ 𝛼1𝑗
⋮ ⋮ ⋱ ⋮
𝛼1𝑗
𝛼2𝑗 ⋯ 1
As shown in the table above, the correlation structure R depends on 𝛼 which can be estimated for exchangeable,
ar1 and unstructured working correlation respectively fromthe following equations;
𝛼 = 𝜑
1
𝑛𝑖 𝑛𝑖 − 1
𝑛
𝑖
𝑅𝑖𝑗 𝑅𝑖𝑘
𝑗 ≠𝑘
(3.1)
𝛼 = 𝜑
1
𝑛𝑖 − 1
𝑛
𝑖
𝑅𝑖𝑗 𝑅𝑖𝑗 +1
𝑗≤𝑛 𝑖−1
(3.2)
𝛼𝑗𝑘 = 𝜑
1
𝑛
𝑅𝑖𝑗 𝑅𝑖𝑘
𝑛
𝑖=1 (3.3)
Where the dispersion parameter estimate 𝜑 is given as;
𝜑 =
1
𝑛 − 𝑝
𝑅𝑖𝑗
2
𝑛 𝑖
𝑗 =1
𝑛
𝑖 =1
(3.4)
5. A Longitudinal Study of Undergraduate Performance in Mathematics, an Application of ....
DOI: 10.9790/7388-05617785 www.iosrjournals.org 81 | Page
In fitting a GEE model, several assumptions concerning the structure of the dataset accounts for the
structure of the model construct. The response measured in this study is a continuous meas ure and hence is
assumed to follow a normal distribution. This assumption allows choosing an identity link function which
relates the covariates to the explained variable. The identity link function is given as;
𝑔(𝜇 𝑖) = 𝜇 𝑖 = 𝑋𝑖 𝛽 (3.5)
Where;
𝜇 𝑖 = average performance
𝑋𝑖 = is a matrix of predictors
𝛽 = regression coefficients
In order to achieve the aims and objectives of these studies, several parameter estimates need to be
evaluated, especially the regression parameter 𝛽. Obtaining an estimate for 𝛽 require solving equation (3.6)
below called the score function or estimating equation, which is approached numerically (Liang and Zeger
1986)
𝑈 𝛼, 𝛽 =
𝜕𝜇 𝑖
𝑇
𝜕𝛽
𝑉−1
𝑦𝑖 − 𝑋𝑖 𝛽
𝐼
𝑖=1
(3.6)
Where;
𝜕 𝜇 𝑖
𝑇
𝜕𝛽
= partial derivative of the 𝜇 𝑖 w.r.t. each regression parameter in the model
𝑉 = 𝐴−
1
2 𝑅(𝛼)𝐴−
1
2 (A variance-covariance matrix for a specified working correlation matrix)
𝑦𝑖 − 𝑋𝑖 𝛽 = the residual.
Unlike the conventional GLM which uses maximum likelihood estimation to obtain the parameters of
the regression model, GEE uses estimating equation (equation 3.2). It uses an iterative procedure to obtain the
regression parameter by assuming independency within cluster to obtain an initial regression parameter an d then
obtain an optimize regression parameter through iteration using any working correlation structure that best
models the correlation within cluster. The most often used iterative equation is given below
𝛽(𝑚+1)
= 𝛽 𝑚
+
𝜕 𝜇 𝑖
𝜕𝛽
𝑉𝑖
−1 𝜕 𝜇 𝑖
𝜕𝛽
𝑛
𝑖=1
−1
𝜕 𝜇 𝑖
𝜕𝛽
𝑉𝑖
−1
𝑦𝑖 − 𝜇 𝑖
𝑛
𝑖=1 (3.7)
Where;
𝑉𝑖 = 𝑉𝑖 (𝛽 𝑚
, 𝛼(𝛽 𝑚
, 𝜑 (𝛽 (𝑚)
))) and
𝜕 𝜇 𝑖
𝜕𝛽
are also evaluated at 𝛽(𝑚)
. The 𝛽 (𝑚)
which serves as the initial
value for the regression parameter is obtained fromthe Generalised Linear Model Method (GLM).
3.2.1 Iterative Process For GEE's
The procedure for the estimation of the regression parameter follows an iterative process as given below:
Obtain the initial parameter assuming the response are uncorrelated ( i.e. independent) using OLS and the
dispersion parameter 𝜑 = 1
Use the estimate 𝛽 𝐺𝐿𝑀 to calculate fitted values 𝜇 𝑖 = 𝑔−1
(𝑋𝑖 𝛽).
compute the Pearson residuals 𝑅𝑖𝑗 and obtain the estimates for 𝜑, 𝛼 and the working variance-covariance
matrix 𝑉𝑖
Using the current estimates 𝛼 , 𝜑 and 𝛽 in the Newton-Raphson iterative method to obtain a new
improved regression parameter estimate
The iterative process is repeated until the regression parameter converges.
4. Results And Discussion
Having ascertained GEE to be a suitable method for analysis, the computation of all parameter
estimates were done using R programming language. Assuming MCAR, geepack package was used in
estimating the regression parameters and was also used to obtain some exploratory analyses both numeric and
graphics.
For all four models fitted, there is no strong difference between independence and AR(1) correlation
structure except the fact that age does not significantly affect the performance of students under independence
correlation structure while it affects the performance under exchangeable correlation structure.
4.1 Assumptions
The following assumptions were used in fitting the model for this study;
1. Link Function
Since the response (score) measured is a continuous variable which is assumed to follow a normal
distribution, the identity link function is used.
6. A Longitudinal Study of Undergraduate Performance in Mathematics, an Application of ....
DOI: 10.9790/7388-05617785 www.iosrjournals.org 82 | Page
i.e. 𝑔 𝜇 𝑖𝑗 = 𝜇 𝑖𝑗
2. Correlated Response
The response measured must be dependent, this is one of the basic assumptions under which GEE
operates. The score collected for each student satisfies this assumption, since multiple scores (score 1,
score 2, score 3) are collected for each student
These are the basic assumptions for the model in equation (2.1)
4.2 Results for Independence Correlation Structure
The following table contains the summary of the estimates obtained using R programming language under an
assumed independence working correlation structure:
Table 4.1: Parameters Obtained from Independence Working Correlation GEE analysis
Effect Estimate Std. Error Wald Pr(>|W|)
Intercept -5.0620 10.9218 0.21 0.643
Semester 10.6139 5.1552 4.24 0.040*
Physics department 2.9871 2.1524 1.93 0.165
Biochemistry department 0.5753 1.7206 0.11 0.738
Age 0.0676 0.0459 2.17 0.140
LoadUnit 2.9543 0.4848 37.13 1.1e-09***
Gender (female) -0.2782 1.5003 0.03 0.853
Semester * Load Unit -0.6298 0.2507 6.31 0.012*
For the demographic variable considered, there was no significant effect for gender. As the semester
increases, the performance of student increases significantly by approximately11 marks. The load unit which is
of paramount interest tends to increase the performance of student by approximately 3 marks which is also
significant.
The load unit over time which is obtained as the interaction between semester and load unit also shows
a significant negative effect on students’ performance.
4.3 Results for Exchangeable Correlation Structure
The following table contains the summary of the estimates obtained using R programming language
under the assumption that the correlation between the responses in a cluster is constant.
Table 4.2: Parameters Obtained from Exchangeable Working Correlation GEE analysis
Effect Estimate Standarderr Wald Pr(>|W|)
Intercept -4.6530 10.8408 0.18 0.6678
Semester 10.5776 5.1517 4.22 0.0400*
Physics department 2.9978 2.1526 1.94 0.1637
Biochemistry department 0.4056 1.7142 0.06 0.8129
Age 0.0564 0.0207 7.40 0.0065**
LoadUnit 2.9471 0.4845 37.00 1.2e-09***
Gender (female) -0.1755 1.4992 0.01 0.9068
Semester * Load Unit -0.6287 0.2505 6.30 0.0121*
This result reveals that four factors out of all the predictors considered have significant effect on
students’ performance. With the estimates very similar to those obtained under independence assumption of the
correlation structure. The estimated correlation matrix is given as:
1 0.446 0.446
0.446 1 0.446
0.446 0.446 1
4.4 Results for Autoregressive Correlation Structure
The following table contains the summary of the estimates obtained using R programming language
under the assumption that the observations obtain in close time frame are more correlated than those obtained in
far time apart.
Table 4.3: Parameters Obtained from Autoregressive Working Correlation GEE analysis
Effect Estimate Standarderr Wald Pr(>|W|)
Intercept -12.2506 10.9288 1.26 0.2623
Semester 11.6269 5.3400 4.74 0.0295*
Physics department 3.0630 2.1699 1.99 0.1581
Biochemistry department -1.6582 1.7644 0.88 0.3473
Age 0.0580 0.0224 6.74 0.0094**
LoadUnit 3.3066 0.4934 44.91 2.1e-11***
Gender (female) -0.1658 1.5464 0.01 0.9146
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Semester * Load Unit -0.6700 0.2601 6.64 0.0100**
The result obtained above also reveals that four of the variables considered have a significant marginal
effect on the students’ performance. As the student stays longer in the school system, the performance increases
by approximately 12 marks, age also have a significant positive effect of about 0.1 marks as the age of the
student increases. The load unit also have a positive significant increase of 3 marks as the load unit increases.
The interactive effect of semester and load unit which measure the long run effect of load unit has a significant
negative effect on the student performance.
The correlation structure estimate is given as;
1 0.537 0.288
0.537 1 0.537
0.288 0.537 1
4.5 Results for Unstructured Correlation Structure
The following table contains the summary of the estimates obtained using R programming language
under the assumption that the correlation within a cluster has no particular pattern. This is very close to the
actual correlation.
Table 4.3: Parameters Obtained from Unstructured Working Correlation GEE analysis
Effect Estimate Standarderr Wald Pr(>|W|)
Intercept -4.4205 10.8366 0.17 0.6833
Semester 10.6532 5.1462 4.29 0.0384*
Physics department 3.0369 2.1484 2.00 0.1575
Biochemistry department 0.5887 1.7127 0.12 0.7311
Age 0.0556 0.0193 8.32 0.0039**
LoadUnit 2.9319 0.4843 36.66 1.4e-09***
Gender (female) -0.2018 1.4960 0.02 0.8927
Semester * Load Unit -0.6303 0.2502 6.35 0.0118*
The result obtained above also reveals that four of the variables considered have a significant marginal
effect on the students’ performance. As the student stays longer in the school system, the performance increases
by approximately 11 marks, age also have a significant positive effect of about 0.1 marks as the age of the
student increases. The load unit also have a positive significant increase of 3 marks as the load unit increases.
The interactive effect of semester and load unit which measure the long run effect of load unit has a significant
negative effect on the student performance.
The correlation structure estimate is given as;
1 0.452 0.487
0.452 1 0.400
0.487 0.400 1
4.6 Model Diagnostics
Since four different models are fitted using four assumed working correlation matrices, the need to
select the best model that fit the data is necessary, even though the results obtained by these four models look
similar. Quasi Information Criteria (QIC) which is a special kind of information criteria used to select model
formed from quasi-likelihood. The rule of thumb selects the model with the least QIC value. The QIC value
obtained for the four working correlation structure are (independence, autoregressive order 1, exchangeable and
unstructured) are 150855.300, 151359.814, 150860.934 and 153272.179 consecutively. The smallest of all these
is the independence working correlation structure, but due to the theoretical structure of the dataset which
indicate presence of correlation, the least of the working correlation structure that accounts for correlation is
adjudge the best, hence the model with exchangeable working correlation structure is considered the best model.
Table 9: Summary of GEE Models
Variables
GEEMODELS
Independent Exchangeable AR(1) Unstructured
Estimate p-value Estimate p-value Estimate p-value Estimate p-value
Intercept -5.0620
(10.9218)
0.643 -4.6530
(10.8408)
0.678 -12.2506
(10.9288)
0.2623 -4.4205
(10.8366)
0.6833
Semester 10.6139
(5.1552)
0.040* 10.5776
(5.1517)
0.0400* 11.629
(5.3400)
0.0295* 10.6532
(5.1462)
0.0384*
Physics
department
2.9871
(2.1524)
0.165 2.9978
(2.1526)
0.1637 3.0630
(2.1699)
0.1581 3.0369
(2.1484)
0.1575
Biochemistry
department
0.5753
(1.7206)
0.738 0.4056
(1.7142)
0.8129 -1.6582
(1.7644)
0.3473 0.5887
(1.7127)
0.7311
Age 0.0676 0.140 0.0564 0.0065** 0.0580 0.0094** 0.0556 0.0039**
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(0.0459) (0.0207) (0.0224) (0.0193)
Load Unit 2.9543
(0.4848)
1.1e-09*** 2.9471
(0.4845)
1.2e-09*** 3.3066
(0.4934)
2.1e-
11***
2.9319
(0.4843)
1.4e-09***
Gender
(female)
-0.2782
(1.5003)
0.853 -0.1755
(1.4992)
0.9068 -0.1658
(1.5464)
0.9146 -0.2018
(1.4960)
0.8927
Semester
*Load Unit
-0.6298
(0.2507)
0.012* -0.6287
(0.2505)
0.0121* -0.6700
(0.2601)
0.0100** -0.6303
(0.2502)
0.0118*
Numbers in parentheses are robust standard errors
The inferences that could be made regarding the variable effects do not change substantially across the
four models: examining GEE estimates from the different correlation structures reveals that those from the
independence and exchangeable models are more identical compared to AR(1) and unstructured. However, four
of the predictor variables significantly affects student’s performance under exchangeable working correlation
structure while only three variables significantly affects student performance under independent working
correlation. All the variable have the same directional effect on the response variable but different not
significant magnitude.
5. Conclusion
In this paper, we applied GEE to educational dataset using geepack package in R statist ical
programming language which assumes that any missing observation is missed completely at random (MCAR) to
test the research hypothesis that students’ performance in mathematics is related to semester, department, age
and load unit. We found that load unit, semester, age and the interactive effect between semester and load unit
affects the students’ performance in mathematics. Based on the theoretical structure of the dataset used, the
exchangeable working correlation matrix was adjudged the appropriate working correlation structure since it
accounts for the dependency within scores obtained for each student. However student performance is not
affected by gender and age category.
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