Investigation of affective traits affecting mathematics achievement by SEM and MARS methods

Öz

The purpose of the study is to analyze the affective traits that affect mathematics achievement through Structural Equation Modeling (SEM) as a traditional regression model and Multivariate Adaptive Regression Splines (MARS), as one of the data mining methods. Structural Equation Modeling, one of the regression-based methods, is quite popular for social sciences due to the various advantages it offers; however, it requires very intensive assumptions. MARS method, on the other hand, is a multivariate and adaptive nonparametric statistical regression method used for data classification and modeling. MARS does not need any assumptions such as normality, linearity, homogeneity. It allows variables that do not provide linearity to be included in the analysis. The present study examines whether it is possible to use the MARS method, which is a more flexible method compared to SEM, taking both methods into account. Regarding this goal, the SEM model was created with the program R using the affective data and the achievement variable picked from TIMMS 2019 data. Then, the MARS method was created using the SPM (Salford Predictive Modeler) program. The results of the study showed that at certain points the MARS model gave similar results to the SEM model and MARS model is more compatible with the literature.

Anahtar Kelimeler

• Multivariate Adaptive Regression Splines
• Structural Equation Model
• Data mining
• TIMMS

References

1. Abdel-Aty, M., & Haleem, K. (2011). Analyzing angle crashes at unsignalized intersections using machine learning techniques. Accident Analysis & Prevention, 43(1), 461-470. https://doi.org/10.1016/j.aap.2010.10.002
2. Adıgüzel, A., & Karadaş, H. (2013). Ortaöğretim öğrencilerinin okula ilişkin tutumlarının devamsızlık ve okul başarıları arasındaki ilişki [The level of effect of high school students’ attitudes towards school on their absenteeism and school success] Yüzüncü Yıl University Journal of the Faculty of Education, 10(1), 49 67. https://dergipark.org.tr/en/pub/yyuefd/issue/13705/165929
3. Akbıyık, C., & Kestel, M. (2016). Siber zorbalığın öğrencilerin akademik, sosyal ve duygusal durumları üzerindeki etkisinin incelenmesi [An investigation of effects of cyber bullying on students’ academic, social and emotional states] Mersin University Journal of the Faculty of Education, 12(3), 844-859. https://doi.org/10.17860/mersinefd.282384
4. AL-Qinani, I.H. (2016). Multivariate adaptive regression splines (MARS) heuristic model: Application of heavy metal prediction. International Journal of Modern Trends in Engineering and Research, 3(8), 223 229. https://doi.org/10.21884/IJMTER.2016.3027.7NUQV
5. Anıl, D. (2010). Uluslararası öğrenci başarılarını değerlendirme programı (PISA)’nda Türkiye’deki öğrencilerin fen bilimleri başarılarını etkileyen faktörler [Factors effecting science achievement of science students in programme for international students’ achievement (PISA) in Turkey]. Education and Science, 34(152).
6. Arslan Ö.S., & Savaşer, S. (2009). Okulda zorbalık [School bullying] Milli Eğitim, 38(184), 218-227. https://dergipark.org.tr/en/pub/milliegitim/issue/36201/407174
7. Atik, S. (2016). Akademik başarının yordayıcıları olarak öğretmene güven, okula karşı tutum, okula yabancılaşma ve okul tükenmişliği [Trust in teacher, attitude towards school,alienation from school and school burnout aspredictors of academic achievement] (Unpublished Doctoral dissertation) İnönü University
8. Bahçetepe, Ü., & Giorgetti, F.M. (2015). Akademik başarı ile okul iklimi arasındaki ilişki [The relation between the academic achievement and the school climate]. İstanbul Eğitimde Yenilikçilik Dergisi, 1(3), 83 101. https://dergipark.org.tr/en/download/article file/436183

9. Bolder, J., & Rubin, T. (2007). Optimization in a simulation setting: Use of function approximation in debt strategy analysis, Bank of Canada Working Paper, 1-92. http://dx.doi.org/10.2139/ssrn.1082840
10. Candemir, M. (2018). Antecedents and consequences of Turkish Millennials’ ELoyalty: A Structural Equation Modeling Application [Unpublished master’s thesis]. Marmara University
11. Clement, K.A., Victor, A.T., & Yao, Y.Z. (2020). Multivariate Adaptive Regression Splines (MARS) approach to blast-induced ground vibration prediction, International Journal of Mining, Reclamation and Environment, 34(3), 198 222. https://doi.org/10.1080/17480930.2019.1577940
12. Cumhur, F. (2018). The investigation of the factors affecting the mathematical success of students in the context of teachers' opinions and suggestions. Journal of Social and Humanities Sciences Research (JSHSR), 5(26), 2679 2693. http://dx.doi.org/10.26450/jshsr.647
13. Deichmann, J., Eshghi, A., Haughton, D., Sayek, S., & Teebagy, N. (2002). Application of multiple adaptive regression splines (MARS) in direct response modeling. Journal of Interactive Marketing, 16(4), 15-27. https://doi.org/10.1002/dir.10040
14. Demir, İ., & Kılıç, S. (2010). Öğrencilerin matematiğe karşı tutumlarının matematik başarısı üzerine etkisi. [Effects of students’ self-related cognitions on matematics achievement] İstanbul Aydın Üniversitesi Fen Bilimleri Dergisi, 2(4), 50 70. https://dergipark.org.tr/en/pub/iaud/issue/30050/32446
15. Dursun, Y., & Kocagöz, E. (2010). Yapisal eşitlik modellemesi ve regresyon: karşılaştırmalı bir analiz [Structural equation modeling and regression: a comparative analysis] Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 35, 1-17. https://dergipark.org.tr/en/pub/erciyesiibd/issue/5892/77926
16. Emre, İ.E., & Erol, Ç.S. (2017). Veri analizinde istatistik mi veri madenciliği mi? [Statistics or data mining for data analysis] Bilişim Teknolojileri Dergisi, 10(2), 161-167. https://doi.org/10.17671/gazibtd.309297
17. Eraslan, A. (2009). Finlandiya'nın PISA'daki başarısının nedenleri: Türkiye için alınacak dersler [Reasons behind the Success of Finland in PISA: Lessons for Turkey] Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 3(2), 238-248. https://dergipark.org.tr/en/pub/balikesirnef/issue/3369/46514
18. Fayyad, U., Piatetsky-Shapiro, G., Smyth, P., & Uthurusamy, R. (1996). Advances in Knowledge Discovery and Data Mining. AAAI/MIT Press.
19. Finney, S.J., DiStefano, C., Hancock, G.R., & Mueller, R.O. (2006). Structural equation modeling: A second course. LAP-Information Age Publishing Inc.
20. Güneş, S., Görmüş, Ş., Yeşilyurt, F. & Tuzcu, G. (2012). ÖSYS başarısını etkileyen faktörlerin analizi [The determinants of OSYS success] Pamukkale Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 11, 71-81.
21. Güngör, A.A., Eryılmaz, A., & Fakıoğlu, T. (2007). The relationship of freshmen’s physics achievement and their related affective characteristics. Journal of Research in Science Teaching, 44 (8), 1036-1056. https://doi.org/10.1002/tea.20200
22. Güzel, H. (2004). Genel fizik ve matematik derslerindeki başarı ile matematiğe karşı olan tutum arasındaki ilişki [The relationship between success in general physics and mathematics courses and attitude towards mathematics]. Journal of Turkish Science Education, 1(1), 49- 58. https://www.tused.org/index.php/tused/article/view/41/16
23. Huyut, M.T., & Keskin, S. (2017). Matematik başarısına etki eden faktörlerin: çevresel faktörlerin çoklu uyum analizi ile belirlenmesi [Determination of factors affecting of mathematics success: environmental factors with multiple correspondence analysis] Türkiye Teknoloji ve Uygulamalı Bilimler Dergisi, 1(2), 48 59. https://dergipark.org.tr/en/pub/tubid/issue/32796/303761
24. Karasar, N. (2015). Bilimsel araştırma yöntemleri [Science research method]. Nobel Akademik Yayıncılık.
25. Karataş, H. (2011). İlköğretim okullarında zorbalığa yönelik geliştirilen programın etkisinin incelenmesi [Examining the effect of the program developed to address bullying in primary schools]. [Unpublished Doctoral dissertation] Dokuz Eylül University
26. Kline, R.B. (2015). Principles and practice of structural equation modeling. Guilford Publications.
27. Lee, T.S., Chiu, C.C., Chou, Y.C., & Lu, C.J. (2006). Mining the customer credit using classification and regression tree and multivariate adaptive regression splines. Computational Statistics & Data Analysis, 50(4), 1113 1130. https://doi.org/10.1016/j.csda.2004.11.006
28. Lee, T.S., & Chen, I.F. (2005). A two-stage hybrid credit scoring model using artificial neural networks and multivariate adaptive regression splines. Expert Systems with Applications, 28, 743-752. https://doi.org/10.1016/j.eswa.2004.12.031
29. Lehman, R. (2006). The role of emotion in creating instructor and learner presence in the distance education experience. Journal of Cognitive Affective Learning, 2 (2), 12-26.
30. Li, B., Bakshi, B.R., & Goel, P.K. (2009). Other Methods in Nonlinear Regression. In Comprehensive Chemometrics, edited by S. D. Brown, R. Tauler, and B. Walczak, 463-476. Elsevier.
31. Lu, C.J., Lee, T.S. & Lian, C.M. (2012). Sales forecasting for computer wholesalers: A comparison of multivariate adaptive regression splines and artificial neural networks. Decision Support Systems, 54(1), 584-596. https://doi.org/10.1016/j.dss.2012.08.006
32. MEB. (2019). TIMSS 2019 Ulusal Matematik ve Fen Ön Raporu: 4. ve 8. Sınıflar [TIMSS 2019 National mathematics and sciences preliminary report 4th and 8 th grades]. http://odsgm.meb.gov.tr/meb_iys_dosyalar/2020_12/10175514_TIMSS_2019_Turkiye_On_Raporu_.pdf
33. Muzır, E. (2011). Basel II düzenlemeleri doğrultusunda kredi riski analizi ve ölçümü: geleneksel ekonometrik modellerin yapay sinir ağları ve MARS modelleriyle karşılaştırılmasına yönelik ampirik bir çalışma [Credit risk analysis and measurement in accordance with Basel II regulations: An empirical study to compare traditional econometric models to Artificial Neural Networks and MARS models] [Unpublished Doctoral dissertation]. İstanbul University
34. Orhan, H., Teke, E.Ç., & Karcı, Z. (2018). Laktasyon eğrileri modellemesinde çok değişkenli uyarlanabilir regresyon eğrileri (MARS) yönteminin uygulanması [Application of multivariate adaptive regression splines (MARS) for modeling the lactation curves] Kahramanmaraş Sütçü İmam Üniversitesi Tarım ve Doğa Dergisi, 21(3), 363-373. https://doi.org/10.18016/ ksudobil.334237
35. Oruç, M.A. (2019). İstihbaratın geleceği: Siber uzayda istihbarat ve karşı istihbarat faaliyetlerinde yapay zekâ ve veri bilimi kullanımı [Future of intelligence: The using artificial intelligence and data science in intelligence and counter intelligence activities in cyber space] [Unpublished master’s thesis]. İstanbul Aydın University
36. Ölçüoğlu, R., & Çetin, S. (2016). TIMSS 2011 sekizinci sınıf öğrencilerinin matematik başarısını etkileyen değişkenlerin bölgelere göre incelenmesi. [The Investigation of the Variables That Affecting Eight Grade Students’ TIMSS 2011 Math Achievement According to Regions]. Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 7(1), 202-220. https://doi.org/10.21031/epod.34424
37. Özfalcı, Y (2008). Çok değişkenli uygulanabilir regresyon kesitleri: MARS [Multivariate adaptive regression splines: MARS] [Unpublished master’s thesis]. Gazi University.
38. Parsaie, A., Haghiabi, A.H., Saneie, M., & Torabi, H. (2016). Prediction of energy dissipation on the stepped spillway using the multivariate adaptive regression splines. ISH Journal of Hydraulic Engineering, 22(3), 281 292. https://doi.org/10.1080/09715010. 2016.1201782
39. Pekel-Uludagli, N., & Uçanok, Z. (2005). Akran zorbaligi gruplarinda yalnizlik ve akademik basari ile sosyometrik statüye göre zorba/kurban davranis türleri [Loneliness, academic achievement and types of bullying behavior according to sociometric status in bully/victim groups]. Türk Psikoloji Dergisi, 20(56), 77. https://psycnet.apa.org /record/2006-01737-005
40. Plotnikova, V., Dumas, M., & Milani, F. (2020). Adaptations of data mining methodologies: a systematic literature review. PeerJ. Computer science, 6, 267. https://doi.org/10.7717/peerjcs.267
41. Rodríguez, C.M., & Wilson, D.T. (2002). Relationship bonding and trust as a foundation for commitment in US–Mexican strategic alliances: A structural equation modeling approach. Journal of International Marketing, 10(4), 53 76. https://doi.org/10.1509/jimk.10.4.53.19553
42. Sarıer, Y. (2020). TIMSS uygulamalarında Türkiye’nin performansı ve akademik başarıyı yordayan değişkenler [Turkey's performance in TIMSS applications and variables predicting academic achievement]. Temel Eğitim, 2(2), 6 27. https://dergipark.org.tr/en/pub/temelegitim/issue/57288/745624
43. Şen, S. (2020). Mplus ile yapısal eşitlik modellemesi uygulamaları. Nobel Yayınları.
44. Şevgin, H. (2020). ABİDE 2016 fen başarısının yordanmasında MARS ve brt veri madenciliği yöntemlerinin karşılaştırılması [Predicting the ABIDE 2016 science achievement: The comparison of MARS and BRT data mining methods] [Unpublished master’s thesis]. Gazi University.
45. Temel, G.O., Ankarali, H., & Yazici, A.C. (2010). Regresyon modellerine alternatif bir yaklasim: MARS [An alternative approach to regression models: MARS.] Türkiye Klinikleri Biyoistatistik, 2(2), 58.
46. The jamovi project (2021). Jamovi (Version 1.6) [Computer Software]. https://www.jamovi.org/
47. Wang, J. (2007). A trend study of self-concept and mathematics achievement in a cross cultural context. Mathematics Education Research, 19(3), 33-47. https://doi.org/10.1007/ BF03217461
48. Yoon, S., Co, M.C., Jr, Suero-Tejeda, N., & Bakken, S. (2016). A Data mining approach for exploring correlates of self-reported comparative physical activity levels of urban latinos. Studies in Health Technology and Informatics, 225, 553–557. https:// doi.org/ 10.3233/978-1-61499-658-3-553
49. Zakaria, E., & Nordin, N.M. (2008). The effects of mathematics anxiety on matriculation students as related to motivation and achievement. Eurasia Journal of Mathematics, Science & Technology Education, 4(1), 27-30. https://doi.org/10.12973/ejmste/75303
50. Zateroğlu, M.T., & Kandırmaz (2018). Türkiye için güneşlenme süresi değişiminin izlenmesi, değerlendirilmesi ve bazı meteorolojik verilerle ilişkisinin belirlenmesi [Observation and evaluation of sunshine duration changes in Turkey and determination of relations with some meteorological parameters]. Ç.Ü Fen ve Mühendislik Bilimleri Dergisi, 35(3), 105-114.
51. Zhang, W., & Goh, A.T. (2016). Multivariate adaptive regression splines and neural network models for prediction of pile drivability. Geoscience Frontiers, 7(1), 45-52. https://doi.org/10.1016/j.gsf.2014.10.003
52. Zhang, W., Wu, C., Li, Y., Wang, L., & Samui, P. (2021). Assessment of pile drivability using random forest regression and multivariate adaptive regression splines. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 15(1), 27-40. https://doi.org/10.1080/17499518.2019.1674340
53. Zhou, Y., & Leung, H. (2007). Predicting object-oriented software maintainability using multivariate adaptive regression splines. Journal of Systems and Software, 80(8), 1349-1361. https://doi.org/10.1016/j.jss.2006.10.049