Matematik Okuryazarlığını Yordamada İstatistiksel ve Makine Öğrenmesi Yaklaşımlarının Karşılaştırılması: PISA 2022 Türkiye Örneği

Abstract

Bu çalışma, PISA 2022’ye katılan Türkiye’deki öğrencilerin matematik okuryazarlığını yordamada istatistiksel ve makine öğrenmesi yöntemlerini karşılaştırmaktadır. Bilişsel, duyuşsal ve bağlamsal boyutları yansıtan 13 standartlaştırılmış yordayıcı değişkene ait 6.427 öğrenci verisi kullanılarak çoklu doğrusal regresyon, en küçük mutlak küçültme ve seçim operatörü (LASSO), rassal ormanlar, aşırı gradyan artırma (XGBoost), yapay sinir ağları ve bir yığıt (stacking) modeli 10 katlı çapraz doğrulama tasarımıyla değerlendirilmiştir. Bulgular, yığıt modellerin doğrusal modellere kıyasla daha yüksek doğruluk sağladığını göstermiştir: yığıt modeli en yüksek doğruluğa ulaşmış (fold dışı R²=.319;RMSE=.777), bunu XGBoost (R²=.313) ve rassal ormanlar (R²=.304) izlemiştir. Doğrusal modeller ise daha düşük sonuçlar vermiştir (çoklu doğrusal regresyon R²≈.270; LASSO R²=.273). Ortalama mutlak hata değerleri modeller arasında oldukça benzer bulunmuştur (≈ .633–.658) ve foldlar arası farklar üç ondalıkta yuvarlamadan kaynaklanacak kadar küçüktür. Artık analizleri, yığıt modellerin daha kararlı hata yapısına sahip olduğunu, doğrusal modellerin ise daha belirgin heteroskedastisite gösterdiğini ortaya koymuştur. Tüm modellerde sosyoekonomik durum en güçlü yordayıcı olarak öne çıkmış, bunu matematik özyeterliği ve sınıf disiplini izlemiştir. Bu durum, öğrenci inançlarının ve sınıf ortamının birlikte belirleyici rol oynadığını göstermektedir. Bulgular, yordama başarımı ve değişken önem düzeylerinin belirlenmesinde yığıt gibi birleşik yöntemlerin avantajlarını vurgulamakta ve sosyoekonomik eşitsizliklerin eğitimsel sonuçlar üzerindeki etkisinin sürdüğüne dikkat çekmektedir.

Keywords

• matematik okuryazarlığı
• makine öğrenmesi
• PISA 2022
• yordayıcı modelleme
• eğitimsel veri madenciliği

Comparison of Statistical and Machine Learning Approaches for Predicting Mathematical Literacy: Evidence from PISA 2022 Türkiye

Abstract

This study compares statistical and machine learning methods for predicting mathematical literacy among students in Türkiye who participated in PISA 2022. Using data on 6,427 students and 13 standardized predictors capturing cognitive, affective, and contextual dimensions, we evaluated multiple linear regression, least absolute shrinkage and selection operator, random forests, extreme gradient boosting, artificial neural networks, and a stacking ensemble within a 10-fold cross-validation design. Ensemble approaches outperformed linear methods: the stacking model achieved the highest accuracy (out-of-fold R² = .319; RMSE = .777), followed closely by extreme gradient boosting (R² = .313) and random forests (R² = .304). Linear models yielded weaker results (multiple linear regression R² ≈ .270; least absolute shrinkage and selection operator R² = .273). Mean absolute error values were nearly identical across models (≈ .633–.658), with minimal between-fold variation due to rounding at three decimals. Residual analyses indicated that ensemble models produced more stable error structures, whereas linear methods showed stronger heteroskedasticity. Across all approaches, socioeconomic status consistently emerged as the strongest predictor, followed by mathematics self-efficacy and disciplinary climate, underscoring the dual roles of student beliefs and classroom environment. These findings highlight the advantages of ensemble methods for predictive performance and variable-importance estimation, emphasizing the ongoing impact of socioeconomic inequalities on educational outcomes.

Keywords

• mathematical literacy
• machine learning
• PISA 2022
• predictive modeling
• educational data mining

References

1. Abd El-Salam, M. E.-F. (2013). The efficiency of some robust ridge regression for handling multicollinearity and non-normals errors problems. Applied Mathematical Sciences, 7(77–80), 3831–3846. https://doi.org/10.12988/ams.2013.36297
2. Agasisti, T., & Longobardi, S. (2014). Inequality in education: Can Italian disadvantaged students close the gap? Journal of Behavioral and Experimental Economics, 52, 8–20. https://doi.org/10.1016/j.socec.2014.05.002
3. Akiba, T., Sano, S., Yanase, T., Ohta, T., & Koyama, M. (2019). Optuna: A next-generation hyperparameter optimization framework. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD ’19), 2623–2631. Association for Computing Machinery. https://doi.org/10.1145/3292500.3330701
4. Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181–185. https://doi.org/10.1111/1467-8721.00196
5. Bandura, A. (1986). The explanatory and predictive scope of self-efficacy theory. Journal of Social and Clinical Psychology, 4(3), 359–373. https://doi.org/10.1521/jscp.1986.4.3.359
6. Bao, Y., & Wen, H. (2024). Research on prediction of anti-fraud in automobile finance based on XGBoost machine learning algorithm. Proceedings of the International Conference on Digital Economy, Blockchain and Artificial Intelligence (DEBAI 2024), 367–375. Association for Computing Machinery. https://doi.org/10.1145/3700058.3700116
7. Baskin, I. I., Marcou, G., Horvath, D., & Varnek, A. (2017). Stacking. In J. Bajorath (Ed.), Tutorials in chemoinformatics (pp. 271–278). Wiley. https://doi.org/10.1002/9781119161110.ch19
8. Bergstra, J., & Bengio, Y. (2012). Random search for hyper-parameter optimization. Journal of Machine Learning Research, 13, 281–305.

9. Breiman, L. (1996). Bagging predictors. Machine Learning, 24(2), 123–140. https://doi.org/10.1007/BF00058655
10. Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324
11. Breusch, T. S., & Pagan, A. R. (1979). A simple test for heteroscedasticity and random coefficient variation. Econometrica, 47(5), 1287–1294. https://doi.org/10.2307/1911963
12. Chatzimparmpas, A., Martins, R. M., Kucher, K., & Kerren, A. (2021). StackGenVis: Alignment of data, algorithms, and models for stacking ensemble learning using performance metrics. IEEE Transactions on Visualization and Computer Graphics, 27(2), 1547–1557. https://doi.org/10.1109/TVCG.2020.3030352
13. Chen, T., & Guestrin, C. (2016). XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD ’16), 785–794. Association for Computing Machinery. https://doi.org/10.1145/2939672.2939785
14. Cutler, D. R., Edwards, T. C., Beard, K. H., Cutler, A., Hess, K. T., Gibson, J., & Lawler, J. J. (2007). Random forests for classification in ecology. Ecology, 88(11), 2783–2792. https://doi.org/10.1890/07-0539.1
15. de Amorim, L. B., Cavalcanti, G. D. C., & Cruz, R. M. O. (2023). The choice of scaling technique matters for classification performance. Applied Soft Computing, 121, Article 109924. https://doi.org/10.1016/j.asoc.2022.109924
16. de Oña, J., & Garrido, C. (2014). Extracting the contribution of independent variables in neural network models: A new approach to handle instability. Neural Computing and Applications, 25(3–4), 859–869. https://doi.org/10.1007/s00521-014-1573-5
17. Desoete, A., & Veenman, M. V. J. (2006). Introduction. In A. Desoete & M. V. J. Veenman (Eds.), Metacognition in mathematics education (pp. 1–10). Nova Science.
18. Duff, A. (2004). Understanding academic performance and progression of first-year accounting and business economics undergraduates: The role of approaches to learning and prior academic achievement. Accounting Education, 13(4), 409–430. https://doi.org/10.1080/0963928042000306800
19. Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004). Least angle regression. Annals of Statistics, 32(2), 407–499. https://doi.org/10.1214/009053604000000067
20. Epifanio, I. (2017). Intervention in prediction measure: A new approach to assessing variable importance for random forests. BMC Bioinformatics, 18, Article 230. https://doi.org/10.1186/s12859-017-1650-8
21. Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London. Series A, 222, 309–368. https://doi.org/10.1098/rsta.1922.0009
22. Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231–235). Lawrence Erlbaum.
23. Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. Annals of Statistics, 29(5), 1189–1232. https://doi.org/10.1214/aos/1013203451
24. Friedman, J., Hastie, T., & Tibshirani, R. (2009). The elements of statistical learning (2nd ed.). Springer.
25. Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22. https://doi.org/10.18637/jss.v033.i01
26. Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association, 32(200), 675–701. https://doi.org/10.1080/01621459.1937.10503522
27. Garson, G. D. (1991). Interpreting neural-network connection weights. AI Expert, 6(4), 47–51.
28. Genuer, R., Poggi, J.-M., & Tuleau-Malot, C. (2010). Variable selection using random forests. Pattern Recognition Letters, 31(14), 2225–2236. https://doi.org/10.1016/j.patrec.2010.03.014
29. Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT Press.
30. Hastie, T., Tibshirani, R., & Friedman, J. (2021). The elements of statistical learning: Data mining, inference, and prediction (2nd ed., corrected printing). Springer. https://doi.org/10.1007/978-0-387-84858-7
31. Huber, P. J. (1981). Robust statistics. Wiley.
32. Huber, P. J., & Ronchetti, E. M. (2009). Robust statistics (2nd ed.). Wiley. https://doi.org/10.1002/9780470434697
33. Hussain, J. N. (2020). High dimensional data challenges in estimating multiple linear regression. Journal of Physics: Conference Series, 1591(1), 012035. https://doi.org/10.1088/1742-6596/1591/1/012035
34. İc, U., & Tutak, T. (2018). Correlation between computer and mathematical literacy levels of 6th grade students. European Journal of Educational Research, 7(2), 303–312. https://doi.org/10.12973/eu-jer.7.2.303
35. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2021). An introduction to statistical learning with applications in R (2nd ed.). Springer. https://doi.org/10.1007/978-1-0716-1418-1
36. Janitza, S., Strobl, C., & Boulesteix, A.-L. (2016). An AUC-based permutation variable importance measure for random forests. BMC Bioinformatics, 14, 119. https://doi.org/10.1186/1471-2105-14-119
37. Karakolidis, A., Pitsia, V., & Emvalotis, A. (2016). Mathematics low achievement in Greece: A multi-level analysis of the Programme for International Student Assessment (PISA) 2012 data. Themes in Science and Technology Education, 9(1), 3–24.
38. Karasar, N. (2022). Bilimsel araştırma yöntemi. Nobel Yayıncılık.
39. Kim, J. H. (2019). Multicollinearity and misleading statistical results. Korean Journal of Anesthesiology, 72(6), 558–569. https://doi.org/10.4097/kja.19087
40. Knisleya, J., Lee Glenn, L., Joplin, K., & Carey, P. (2007). Artificial neural networks for data mining and feature extraction. In Quantitative medical data analysis using mathematical tools and statistical techniques (pp. 321–332). World Scientific. https://doi.org/10.1142/9789812772121_0015
41. Kovacs, Z., Kantor, D. B., & Fekete, A. (2008). Comparison of quantitative determination techniques with electronic tongue measurements. In Proceedings of the American Society of Agricultural and Biological Engineers Annual International Meeting (ASABE 2008) (Vol. 11, pp. 6603–6615). American Society of Agricultural and Biological Engineers. https://doi.org/10.13031/2013.25381
42. Kowarik, A., & Templ, M. (2016). Imputation with the R package VIM. Journal of Statistical Software, 74(7), 1–16. https://doi.org/10.18637/jss.v074.i07
43. LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436–444. https://doi.org/10.1038/nature14539
44. Li, Y., Chen, C.-Y., & Wasserman, W. W. (2016). Deep feature selection: Theory and application to identify enhancers and promoters. Journal of Computational Biology, 23(5), 322–336. https://doi.org/10.1089/cmb.2015.0189
45. Li, J., Cheng, J., Shi, J., & Huang, F. (2016). Brief introduction of back propagation (BP) neural network algorithm and its improvement. In Advances in Computer Science and Information Engineering (pp. 553–558). Springer. https://doi.org/10.1007/978-3-642-30223-7_87
46. Liu, J., & Jia, C. (2022). A novel stacking ensemble learning framework for credit scoring. Applied Intelligence, 52(8), 7830–7844. https://doi.org/10.1007/s10489-021-02712-3
47. Lou, Y., & Colvin, K. F. (2025). Performance prediction using educational data mining techniques: A comparative study. Discover Education, 4(112). https://doi.org/10.1007/s44217-025-00502-w
48. Lundberg, S. M., & Lee, S.-I. (2017). A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems, 30, 4765–4774. https://papers.nips.cc/paper_files/paper/2017/file/8a20a8621978632d76c43dfd28b67767-Paper.pdf
49. Manzali, Y., & Elfar, M. (2023). Random forest pruning techniques: A recent review. Operations Research Forum, 4(2), 43. https://doi.org/10.1007/s43069-023-00223-6
50. Maronna, R. A., Martin, R. D., & Yohai, V. J. (2006). Robust statistics: Theory and methods. Wiley. https://doi.org/10.1002/0470010940
51. Menahem, E., Rokach, L., & Elovici, Y. (2009). Troika—An improved stacking schema for classification tasks. Information Sciences, 179(24), 4097–4122. https://doi.org/10.1016/j.ins.2009.08.025
52. Ministry of National Education [MEB]. (2023). PISA 2022 Türkiye Raporu. Ankara: MEB. https://pisa.meb.gov.tr
53. Moloi, T. (2011). Linking mathematical literacy to ICT: A good mix for community development in South Africa. In E. A. Odera (Ed.), Cases on developing countries and ICT integration: Rural community development (pp. 203–214). IGI Global. https://doi.org/10.4018/978-1-61692-842-9.ch013
54. Morony, S., Kleitman, S., Lee, Y. P., & Stankov, L. (2013). Predicting achievement: Confidence vs self-efficacy, anxiety, and self-concept in Confucian and European countries. International Journal of Educational Research, 58, 79–96. https://doi.org/10.1016/j.ijer.2012.11.002
55. Organization for Economic Co-operation and Development. (2019). PISA 2018 results: Where all students can succeed (Volume II): Equity in education. OECD Publishing. https://doi.org/10.1787/b5fd1b8f-en
56. Organization for Economic Co-operation and Development. (2021). PISA 2018 results (Volume I): What students know and can do. OECD Publishing. https://doi.org/10.1787/5f07c754-en
57. Organization for Economic Co-operation and Development. (2023a). PISA 2022 results (Volume I). OECD Publishing.
58. Organization for Economic Co-operation and Development. (2023b). PISA 2022 assessment and analytical framework. OECD Publishing. https://www.oecd.org/content/dam/oecd/en/publications/reports/2023/08/pisa-2022-assessment-and-analytical-framework_a124aec8/dfe0bf9c-en.pdf
59. Organisation for Economic Co-operation and Development [OECD]. (2023). PISA 2022 results (Volume I & II): Türkiye country note. OECD Publishing. https://www.oecd.org/pisa/publications
60. Organization for Economic Co-operation and Development. (2024). Bridging talent shortages in tech: Skills-first hiring, micro-credentials and inclusive outreach. OECD Publishing. https://doi.org/10.1787/f35da44f-en
61. Padilla, J. C. (2023). Multivariable regression models. In Translational sports medicine (pp. 141–143). Elsevier. https://doi.org/10.1016/B978-0-323-91259-4.00028-X
62. Patra, S. S., Jena, O. P., Kumar, G., Pramanik, S., Misra, C., & Singh, K. N. (2021). Random forest algorithm in imbalance genomics classification. In Data analytics in bioinformatics: A machine learning perspective (pp. 173–190). Wiley. https://doi.org/10.1002/9781119785620.ch7
63. Priscilla, C. V., & Prabha, D. P. (2020). Influence of optimizing XGBoost to handle class imbalance in credit card fraud detection. In Proceedings of the 3rd International Conference on Smart Systems and Inventive Technology (ICSSIT 2020) (pp. 1309–1315). IEEE. https://doi.org/10.1109/ICSSIT48917.2020.9214206
64. Probst, P., & Boulesteix, A.-L. (2018). To tune or not to tune the number of trees in random forest. Journal of Machine Learning Research, 18, 1–8.
65. Putatunda, S., & Rama, K. (2019). A modified Bayesian optimization based hyper-parameter tuning approach for extreme gradient boosting. In 2019 15th International Conference on Information Processing (ICInPro) (pp. 1–6). IEEE. https://doi.org/10.1109/ICInPro47689.2019.9092025
66. R Core Team. (2025). R: A language and environment for statistical computing. R Foundation for Statistical Computing.
67. Raglin, A., & Moraffah, R. (2023). Data integrity and artificial reasoning. In Proceedings of the 2023 IEEE 5th International Conference on Cognitive Machine Intelligence (CogMI) (pp. 93–96). IEEE. https://doi.org/10.1109/CogMI58952.2023.00022
68. Reinsel, G. C., Velu, R. P., & Chen, K. (2022). High-dimensional reduced-rank regression. In Lecture notes in statistics (Vol. 225, pp. 279–309). Springer. https://doi.org/10.1007/978-1-0716-2793-8_10
69. Rothacher, Y., & Strobl, C. (2024). Identifying informative predictor variables with random forests. Journal of Educational and Behavioral Statistics, 49(4), 595–629. https://doi.org/10.3102/10769986231193327
70. Rousseeuw, P. J. (1984). Least median of squares regression. Journal of the American Statistical Association, 79(388), 871–880. https://doi.org/10.1080/01621459.1984.10477105
71. Rousseeuw, P. J., & Van Driessen, K. (1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41(3), 212–223.
72. Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323(6088), 533–536. https://doi.org/10.1038/323533a0
73. Rusyana, A., Wigena, A. H., Sumertajaya, I. M., & Sartono, B. (2024). Unifying variable importance scores from different machine learning models using simulated annealing. Ingenierie des Systemes d’Information, 29(2), 649–657. https://doi.org/10.18280/isi.290226
74. Sagi, O., & Rokach, L. (2018). Ensemble learning: A survey. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 8(4), e1249. https://doi.org/10.1002/widm.1249
75. Schubert, E., & Gertz, M. (2017). Intrinsic t-stochastic neighbor embedding for visualization and outlier detection: A remedy against the curse of dimensionality? In Lecture notes in computer science (Vol. 10609, pp. 188–203). Springer. https://doi.org/10.1007/978-3-319-68474-1_13
76. Sirin, S. R. (2005). Socioeconomic status and academic achievement: A meta-analytic review of research. Review of Educational Research, 75(3), 417–453. https://doi.org/10.3102/00346543075003417
77. Sotiroudis, S. P., Goudos, S. K., & Siakavara, K. (2020). Feature importances: A tool to explain radio propagation and reduce model complexity. Telecom, 1(2), 9. https://doi.org/10.3390/telecom1020009
78. Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology, 15(1), 72–101. https://doi.org/10.2307/1412159
79. Stekhoven, D. J., & Bühlmann, P. (2012). MissForest—Non-parametric missing value imputation for mixed type data. Bioinformatics, 28(1), 112–118. https://doi.org/10.1093/bioinformatics/btr597
80. Sullivan, S. (2024). Correlational designs. In B. L. Hott, F. J. Brigham, & C. Peltier (Eds.), Research methods in special education (1st ed., chap. 7). Routledge. https://doi.org/10.4324/9781003526315
81. Talib, B. A., & Midi, H. (2009). Robust estimator to deal with regression models having both continuous and categorical regressors: A simulation study. Malaysian Journal of Mathematical Sciences, 3(2), 161–181.
82. Tierney, N., Cook, D., McBain, M., & Fay, C. (2023). naniar: Data structures, summaries, and visualisations for missing data (R package version).
83. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
84. van Buuren, S., & Groothuis-Oudshoorn, K. (2011). mice: Multivariate imputation by chained equations in R. Journal of Statistical Software, 45(3), 1–67. https://doi.org/10.18637/jss.v045.i03
85. Vecoven, N., Begon, J.-M., Sutera, A., Geurts, P., & Huynh-Thu, V. A. (2020). Nets versus trees for feature ranking and gene network inference. In Lecture notes in computer science (Vol. 12323, pp. 231–245). Springer. https://doi.org/10.1007/978-3-030-61527-7_16
86. Venables, W. N., & Ripley, B. D. (2002). Modern applied statistics with S (4th ed.). Springer. https://doi.org/10.1007/978-0-387-21706-2
88. Verma, M., Singh, S., & Agrawal, K. K. (2018). Investigation of multiple models of artificial neural networks. In 2018 International Conference on Intelligent Sustainable Systems (ICISS) (pp. 1062–1067). IEEE. https://doi.org/10.1109/ISS1.2017.8389343
89. Wang, D., & Yue, X. (2019). The weighted multiple meta-models stacking method for regression problem. In Proceedings of the Chinese Control Conference (CCC) (pp. 7511–7516). IEEE. https://doi.org/10.23919/ChiCC.2019.8865869
90. Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80–93. https://doi.org/10.2307/3001968
91. Wolpert, D. H. (1992). Stacked generalization. Neural Networks, 5(2), 241–259. https://doi.org/10.1016/S0893-6080(05)80023-1
92. Wright, M. N., & Ziegler, A. (2017). ranger: A fast implementation of random forests for high dimensional data in C++ and R. Journal of Statistical Software, 77(1), 1–17. https://doi.org/10.18637/jss.v077.i01
93. Wu, M. (2005). The role of plausible values in large-scale surveys. Studies in Educational Evaluation, 31(2–3), 114–128. https://doi.org/10.1016/j.stueduc.2005.05.005
94. Yan, K. (2021). Student performance prediction using XGBoost method from a macro perspective. In Proceedings of the 2021 2nd International Conference on Computing and Data Science (CDS 2021) (pp. 453–459). IEEE. https://doi.org/10.1109/CDS52072.2021.00084
95. Yohai, V. J. (1987). High breakdown-point and high efficiency estimates for regression. Annals of Statistics, 15(2), 642–656. https://doi.org/10.1214/aos/1176350366
96. Zhang, W., Li, H., Han, L., Chen, L., & Wang, L. (2022). Slope stability prediction using ensemble learning techniques: A case study in Yunyang County, Chongqing, China. Journal of Rock Mechanics and Geotechnical Engineering, 14(4), 1089–1099. https://doi.org/10.1016/j.jrmge.2021.12.011
97. Zheng, S., Huang, T., Yang, R., Li, L., Qiao, M., Chen, C., & Lyu, J. (2021). Validation of multivariate selection method in clinical prediction models: Based on MIMIC database [多变量选择方法在临床预测模型中的验证：基于 MIMIC 数据库]. Chinese Journal of Evidence-Based Medicine, 21(12), 1463–1467. https://doi.org/10.7507/1672-2531.202107175
98. Zheng, X., Wang, Y., Jia, L., Xiong, D., & Qiang, J. (2020). Network intrusion detection model based on Chi-square test and stacking approach. In Proceedings of the 7th International Conference on Information Science and Control Engineering (ICISCE) (pp. 894–899). IEEE. https://doi.org/10.1109/ICISCE50968.2020.00185
99. Zhou, Y., Liu, T., Wang, J., & Cheng, J. (2024). Fast classification model based on genetic algorithm and XGBoost–RandomForest stacking model. In Proceedings of the 14th International Conference on Information Science and Technology (ICIST 2024) (pp. 7–12). IEEE. https://doi.org/10.1109/ICIST63249.2024.10805304
100. Zhu, T. (2020). Analysis on the applicability of the random forest. Journal of Physics: Conference Series, 1607(1), 012123. https://doi.org/10.1088/1742-6596/1607/1/012123
101. Ziegler, A., & König, I. R. (2014). Mining data with random forests: Current options for real-world applications. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 4(1), 55–63. https://doi.org/10.1002/widm.1114
102. Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 301–320. https://doi.org/10.1111/j.1467-9868.2005.00503.x
103. Zounemat-Kermani, M., Batelaan, O., Fadaee, M., & Hinkelmann, R. (2021). Ensemble machine learning paradigms in hydrology: A review. Journal of Hydrology, 598, 126266. https://doi.org/10.1016/j.j.jhydrol.2021.126266