
Assessing the Causal Effect of Special Education Services on Math Achievement: A Causal Inference and Machine Learning Study
- 1 The Chinese University of Hong Kong
* Author to whom correspondence should be addressed.
Abstract
This study aims to assess the Average Treatment Effect (ATE) of receiving special education services on revised Item Response Theory (IRT) scaled math achievement test scores. By employing a methodological repertoire comprising linear regression with ordinary least squares (OLS), propensity score matching (PSM), Bayesian Additive Regression Trees (BART), and Multilayer Perceptron (MLP), we examine the impact of these interventions. Leveraging data from the Early Childhood Longitudinal Study Kindergarten 2010-11 cohort (ECLS-K:2011), we systematically analyze the ATE of special education services on students' math achievement. The results show that all models yield negative ATE results, suggesting a deleterious effect of special education services on fifth-grade math scores. Furthermore, we employ Principal Component Analysis (PCA) to corroborate these findings, aligning with outcomes obtained from causal inference and Machine Learning (ML) based methods. This research emphasizes the importance of method diversity in educational research and highlights the need for assessments of intervention effectiveness to help educational practices and policies.
Keywords
causal inference, machine learning, early childhood longitudinal study kindergarten (ECLS-K), average treatment effect (ATE)
[1]. Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of educational Psychology, 66(5), 688.
[2]. Rubin, D. B. (1977). Assignment to treatment group on the basis of a covariate. Journal of educational Statistics, 2(1), 1-26.
[3]. Rubin, D. B. (1978). Bayesian inference for causal effects: The role of randomization. The Annals of statistics, 34-58.
[4]. Rubin, D. B. (1980). Randomization analysis of experimental data: The Fisher randomization test comment. Journal of the American statistical association, 75(371), 591-593.
[5]. Rubin, D. B. (2005). Causal inference using potential outcomes: Design, modeling, decisions. Journal of the American Statistical Association, 100(469), 322-331.
[6]. Pearl, J. (2018). Theoretical impediments to machine learning with seven sparks from the causal revolution. arXiv preprint arXiv:1801.04016.
[7]. Fisher, R. A. (1956). Statistical methods and scientific inference.
[8]. Splawa-Neyman, J., Dabrowska, D. M., & Speed, T. P. (1990). On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Statistical Science, 465-472.
[9]. Pearl, J., & Shafer, G. (1995). Probabilistic reasoning in intelligent systems: Networks of plausible inference. Synthese-Dordrecht, 104(1), 161.
[10]. Holland, P. W. (1986). Statistics and causal inference. Journal of the American statistical Association, 81(396), 945-960
[11]. Abadie, A., Angrist, J., & Imbens, G. (2002). Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings. Econometrica, 70(1), 91-117.
[12]. Imbens, G. W. (2004). Nonparametric estimation of average treatment effects under exogeneity: A review. Review of Economics and statistics, 86(1), 4-29.
[13]. Imbens, G. W., & Rubin, D. B. (2015). Causal inference in statistics, social, and biomedical sciences. Cambridge university press.
[14]. Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41-55.
[15]. Hitchcock, C. (2020). Communicating causal structure. In Perspectives on Causation: selected papers from the Jerusalem 2017 workshop (pp. 53-71). Springer International Publishing.
[16]. Prosperi, M., Guo, Y., Sperrin, M., Koopman, J. S., Min, J. S., He, X., ... & Bian, J. (2020). Causal inference and counterfactual prediction in machine learning for actionable healthcare. Nature Machine Intelligence, 2(7), 369-375.
[17]. Pearl, J. (2019). The seven tools of causal inference, with reflections on machine learning. Communications of the ACM, 62(3), 54-60.
[18]. Grimmer, J. (2015). We are all social scientists now: How big data, machine learning, and causal inference work together. PS: Political Science & Politics, 48(1), 80-83.
[19]. Athey, S. (2015, August). Machine learning and causal inference for policy evaluation. In Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining (pp. 5-6).
[20]. Hair Jr, J. F., & Sarstedt, M. (2021). Data, measurement, and causal inferences in machine learning: opportunities and challenges for marketing. Journal of Marketing Theory and Practice, 29(1), 65-77.
[21]. Ramachandra, V. (2018). Deep learning for causal inference. arXiv preprint arXiv:1803.00149.
[22]. Kreif, N., & DiazOrdaz, K. (2019). Machine learning in policy evaluation: new tools for causal inference. arXiv preprint arXiv:1903.00402.
[23]. Pearl, J. (2018). Theoretical impediments to machine learning with seven sparks from the causal revolution. arXiv preprint arXiv:1801.04016.
[24]. Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis. John Wiley & Sons.
[25]. Schaffrin, B., & Wieser, A. (2008). On weighted total least-squares adjustment for linear regression. Journal of geodesy, 82, 415-421.
[26]. Caliendo, M., & Kopeinig, S. (2008). Some practical guidance for the implementation of propensity score matching. Journal of economic surveys, 22(1), 31-72.
[27]. Abadie, A., & Imbens, G. W. (2016). Matching on the estimated propensity score. Econometrica, 84(2), 781-807.
[28]. Sperandei, S. (2014). Understanding logistic regression analysis. Biochemia medica, 24(1), 12-18.
[29]. Pregibon, D. (1981). Logistic regression diagnostics. The annals of statistics, 9(4), 705-724.
[30]. Gourieroux, C., & Monfort, A. (1981). Asymptotic properties of the maximum likelihood estimator in dichotomous logit models. Journal of Econometrics, 17(1), 83-97.
[31]. Moré, J. J., & Sorensen, D. C. (1982). Newton's method (No. ANL-82-8). Argonne National Lab.(ANL), Argonne, IL (United States).
[32]. Berahas, A. S., Bollapragada, R., & Nocedal, J. (2020). An investigation of Newton-sketch and subsampled Newton methods. Optimization Methods and Software, 35(4), 661-680.
[33]. Schmidt, M., Kim, D., & Sra, S. (2011). Projected Newton-type methods in machine learning.
[34]. Kent, D. M., & Hayward, R. A. (2007). Limitations of applying summary results of clinical trials to individual patients: the need for risk stratification. Jama, 298(10), 1209-1212.
[35]. Guo, G., Wang, H., Bell, D., Bi, Y., & Greer, K. (2003). KNN model-based approach in classification. In On The Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE: OTM Confederated International Conferences, CoopIS, DOA, and ODBASE 2003, Catania, Sicily, Italy, November 3-7, 2003. Proceedings (pp. 986-996). Springer Berlin Heidelberg.
[36]. Zhang, M. L., & Zhou, Z. H. (2007). ML-KNN: A lazy learning approach to multi-label learning. Pattern recognition, 40(7), 2038-2048.
[37]. Chipman, H. A., George, E. I., & McCulloch, R. E. (2010). BART: Bayesian additive regression trees.
[38]. Gardner, M. W., & Dorling, S. R. (1998). Artificial neural networks (the multilayer perceptron)—a review of applications in the atmospheric sciences. Atmospheric environment, 32(14-15), 2627-2636.
[39]. Popescu, M. C., Balas, V. E., Perescu-Popescu, L., & Mastorakis, N. (2009). Multilayer perceptron and neural networks. WSEAS Transactions on Circuits and Systems, 8(7), 579-588.
[40]. Cimpian, J. R., Lubienski, S. T., Timmer, J. D., Makowski, M. B., & Miller, E. K. (2016). Have gender gaps in math closed? Achievement, teacher perceptions, and learning behaviors across two ECLS-K cohorts. AERA Open, 2(4), 2332858416673617.
[41]. Little, M. (2017). Racial and socioeconomic gaps in executive function skills in early elementary school: Nationally representative evidence from the ECLS-K: 2011. Educational Researcher, 46(2), 103-109.
Cite this article
Li,L. (2024). Assessing the Causal Effect of Special Education Services on Math Achievement: A Causal Inference and Machine Learning Study. Advances in Social Behavior Research,7,20-27.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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