The causal effect of class size on academic achievement: Multivariate instrumental variable estimators with data missing at random

Journal of Educational and Behavioral Statistics

Volumn 36, Issue 2, 2011, Pages 154-185

  Shin, Yongyun ^a   Raudenbush, Stephen W ^b  

^a VIRGINIA COMMONWEALTH UNIVERSITY   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

causal effect; class size; ignorable missing data; instrumental variable; maximum likelihood; simultaneous equation model

Indexed keywords

EID: 79955051771     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/1076998610388632     Document Type: Article

References (56)

1. Angrist, J.D., & Imbens, G.W. (1995). Two-stage least squares estimation of average causal effects in models with variable treatment intensity. Journal of the American Statistical Association, 90, 431-442.
2. Angrist, J.D., Imbens, G.W., & Rubin, D.B. (1996). Identification of causal effects using instrumental variables. Journal of the American Statistical Association, 91, 444-455.
3. Arbuckle, J.L. (1996). Full information estimation in the presence of incomplete data. In G. A. Marcoulides & R. E. Schumacker (Ed.), Advanced structural equation modeling: Issues and techniques. Mahwah, NJ: Lawrence Erlbaum.
4. Bentler, P. (1995). EQS structural equations program manual. Encino, CA: Multivariate Software.
5. Bollen, K.A. (1989). Structural equations with latent variables. New York: John Wiley & Sons.
6. Bollen, K.A. (1996). An alternative two stage least squares estimator for latent variable equations. Psychometrika, 61, 109-121.
7. Bollen, K.A., Kirby, J.B., Curran, P.J., Paxton, P.M., & Chen, F. (2007). Latent variable models under misspecification: Two-stage least squares and maximum likelihood estimators. Sociological Methods & Research, 36, 48-86.
8. Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of Reliability and Statistical Studies, 76, 1-38.
9. Dempster, A.P., Rubin, D.B., & Tsutakawa, R.K. (1981). Estimation in covariance components models. Journal of the American Statistical Association, 76, 341-353.
10. Ecob, R., & Goldstein, H. (1983). Instrumental variable methods for the estimation of test score reliability. Journal of Educational Statistics, 8, 223-241.
11. Finn, J.D., & Achilles, C.M. (1990). Answers and questions about class size: A statewide experiment. American Educational Research Journal, 27, 557-577.
12. Finn, J.D., Boyd-Zaharias, J., Fish, R.M., & Gerber, S.B. (2007). Project STAR and beyond: Database user's guide. Lebanon, TN: HEROS.
13. Frangakis, C.E., Brookmeyer, R.S., Varadhan, R., Mahboobeh, S., Valhov, D., & Strathdee, S.A. (2004). Methodology for evaluating a partially controlled longitudinal treatment using principal stratification, with application to a needle exchange program. Journal of the American Statistical Association, 99, 239-249.
14. Frangakis, C.E., & Rubin, D.B. (1999). Addressing complications of intention-to-treat analysis in the combined presence of all-or-none treatment-noncompliance and subsequent missing outcomes. Biometrika, 86, 365-379.
15. Frangakis, C.E., & Rubin, D.B. (2002). Principal stratification in causal inference. Biometrics, 58, 21-29.
16. Frangakis, C.E., Rubin, D.B., & Zhou, X. (2002). Clustered encouragement designs with individual noncompliance: Bayesian inference with randomization, and application to advance directive forms. Biostatistics, 3, 147-164.
17. Goldstein, H. (2003). Multilevel statistical models. London, England: Edward Arnold.
18. Goldstein, H., & Blatchford, P. (1998). Class size and educational achievement: A review of methodology with particular reference to study design. British Educational Research Journal, 24, 255-268.
19. Goldstein, H., Yang, M., Omar, R., Turner, R., & Thompson, S. (2000). Meta-analysis using multilevel models with an application to the study of class size effects. Journal of Reliability and Statistical Studies, 49, 399-412.
20. Greene, W.H. (2002). Econometric analysis. Upper Saddle River, NJ: Prentice Hall.
21. Hanushek, E.A. (1999). Some findings from an independent investigation of the Tennessee STAR experiment and from other investigations of class size effects. Educational Evaluation and Policy Analysis, 21, 143-163.
22. Holland, P.W. (1986). Statistics and causal inference. Journal of the American Statistical Association, 81, 945-970.
23. Hong, G., & Raudenbush, S.W. (2006). Evaluating kindergarten retention policy: A case study of causal inference for multilevel observational data. Journal of the American Statistical Association, 101, 901-910.
24. Jöreskog, K.G., & Sörbom, D. (1996). LISREL 8. Chicago, IL: Scientific Software International.
25. Imbens, G.W., & Rubin, D.B. (1997a). Bayesian inference for causal effects in randomized experiments with noncompliance. The Annals of Statistics, 25, 305-327.
26. Imbens, G.W., & Rubin, D.B. (1997b). Estimating outcome distributions for compliers in instrumental variables models. Review of Economic Studies, 64, 555-574.
27. Kaplan, D. (2000). Structural equation modeling: Foundations and extensions. Newbury Park, CA: Sage.
28. Krueger, A.B. (1999). Experimental estimates of education production functions. Quarterly Journal of Economics, 114, 497-532.
29. Krueger, A.B., & Whitmore, D.M. (2001). The effect of attending a small class in the early grades on college-test taking and middle school test results: Evidence from project STAR. The Economic Journal, 111, 1-28.
30. Little, R.J.A., & Rubin, D.B. (2002). Statistical analysis with missing data. New York, NY: Wiley.
31. Little, R.J.A., & Yau, L.H.Y. (1998). Statistical techniques for analyzing data from prevention trials: Treatment of no-shows using Rubin's causal model. Psychological Methods, 3, 147-159.
32. Liu, M., Taylor, J.M.G., & Belin, T.R. (2000). Multiple imputation and posterior simulation for multivariate missing data in longitudinal studies. Biometrics, 56, 1157-1163.
33. Longford, N.T. (1987). A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects. Biometrika, 74, 817-827.
34. Magnus, J.R., & Neudecker, H. (1988). Matrix differential calculus with applications in statistics and econometrics. New York: Wiley.
35. Mealli, F., Imbens, G.W., Ferro, S., & Biggeri, A. (2004). Analyzing a randomized trial on breast self-examination with noncompliance and missing outcomes. Biostatistics, 5, 207-222.
36. Milesi, C., & Gamoran, A. (2006). Effects of class size and instruction on kindergarten achievement. Educational Evaluation and Policy Analysis, 28, 287-313.
37. Mosteller, F. (1995). The Tennessee study of class size in the early school grades. The Future of Children: Critical Issues for Children and Youths, 5, 113-127.
38. Muthén, B.O. (1994). Multilevel covariance structure analysis. Sociological Methods and Research, 22, 376-398.
39. Nye, B., Hedges, L.V., & Konstantopoulos, S. (1999). The long-term effects of small classes: A five-year follow-up of the Tennessee class size experiment. Educational Evaluation and Policy Analysis, 21, 127-142.
40. Nye, B., Hedges, L.V., & Konstantopoulos, S. (2000). The effects of small classes on academic achievement: The results of the Tennessee class size experiment. American Educational Research Journal, 1, 123-151.
41. Nye, B., Konstantopoulos, S., & Hedges, L.V. (2004). How large are teacher effects? Educational Evaluation and Policy Analysis, 26, 237-257.
42. Orchard, T., & Woodbury, M.A. (1972). A missing information principle: Theory and applications. Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, 1, 697-715.
43. Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge, UK: Cambridge University Press.
44. Pinheiro, J.C., & Bates, D.M. (2000). Mixed-effects models in S and S-plus. New York, NY: Springer.
45. Raudenbush, S.W., & Bryk, A.S. (2002). Hierarchical linear models. Newbury Park, CA: Sage.
46. Raudenbush, S.W., Bryk, A.S., Cheong, Y., & Congdon, R.T. (2004). HLM 6: Hierarchical linear and nonlinear modeling. Lincolnwood, IL: Scientific Software International.
47. Raudenbush, S.W., & Sampson, R. (1999). Assessing direct and indirect effects in multilevel designs with latent variables. Sociological Methods & Research, 28, 123-153.
48. Rubin, D.B. (1976). Inference and missing data. Biometrika, 63, 581-592.
49. Rubin, D.B. (1978). Bayesian inference for causal effects: The role of randomization. The Annals of Statistics, 6, 34-58.
50. Rubin, D.B. (1987). Multiple imputation for nonresponse in surveys. New York, NY: John Wiley.
51. Schafer, J.L. (1997). Analysis of incomplete multivariate data. London, UK: Chapman & Hall.
52. Schafer, J.L., & Yucel, R.M. (2002). Computational strategies for multivariate linear mixed-effects models with missing values. Journal of the Computational and Graphical Statistics, 11, 437-457.
53. Shin, Y., & Raudenbush, S.W. (2007). Just-identified versus over-identified two-level hierarchical linear models with missing data. Biometrics, 63, 1262-1268.
54. Stolzenberg, R.M., & Waite, L.J. (1977). Age, fertility expectations and plans for employment. American Sociological Review, 42, 769-783.
55. Verbitsky, N., & Raudenbush, S.W. (2004). Causal inference in spatial setting. Proceedings of the Social Statistics Section, American Statistical Association, 2369-2374.
56. Word, E., Johnston, J., Bain, H., Fulton, B., Zaharias, J., Achilles, C., Lintz, M., Folger, J., & Breda, C. (1990). The state of Tennessee's Student/Teacher Achievement Ratio (STAR) project: Final summary report 1985-1990. Nashville: Tennessee State Department of Education.