IDEAS home Printed from https://ideas.repec.org/a/sae/evarev/v43y2019i6p335-369.html
   My bibliography  Save this article

Impact Evaluation Using Analysis of Covariance With Error-Prone Covariates That Violate Surrogacy

Author

Listed:
  • J. R. Lockwood
  • Daniel F. McCaffrey

Abstract

Background: Analysis of covariance (ANCOVA) is commonly used to adjust for potential confounders in observational studies of intervention effects. Measurement error in the covariates used in ANCOVA models can lead to inconsistent estimators of intervention effects. While errors-in-variables (EIV) regression can restore consistency, it requires surrogacy assumptions for the error-prone covariates that may be violated in practical settings. Objectives: The objectives of this article are (1) to derive asymptotic results for ANCOVA using EIV regression when measurement errors may not satisfy the standard surrogacy assumptions and (2) to demonstrate how these results can be used to explore the potential bias from ANCOVA models that either ignore measurement error by using ordinary least squares (OLS) regression or use EIV regression when its required assumptions do not hold. Results: The article derives asymptotic results for ANCOVA with error-prone covariates that cover a variety of cases relevant to applications. It then uses the results in a case study of choosing among ANCOVA model specifications for estimating teacher effects using longitudinal data from a large urban school system. It finds evidence that estimates of teacher effects computed using EIV regression may have smaller bias than estimates computed using OLS regression when the data available for adjusting for students’ prior achievement are limited.

Suggested Citation

  • J. R. Lockwood & Daniel F. McCaffrey, 2019. "Impact Evaluation Using Analysis of Covariance With Error-Prone Covariates That Violate Surrogacy," Evaluation Review, , vol. 43(6), pages 335-369, December.
    • Handle: RePEc:sae:evarev:v:43:y:2019:i:6:p:335-369
    DOI: 10.1177/0193841X19877969
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0193841X19877969
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0193841X19877969?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Tahir Andrabi & Jishnu Das & Asim Ijaz Khwaja & Tristan Zajonc, 2011. "Do Value-Added Estimates Add Value? Accounting for Learning Dynamics," American Economic Journal: Applied Economics, American Economic Association, vol. 3(3), pages 29-54, July.
    2. Harris, Douglas N. & Sass, Tim R., 2011. "Teacher training, teacher quality and student achievement," Journal of Public Economics, Elsevier, vol. 95(7-8), pages 798-812, August.
    3. Jesse Rothstein, 2009. "Student Sorting and Bias in Value-Added Estimation: Selection on Observables and Unobservables," Education Finance and Policy, MIT Press, vol. 4(4), pages 537-571, October.
    4. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    5. repec:mpr:mprres:7943 is not listed on IDEAS
    6. Yang L. & Tsiatis A. A., 2001. "Efficiency Study of Estimators for a Treatment Effect in a Pretest-Posttest Trial," The American Statistician, American Statistical Association, vol. 55, pages 314-321, November.
    7. Sass, Tim R. & Hannaway, Jane & Xu, Zeyu & Figlio, David N. & Feng, Li, 2012. "Value added of teachers in high-poverty schools and lower poverty schools," Journal of Urban Economics, Elsevier, vol. 72(2), pages 104-122.
    8. Peter M. Steiner & Thomas D. Cook & William R. Shadish, 2011. "On the Importance of Reliable Covariate Measurement in Selection Bias Adjustments Using Propensity Scores," Journal of Educational and Behavioral Statistics, , vol. 36(2), pages 213-236, April.
    9. Marie-Ann Sengewald & Steffi Pohl, 2019. "Compensation and Amplification of Attenuation Bias in Causal Effect Estimates," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 589-610, June.
    10. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    11. Daniel F. McCaffrey & J. R. Lockwood & Claude M. Setodji, 2013. "Inverse probability weighting with error-prone covariates," Biometrika, Biometrika Trust, vol. 100(3), pages 671-680.
    12. J. R. Lockwood & Daniel F. McCaffrey, 2016. "Matching and Weighting With Functions of Error-Prone Covariates for Causal Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1831-1839, October.
    13. Charles T. Clotfelter & Helen F. Ladd & Jacob L. Vigdor, 2006. "Teacher-Student Matching and the Assessment of Teacher Effectiveness," Journal of Human Resources, University of Wisconsin Press, vol. 41(4).
    14. Manabu Kuroki & Judea Pearl, 2014. "Measurement bias and effect restoration in causal inference," Biometrika, Biometrika Trust, vol. 101(2), pages 423-437.
    15. Grace Y. Yi & Yanyuan Ma & Raymond J. Carroll, 2012. "A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error," Biometrika, Biometrika Trust, vol. 99(1), pages 151-165.
    16. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    17. J. R. Lockwood & Daniel F. McCaffrey, 2017. "Simulation-Extrapolation with Latent Heteroskedastic Error Variance," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 717-736, September.
    18. Matthew T. Johnson & Stephen Lipscomb & Brian Gill, 2015. "Sensitivity of Teacher Value-Added Estimates to Student and Peer Control Variables (Journal Article)," Mathematica Policy Research Reports 4a9776a57ae9477e80df47e7d, Mathematica Policy Research.
    19. repec:mpr:mprres:7942 is not listed on IDEAS
    20. Dan Goldhaber & Michael Hansen, 2010. "Using Performance on the Job to Inform Teacher Tenure Decisions," American Economic Review, American Economic Association, vol. 100(2), pages 250-255, May.
    21. John P. Papay & Richard J. Murnane & John B. Willett, 2016. "The Impact of Test Score Labels on Human-Capital Investment Decisions," Journal of Human Resources, University of Wisconsin Press, vol. 51(2), pages 357-388.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. J. R. Lockwood & D. McCaffrey, 2020. "Using hidden information and performance level boundaries to study student–teacher assignments: implications for estimating teacher causal effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1333-1362, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. R. Lockwood & D. McCaffrey, 2020. "Using hidden information and performance level boundaries to study student–teacher assignments: implications for estimating teacher causal effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1333-1362, October.
    2. Marie-Ann Sengewald & Steffi Pohl, 2019. "Compensation and Amplification of Attenuation Bias in Causal Effect Estimates," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 589-610, June.
    3. Koedel, Cory & Mihaly, Kata & Rockoff, Jonah E., 2015. "Value-added modeling: A review," Economics of Education Review, Elsevier, vol. 47(C), pages 180-195.
    4. Trang Quynh Nguyen & Elizabeth A. Stuart, 2020. "Propensity Score Analysis With Latent Covariates: Measurement Error Bias Correction Using the Covariate’s Posterior Mean, aka the Inclusive Factor Score," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 598-636, October.
    5. Koedel Cory & Leatherman Rebecca & Parsons Eric, 2012. "Test Measurement Error and Inference from Value-Added Models," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-37, November.
    6. Hermann, Zoltán & Horváth, Hedvig, 2022. "Tanári eredményesség és tanár-diák összepárosítás az általános iskolákban. Empirikus mintázatok három magyarországi tankerület adatai alapján [Teacher effectiveness and teacher-student matching in ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(11), pages 1377-1406.
    7. Eric Parsons & Cory Koedel & Li Tan, 2019. "Accounting for Student Disadvantage in Value-Added Models," Journal of Educational and Behavioral Statistics, , vol. 44(2), pages 144-179, April.
    8. Canales, Andrea & Maldonado, Luis, 2018. "Teacher quality and student achievement in Chile: Linking teachers' contribution and observable characteristics," International Journal of Educational Development, Elsevier, vol. 60(C), pages 33-50.
    9. Nirav Mehta, 2019. "Measuring quality for use in incentive schemes: The case of “shrinkage” estimators," Quantitative Economics, Econometric Society, vol. 10(4), pages 1537-1577, November.
    10. Figlio, D. & Karbownik, K. & Salvanes, K.G., 2016. "Education Research and Administrative Data," Handbook of the Economics of Education,, Elsevier.
    11. Maria D. Fitzpatrick & Michael F. Lovenheim, 2014. "Early Retirement Incentives and Student Achievement," American Economic Journal: Economic Policy, American Economic Association, vol. 6(3), pages 120-154, August.
    12. Nirav Mehta, 2019. "Measuring quality for use in incentive schemes: The case of “shrinkage” estimators," Quantitative Economics, Econometric Society, vol. 10(4), pages 1537-1577, November.
    13. Cory Koedel & Eric Parsons & Michael Podgursky & Mark Ehlert, 2015. "Teacher Preparation Programs and Teacher Quality: Are There Real Differences Across Programs?," Education Finance and Policy, MIT Press, vol. 10(4), pages 508-534, October.
    14. Hinrichs, Peter, 2021. "What kind of teachers are schools looking for? Evidence from a randomized field experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 186(C), pages 395-411.
    15. Jesse Rothstein, 2010. "Teacher Quality in Educational Production: Tracking, Decay, and Student Achievement," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(1), pages 175-214.
    16. Cory Koedel & Mark Ehlert & Eric Parsons & Michael Podgursky, 2012. "Selecting Growth Measures for School and Teacher Evaluations," Working Papers 1210, Department of Economics, University of Missouri.
    17. Johan Coenen & Ilja Cornelisz & Wim Groot & Henriette Maassen van den Brink & Chris Van Klaveren, 2018. "Teacher Characteristics And Their Effects On Student Test Scores: A Systematic Review," Journal of Economic Surveys, Wiley Blackwell, vol. 32(3), pages 848-877, July.
    18. Peter Z. Schochet, "undated". "Statistical Theory for the RCT-YES Software: Design-Based Causal Inference for RCTs," Mathematica Policy Research Reports a0c005c003c242308a92c02dc, Mathematica Policy Research.
    19. Qin, Lixia & Bowen, Daniel H., 2019. "The distributions of teacher qualification: A cross-national study," International Journal of Educational Development, Elsevier, vol. 70(C), pages 1-1.
    20. Keller, Bryan & Wong, Vivian C & Park, Sangbaek & Zhang, Jingru & Sheehan, Patrick & Steiner, Peter M., 2024. "A new four-arm within-study comparison: Design, implementation, and data," OSF Preprints 2gur9, Center for Open Science.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:evarev:v:43:y:2019:i:6:p:335-369. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.