IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v39y2014i1p22-52.html
   My bibliography  Save this article

Correcting for Test Score Measurement Error in ANCOVA Models for Estimating Treatment Effects

Author

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

Abstract

A common strategy for estimating treatment effects in observational studies using individual student-level data is analysis of covariance (ANCOVA) or hierarchical variants of it, in which outcomes (often standardized test scores) are regressed on pretreatment test scores, other student characteristics, and treatment group indicators. Measurement error in the prior test scores, which typically is both large and heteroscedastic, is regularly overlooked in empirical analyses and may erode the ability of regression models to adjust for student factors and may result in biased treatment effect estimates. We develop extensions of method-of-moments, Simulation-Extrapolation, and latent regression approaches to correcting for measurement error using the conditional standard errors of measure of test scores, and demonstrate their effectiveness relative to simpler alternatives using both simulation and a case study of teacher value-added effect estimation using longitudinal data from a large suburban school district.

Suggested Citation

  • J. R. Lockwood & Daniel F. McCaffrey, 2014. "Correcting for Test Score Measurement Error in ANCOVA Models for Estimating Treatment Effects," Journal of Educational and Behavioral Statistics, , vol. 39(1), pages 22-52, February.
    • Handle: RePEc:sae:jedbes:v:39:y:2014:i:1:p:22-52
    DOI: 10.3102/1076998613509405
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998613509405
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998613509405?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. Roger Millsap, 2007. "Invariance in Measurement and Prediction Revisited," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 461-473, December.
    2. Derek C. Briggs & Jonathan P. Weeks, 2009. "The Sensitivity of Value-Added Modeling to the Creation of a Vertical Score Scale," Education Finance and Policy, MIT Press, vol. 4(4), pages 384-414, October.
    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. Jean-Paul Fox & Cees Glas, 2003. "Bayesian modeling of measurement error in predictor variables using item response theory," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 169-191, June.
    5. Donald Boyd & Hamilton Lankford & Susanna Loeb & James Wyckoff, 2012. "Measuring Test Measurement Error: A General Approach," NBER Working Papers 18010, National Bureau of Economic Research, Inc.
    6. Silvia Bianconcini & Silvia Cagnone, 2012. "A General Multivariate Latent Growth Model With Applications to Student Achievement," Journal of Educational and Behavioral Statistics, , vol. 37(2), pages 339-364, April.
    7. Devanarayan, Viswanath & Stefanski, Leonard A., 2002. "Empirical simulation extrapolation for measurement error models with replicate measurements," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 219-225, October.
    8. 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.
    9. White, Halbert, 1983. "Corrigendum [Maximum Likelihood Estimation of Misspecified Models]," Econometrica, Econometric Society, vol. 51(2), pages 513-513, March.
    10. Cory Koedel & Julian Betts, 2007. "Re-Examining the Role of Teacher Quality In the Educational Production Function," Working Papers 0708, Department of Economics, University of Missouri.
    11. Kata Mihaly & Daniel F. McCaffrey & J. R. Lockwood & Tim R. Sass, 2010. "Centering and reference groups for estimates of fixed effects: Modifications to felsdvreg," Stata Journal, StataCorp LLC, vol. 10(1), pages 82-103, March.
    12. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "GLLAMM Manual," U.C. Berkeley Division of Biostatistics Working Paper Series 1160, Berkeley Electronic Press.
    13. 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.
    14. Kilchan Choi & Michael Seltzer, 2010. "Modeling Heterogeneity in Relationships Between Initial Status and Rates of Change: Treating Latent Variable Regression Coefficients as Random Coefficients in a Three-Level Hierarchical Model," Journal of Educational and Behavioral Statistics, , vol. 35(1), pages 54-91, February.
    15. Brian Junker & Lynne Schofield & Lowell Taylor, 2012. "The use of cognitive ability measures as explanatory variables in regression analysis," IZA Journal of Labor Economics, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 1(1), pages 1-19, December.
    16. Dale Ballou, 2009. "Test Scaling and Value-Added Measurement," Education Finance and Policy, MIT Press, vol. 4(4), pages 351-383, October.
    17. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    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. Stacy, Brian & Guarino, Cassandra & Wooldridge, Jeffrey, 2018. "Does the precision and stability of value-added estimates of teacher performance depend on the types of students they serve?," Economics of Education Review, Elsevier, vol. 64(C), pages 50-74.
    2. Hwanhee Hong & Kara E. Rudolph & Elizabeth A. Stuart, 2017. "Bayesian Approach for Addressing Differential Covariate Measurement Error in Propensity Score Methods," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1078-1096, December.
    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. Backes, Ben & Cowan, James & Goldhaber, Dan & Koedel, Cory & Miller, Luke C. & Xu, Zeyu, 2018. "The common core conundrum: To what extent should we worry that changes to assessments will affect test-based measures of teacher performance?," Economics of Education Review, Elsevier, vol. 62(C), pages 48-65.
    5. 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.

    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. 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.
    3. Chun Wang & Gongjun Xu & Xue Zhang, 2019. "Correction for Item Response Theory Latent Trait Measurement Error in Linear Mixed Effects Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 673-700, September.
    4. Cory Koedel & Jiaxi Li, 2016. "The Efficiency Implications Of Using Proportional Evaluations To Shape The Teaching Workforce," Contemporary Economic Policy, Western Economic Association International, vol. 34(1), pages 47-62, January.
    5. Koedel, Cory & Mihaly, Kata & Rockoff, Jonah E., 2015. "Value-added modeling: A review," Economics of Education Review, Elsevier, vol. 47(C), pages 180-195.
    6. 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.
    7. Das, Debojyoti & Bhatia, Vaneet & Kumar, Surya Bhushan & Basu, Sankarshan, 2022. "Do precious metals hedge crude oil volatility jumps?," International Review of Financial Analysis, Elsevier, vol. 83(C).
    8. P.A.V.B. Swamy & I-Lok Chang & Jatinder S. Mehta & William H. Greene & Stephen G. Hall & George S. Tavlas, 2016. "Removing Specification Errors from the Usual Formulation of Binary Choice Models," Econometrics, MDPI, vol. 4(2), pages 1-21, June.
    9. Carlo Altavilla & Raffaella Giacomini & Giuseppe Ragusa, 2017. "Anchoring the yield curve using survey expectations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1055-1068, September.
    10. Fernando Rios-Avila & Gustavo J. Canavire-Bacarreza, 2017. "Standard Error Correction in Two-Stage Optimization Models: A Quasi-Maximum Likelihood Estimation Approach," Documentos de Trabajo de Valor Público 15659, Universidad EAFIT.
    11. Sandy Fréret & Denis Maguain, 2017. "The effects of agglomeration on tax competition: evidence from a two-regime spatial panel model on French data," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(6), pages 1100-1140, December.
    12. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    13. Ayouz, Mourad K. & Remaud, Herve, 2003. "The Internationalization Determinants Of The Small Agro-Food Firms: Hypotheses And Statistical Tests," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association, vol. 5(2), pages 1-27.
    14. Broze, Laurence & Gourieroux, Christian, 1998. "Pseudo-maximum likelihood method, adjusted pseudo-maximum likelihood method and covariance estimators," Journal of Econometrics, Elsevier, vol. 85(1), pages 75-98, July.
    15. Sridhar, Shrihari & Naik, Prasad A. & Kelkar, Ajay, 2017. "Metrics unreliability and marketing overspending," International Journal of Research in Marketing, Elsevier, vol. 34(4), pages 761-779.
    16. Yen, Steven T. & Chern, Wen S. & Lee, Hwang-Jaw, 1991. "Effects Of Income Sources On Household Food Expenditures," 1991 Annual Meeting, August 4-7, Manhattan, Kansas 271167, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    17. Ruoxuan Xiong & Allison Koenecke & Michael Powell & Zhu Shen & Joshua T. Vogelstein & Susan Athey, 2021. "Federated Causal Inference in Heterogeneous Observational Data," Papers 2107.11732, arXiv.org, revised Apr 2023.
    18. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    19. Koutmos, Dimitrios, 2012. "An intertemporal capital asset pricing model with heterogeneous expectations," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(5), pages 1176-1187.
    20. Gregory, Allan W. & McCurdy, Thomas H., 1986. "The unbiasedness hypothesis in the forward foreign exchange market: A specification analysis with application to France, Italy, Japan, the United Kingdom and West Germany," European Economic Review, Elsevier, vol. 30(2), pages 365-381, April.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:jedbes:v:39:y:2014:i:1:p:22-52. 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.