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Adjusting for measurement error in the value added model: evidence from Portugal

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The multilevel value added approach to measuring school effectiveness is now widely used. We propose a method to adjust for measurement error to investigate the extent to which this changes school effect estimates. It is applied to longitudinal data collected in the region of Cova da Beira (NUT III) for 1st, 3rd, 5th, 7th and 8th grades. Three different variance component models are considered, depending on the predictor variables included. Assuming measurement error occurs in explanatory and/or response variables, corrections are made for different values of the coefficient of reliability. Moreover, models are fitted under the assumption of either independent or correlated measurement errors.

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  • Aitkin, M., Longford, N.: Statistical modelling issues in school effectiveness studies. J. Roy. Stat. Soc. A 149, 1–43 (1986)

    Article  Google Scholar 

  • Braun, H., Wainer, H.: Value-Added Modeling. In: Rao, C.R., Sinharay, S. (eds.) Handbook of Statistics 26, Psychometrics, pp. 475–501. Elsevier (2007)

  • Ferrão, M.E., Costa, P., Dias, V., Dias, M.: Medição da competência dos alunos do ensino básico em Matemática: 3EMat, uma proposta. [Measuring math skills of students in compulsory education: 3EMat, a proposal]. In: Actas da XI Conferência Internacional de Avaliação Psicológica Proceedings of the XI International Conference on Psychological Evaluation, Braga, Portugal, 5–8 October 2006

  • Fielding, A., Yang, M., Goldstein, H.: Multilevel ordinal models for examination grades. Stat. Model. 3, 127–153 (2003)

    Article  Google Scholar 

  • Goldstein, H.: Methods in school effectiveness research. School Effectiv. School Improv. 8, 369–395 (1997)

    Article  Google Scholar 

  • Goldstein, H.: Multilevel Statistical Models, 3rd edn. Edward Arnold, London (2003)

    Google Scholar 

  • Goldstein, H., Spiegelhalter, D.J.: League tables and their limitations: statistical issues in comparison of institutional performance. J. Roy. Stat. Soc. A 159, 385–443 (1996)

    Article  Google Scholar 

  • Goldstein, H., Browne, W., Rasbash, J.: Partitioning variation in multilevel models. Understand. Stat. 2, 223–232 (2002)

    Article  Google Scholar 

  • Goldstein, H., Rasbash, J., Yang, M., Woodhouse, G., Pan, H., Nuttal, D., Thomas, S.: A multilevel analysis of school examination results. Oxford Rev. Educ. 19, 425–433 (1993)

    Article  Google Scholar 

  • Goldstein, H., Kounali, D., Robinson, A.: Modelling measurement errors and category misclassifications in multilevel models. Statistical Modelling. (to appear)

  • Ladd, H.F., Walsh, R.P.: Implementing value-added measures of school effectiveness: getting the incentives right. Econ. Educ. Rev. 21, 1–17 (2002)

    Article  Google Scholar 

  • Little, R.J.A., Rubin, D.B.: Statistical Analysis with Missing Data, 2nd edn. Wiley, New York (2002)

    Google Scholar 

  • Lord, F.M., Novick, M.R.: Statistical Theories of Mental Test Scores. Addison-Wesley Publishing, Reading, Massachusetts (1968)

    Google Scholar 

  • McPherson, A.: Measuring Added Value in Schools (NCE briefing 1). National Commission on Education, London (1992)

    Google Scholar 

  • Mortimore, P., Sammons, P., Stoll, L., Lewis, D., Ecob, R.: School Matters. Open Books, Wells (1988)

    Google Scholar 

  • Raudenbush, S.W., e Willms, J.D.: The estimation of school effects. J. Educ. Behav. Stat. 20(4), 307–335 (1995)

    Google Scholar 

  • Rubin, D.B., Stuart, E.A., Zanutto, E.L.: A potential outcomes view of value-added assessment in Education. J. Educ. Behav. Stat. 29(1), 103–116 (2004)

    Article  Google Scholar 

  • Scheerens, J.: Effective Schooling: Research, Theory and Practice. Cassell, London (1992)

    Google Scholar 

  • Vicente, P.: Plano amostral do projecto 3EM—Eficáca Escolar no Ensino da Matemática In: Ferrão, M.E., Nunes, C., Braumann, C. (eds.) Estatística: Ciência Interdisciplinar, Proceedings of the XIV Annual Conference of the Portuguese Statistical Society. SPE, Lisboa (2007)

  • Willims, J.D., Raudenbush, S.W.: A longtitudinal hierarchial linear model for estimating school effects and their stability. J. Educ. Meas. 26, 209–232 (1989)

    Article  Google Scholar 

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Correspondence to Maria Eugénia Ferrão.

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Ferrão, M.E., Goldstein, H. Adjusting for measurement error in the value added model: evidence from Portugal. Qual Quant 43, 951–963 (2009).

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