Estimating reliability statistics and measurement error variances using instrumental variables with longitudinal data

Journal article


Goldstein, Harvey, Haynes, Michele, Leckie, George and Tran, Phuong 2020. Estimating reliability statistics and measurement error variances using instrumental variables with longitudinal data. Longitudinal and Life Course Studies. 11 (3), pp. 289 - 306. https://doi.org/10.1332/175795920X15844303873216
AuthorsGoldstein, Harvey, Haynes, Michele, Leckie, George and Tran, Phuong
Abstract

The presence of randomly distributed measurement errors in scale scores such as those used in educational and behavioural assessments implies that careful adjustments are required to statistical model estimation procedures if inferences are required for ‘true’ as opposed to ‘observed’ relationships. In many cases this requires the use of external values for ‘reliability’ statistics or ‘measurement error variances’ which may be provided by a test constructor or else inferred or estimated by the data analyst. Popular measures are those described as ‘internal consistency’ estimates and sometimes other measures based on data grouping. All such measures, however, make particular assumptions that may be questionable but are often not examined. In this paper we focus on scaled scores derived from aggregating a set of indicators, and set out a general methodological framework for exploring different ways of estimating reliability statistics and measurement error variances, critiquing certain approaches and suggesting more satisfactory methods in the presence of longitudinal data. In particular, we explore the assumption of local (conditional) item response independence and show how a failure of this assumption can lead to biased estimates in statistical models using scaled scores as explanatory variables. We illustrate our methods using a large longitudinal data set of mathematics test scores from Queensland, Australia.

Keywordsinstrumental variables; longitudinal data; reliability
Year2020
JournalLongitudinal and Life Course Studies
Journal citation11 (3), pp. 289 - 306
PublisherPolicy Press
ISSN1757-9597
Digital Object Identifier (DOI)https://doi.org/10.1332/175795920X15844303873216
Page range289 - 306
Research GroupInstitute for Learning Sciences and Teacher Education (ILSTE)
Place of publicationUnited Kingdom
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Leckie, George and Goldstein, Harvey 2011. A note on 'The limitations of school league tables to inform school choice'. Journal of the Royal Statistical Society Series A: Statistics in Society. 174 (3), pp. 833 - 836. https://doi.org/10.1111/j.1467-985X.2010.00688.x
Estimating research performance by using research grant award gradings
Goldstein, Harvey 2011. Estimating research performance by using research grant award gradings. Journal of the Royal Statistical Society Series A: Statistics in Society. 174 (1), pp. 83 - 93. https://doi.org/10.1111/j.1467-985X.2010.00657.x
Increasing explanatory behaviour, problem-solving, and reasoning within classes using cooperative group work
Gillies, Robyn and Haynes, Michele 2011. Increasing explanatory behaviour, problem-solving, and reasoning within classes using cooperative group work. Instructional Science. 39 (3), pp. 349 - 366. https://doi.org/10.1007/s11251-010-9130-9
Cognitive development and down syndrome: Age-related change on the Stanford-Binet test (fourth edition)
Couzens, Donna, Cuskelly, Monica and Haynes, Michele 2011. Cognitive development and down syndrome: Age-related change on the Stanford-Binet test (fourth edition). American Journal on Intellectual and Developmental Disabilities. 116 (3), pp. 181 - 204. https://doi.org/10.1352/1944-7558-116.3.181
Understanding uncertainty in school league tables
Leckie, George and Goldstein, Harvey 2011. Understanding uncertainty in school league tables. Fiscal Studies. 32 (2), pp. 207 - 224. https://doi.org/10.1111/j.1475-5890.2011.00133.x
Patchwork intermediation: Challenges and opportunities for regionally coordinated workforce development
Lowe, Nichola, Goldstein, Harvey and Donegan, Mary 2011. Patchwork intermediation: Challenges and opportunities for regionally coordinated workforce development. Economic Development Quarterly: the journal of American economic revitalization. 25 (2), pp. 158 - 171. https://doi.org/10.1177/0891242410383413
Sleep, structured and social time use and young Australian children's physical activity
Yu, Mong L., Ziviani, Jenny and Haynes, Michele 2011. Sleep, structured and social time use and young Australian children's physical activity. Health Promotion Journal of Australia. 22 (3), pp. 203 - 209.
Pupil composition and accountability: An analysis in English primary schools
Kounali, Daphne, Robinson, Anthony, Lauder, Hugh and Goldstein, Harvey 2010. Pupil composition and accountability: An analysis in English primary schools. International Journal of Educational Research. 49 (2-3), pp. 49 - 68. https://doi.org/10.1016/j.ijer.2010.08.001
MCMC sampling for a multilevel model with nonindependent residuals within and between cluster units
Browne, William and Goldstein, Harvey 2010. MCMC sampling for a multilevel model with nonindependent residuals within and between cluster units. Journal of Educational and Behavioral Statistics. 35 (4), pp. 453 - 473. https://doi.org/10.3102/1076998609359788
Pupil composition and accountability: An analysis in English primary schools
Lauder, Hugh, Kounali, Daphne, Robinson, Anthony and Goldstein, Harvey 2010. Pupil composition and accountability: An analysis in English primary schools. International Journal of Educational Research. 45 (2-3), pp. 49 - 68. https://doi.org/10.1016/j.ijer.2010.08.001
Statistical modelling of repeated measurement data
Goldstein, Harvey 2010. Statistical modelling of repeated measurement data. Longitudinal and Life Course Studies. 1 (2), pp. 170 - 185. https://doi.org/10.14301/llcs.v1i2.67
Handling attrition and non-response in longitudinal data
Goldstein, Harvey 2009. Handling attrition and non-response in longitudinal data. Longitudinal and Life Course Studies.
Multilevel multivariate modelling of childhood growth, numbers of growth measurements and adult characteristics
Goldstein, Harvey and Kounali, Daphne 2009. Multilevel multivariate modelling of childhood growth, numbers of growth measurements and adult characteristics. Royal Statistical Society. Journal. Series A: Statistics in Society.
Multilevel models with multivariate mixed response types
Goldstein, Harvey, Carpenter, James R., Kenward, Michael G. and Levin, Kate A. 2009. Multilevel models with multivariate mixed response types. Statistical Modelling.
Comment peut-on utiliser les etudes comparatives internationales pour doter les politiques educatives d'information fiables?
Goldstein, Harvey 2009. Comment peut-on utiliser les etudes comparatives internationales pour doter les politiques educatives d'information fiables? Revue Francaise de Pedagogie.
Comment: Citation Statistics
Goldstein, Harvey and Spiegelhalter, David 2009. Comment: Citation Statistics. Statistical Science.
The limitations of using school league tables to inform school choice
Leckie, George and Goldstein, Harvey 2009. The limitations of using school league tables to inform school choice. Royal Statistical Society. Journal. Series A: Statistics in Society.
Evidence and education policy - some reflections and allegations
Goldstein, Harvey 2008. Evidence and education policy - some reflections and allegations. Cambridge Journal of Education.
Adjusting for measurement error in the value added model: evidence from Portugal
Ferrao, Maria Eugenia and Goldstein, Harvey 2008. Adjusting for measurement error in the value added model: evidence from Portugal. Quality and Quantity. 43, pp. 951 - 963. https://doi.org/10.1007/s11135-008-9171-1
Review of 'Monitoring Educational Achievement'
Goldstein, Harvey 2008. Review of 'Monitoring Educational Achievement'. International Journal of Educational Development.
Modelling measurement errors and category misclassifications in multilevel models
Goldstein, Harvey, Kounali, Daphne and Robinson, Anthony 2008. Modelling measurement errors and category misclassifications in multilevel models. Statistical Modelling.
School league tables: what can they really tell us?
Goldstein, Harvey 2008. School league tables: what can they really tell us? Significance.
The effects of year repetition (redoublement) on the progress of pupils in the first three years of French schooling
Goldstein, Harvey 2008. The effects of year repetition (redoublement) on the progress of pupils in the first three years of French schooling.
Techniques for Monitoring the Comparability of Examination Standards
Goldstein, Harvey 2007. Techniques for Monitoring the Comparability of Examination Standards. United Kingdom: Qualifications and Curriculum Authority.