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Selected Papers on the Measurement of Change

 The following papers on measuring change can be downloaded as pdf files, by clicking on their respective titles. The papers have been presented in reverse chronological order.

In some cases, you can also access the website of the associated journal by clicking on the journal name.

Willett, J. B.  (1997).  Measuring Change: What Individual Growth Modeling Buys You. In E. Amsel and K. A. Renninger (Eds.), Change and Development: Issues of Theory, Method, and Application. Mahwah, NJ: Lawrence Erlbaum Associates, Chapter 11, 213-243.

A lengthier version of Willett (1994), produced for a different audience, describing the benefits of using individual growth modeling in the analysis of change.

Willett, J. B.  (1994).  Measurement of Change.  In T. Husen and T. N. Postlethwaite (Eds.), International Encyclopedia of Education, 2nd. Edition.  Oxford, UK: Elsevier Science Press, 671-678.

A short non-technical overview of, and general introduction to, the benefits of individual growth modeling as the preferred method for the measurement of change.

Willett, J. B.  (1989).  Some Results On Reliability For The Longitudinal Measurement Of Change: Implications For The Design Of Studies Of Individual Growth.  Educational and Psychological Measurement, 49, 587-602.

A short paper showing how the reliability of of individual change measurement depends dramatically on the frequency and spacing of the waves of data used in the analysis.  The paper illustrates the extent of the improvement in reliability for the measurement of change that can be achieved by adding one or two extra waves of data collection to a traditional two-wave design.

Willett, J. B.  (1989).  Questions And Answers In The Measurement Of Change.  In Ernest Z. Rothkopf (Ed.), Review of Research in Education, Volume 15.  Washington, D.C.: American Education Research Association, 345-422.

A lengthy (and tediously complete) overview of issues, problems, and misconceptions in the measurement of change.  The paper contrasts data-analytic approaches using two-wave and multi-wave data, and illustrates how the latter wins out in the end.  It also debunks several of the standard myths about the measurement of change.

Rogosa, D. R., and Willett, J. B.  (1985).  Understanding Correlates Of Change By Modeling Individual Differences In Growth.  Psychometrika, 50, 203-228.

A technical exposition of how the relationship between individual change and its correlates/predictors can be represented in a multilevel model, and how this specification illuminates traditional (and often inappropriate) approaches to the problem of investigating change.  The paper also comments on the relationship between change and initial status, on the notion of linear and non-linear change, and on the flaws that exist in a variety of common residual change strategies.

Rogosa, D. R., and Willett, J. B.  (1985).  Satisfying a Simplex Structure Is Simpler Than It Should Be.  Journal of Educational Statistics, 10(2), 99-107.

Markedly different types of growth (learning) curves may generate indistinguishable covariance structures. We illustrate with an example of a 5x5 covariance matrix representing longitudinal measurements at five occasions. This examples appears to conform closely to a simplex correlation pattern, and a simplex covariance structure provides an excellent fit with LISREL V. However, the known structure of this example differs greatly from a simplex model. In addition to illustrating that the excellent fit of a simplex structure can be misleading, this example provides an opportunity to question common uses of covariance structure models for the study of growth.

Rogosa, D. R., Floden, R., and Willett, J. B.  (1984).  Assessing the Stability of Teacher Behavior.  Journal of Educational Psychology, 76(6), 1000-1027.

The study of the stability of teacher behavior over time is formulated through two questions: Is the behavior of an individual teach consistent over time? and, Are individual differences among teachers consistent over time? The first question has rarefly been addressed in previous investigations of the stability of teacher behavior, and empirical research on the second question has been confused. We develop statistical procedures for addressing both questions. The approaches of previous studies of temporal stability are re-evaluated and methods for assessing the stability of teacher behavior across contexts are described and illustrated with data.

Rogosa, D. R., and Willett, J. B.  (1983).  Demonstrating The Reliability Of The Difference Score In The Measurement Of Change.  Journal of Educational Measurement, 20, 335-343.

This short paper disputes the standard myth that difference scores are "always unreliable," using both an algebraic argument and a worked example.

Contact me: John_Willett@Harvard.Edu

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