Invariance and Item Stability

Kingsbury's (2003) study of the long term stability of item parameter estimates in achievement testing has a number of important features.

First, rather than using parameter estimates from a set of items used in a single test, it investigated the stability of item parameter estimates in two large item banks used by the Northwest Evaluation Association (NWEA) to measure achievement in mathematics (> 2300 items) and reading (c.1400 items) with students from school years 2-10 in seven US states. Sample sizes for the 1999-2000 school year item calibrations ranged from 300 to 10,000 students.

Second, the elapsed time since initial calibration ranged from 7 to 22 years.

Third, and most importantly (for these purposes), "the one-parameter logistic (1PL) IRT model (Wright, 1977) was used to create and maintain the underlying measurement scales used with these banks." While thousands of items have been added to these item banks over the course of time, each item has been connected to the original measurement scale through the use of IRT procedures and systematic Rasch measurement practices (Ingebo, 1997).

The observed correlations between the original and new item difficulties were extremely high (.967 in mathematics, .976 in reading), more like what would be expected if items were given to two samples at the same time, rather than samples separated by a time span from 7 to 20 years. Over that period, the average drift in the item difficulty parameters was .01 standard deviations of the mean item difficulty estimate. In Rasch measurement terms (i.e., focusing on impact on the measurement scales), the largest observed change in student scores moving from the original calibrations to the new calibrations was at the level of the minimal possible difference detectable by the tests, with over 99% of expected changes being less than the minimal detectable difference (Kingsbury, 2003).

NWEA have demonstrated measure-invariance beyond anything achieved anywhere else in the human sciences.

Trevor Bond

Hong Kong Institute of Education

Ingebo, G. S. (1997). Probability in the measure of achievement. Chicago, IL: MESA Press.

Kingsbury, G. (2003, April). A long-term study of the stability of item parameter estimates. Paper presented at the annual meeting of the American Educational Research Association, Chicago.

Wright, B.D. (1977). Solving Measurement Problems with the Rasch model. Journal of Educational Measurement, 14(2), 97-116.

Invariance and Item Stability. Bond, T. … Rasch Measurement Transactions, 2008, 22:1 p. 1159


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Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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