[Rasch] About invariance of measure: Is it possible to locate an author?

Trevor Bond trevor.bond at jcu.edu.au
Fri Sep 18 19:23:07 EST 2009

Agustin asked:
If somebody has further documentation about invariance of item calibration over time and position, 
please let me know.
I think this is a remarkable piece of work:

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 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. Finally, 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).
                                  Bond & Fox, 2007, p91

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,

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