Complex IRT = Simple Rasch

Reise et al. (2001) present what, at first blush, appears to be a complex multi-group IRT analysis, defying objective measurement criteria and beyond the capabilities of standard Rasch software. But closer inspection reveals that their analysis is Wright and Stone (1979) p. 94 redivivus.

Reise at al. administer the same instrument, comprising multiple "facet" strands, to two gender groups, male and female. They want to examine differential test functioning. Here is the core of their description of what they did using PARSCALE:

"First, within each facet scale we estimated a multiple-group IRT model in which the item location parameters ((λi) were freely estimated within groups and all slope parameters (ai) and category parameters ((τiv) were constrained to equality across gender. In this multiple-group model the mean and standard deviation on the latent variable is fixed at 0 and 1 for men but are estimated parameters for women." (p. 96).

Let us deconstruct this paragraph:

"within each facet scale" - i.e., analyzing one strand at a time.

"item location parameters ((λi) were freely estimated within groups" - since the groups share no common persons, this is equivalent to doing separate gender-group analyses.

"all slope parameters (ai) and category parameters ((τiv) were constrained to equality across gender." - these are exactly the specifications for an "Andrich Rating Scale" Rasch analysis of a gender group.

"In this multiple-group model the mean and standard deviation on the latent variable is fixed at 0 and 1 for men" - so the scale origin is chosen so that the mean measure for men is zero, and the measure scaling factor is 1/(men s.d.).

"but are estimated parameters for women." - so the mean of the women's measures is relative to the men's mean, and the men's scaling factor is applied to the women's analysis.

Further, inspection of the Tables in Reise et al. reveals that, for each "facet" strand, the mean of the item location parameters for the men and the women is constrained to be the same.

So, what analysis did Reise et al. actually perform? Two separate "Andrich" Rasch analyses in which the item means are constrained to be the same (the Rasch default), and the scaling factor for both analyses is chosen such that the "men" group's standard deviation is 1.

Moral of the story: if you need to squeeze a "parallel runs" Rasch DIF analysis passed reluctant reviewers, dress it up with a light reworking of another sentence from Reise et al. (p. 96):

"The DIF detection procedure implemented [here is similar to that implemented] by PARSCALE (Muraki & Bock, 1998) [and] is similar to the DIF detection routine implemented by BILOG-MG (Zimowski, Muraki, Mislevy, & Bock, 1996) in that ... maximum likelihood estimation routines are used and contrasts of item parameter estimates are developed."

And then paste in your own version of the Reise et al. paragraph quoted above!

John Michael Linacre
Courtesy of Deon De Bruin

Muraki, E. & Bock, R. D. (1998). PARSCALE (version 3.5): Parameter scaling of rating data. Chicago, IL: Scientific Software, Inc.

Reise, S.P., Smith, L., Furr, R.M. (2001) Invariance on the NEO PI-R Neuroticism Scale. Multivariate Behavioral Research, 36 (1), 83-110

Zimowski, M. F., Muraki, E., Mislevy, R. J., & Bock, R. D. (1996). BILOG-MG: Multiple-Group IRT Analysis and Test Maintenance for Binary Items. Chicago, IL: Scientific Software International.

Available Rasch software is listed at

Complex IRT = Simple Rasch, Linacre J.M., Reise S.P., De Bruin D. … Rasch Measurement Transactions, 2003, 17:3 p.934-934

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
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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