Question: How would a unidimensional model deal with something like the SAT, PISA, or any instrument that has strong multidimensional aspects? My response would be that we should separate the subject matter, but established instruments like these will likely not be changed in order to conform to unidimensional requirements.
Answer: The original thermometers, in the earlier 1600s, were multidimensional. They were open-ended glass tubes that combined the measurement of heat and of atmospheric pressure. Imagine if physicists around 1650 had said "our established open-tube thermometers will likely not be changed in order to conform with unidimensional (heat or atmospheric pressure) requirements."
Now, compare progress in the last 100 years for the social and physical sciences. Which science has the more effective methodology? Could social science research have done worse if it had imposed the unidimensional rigor of physical science upon itself?
SAT scores are treated as though they are unidimensional, so the SAT should be designed that way. Of course, "unidimensional" depends somewhat on the context. In the context of learning difficulties, "subtraction" is a dimension. In the context of academic achievement, "math" is a dimension. It is the same in physics; in some situations, "heat transmission by radiation", "heat transmission by conduction" and "heat transmission by convection" are different dimensions, but, for most purposes, "heat" is one dimension.
John M. Linacre
Rasch Q&A: empirical multidimensionality or imposed unidimensionality? John M. Linacre Rasch Measurement Transactions, 2012, 26:2 p. 1372
Please help with Standard Dataset 4: Andrich Rating Scale Model
|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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