Comparing Rasch measurement and factor analysis

This article illustrates how Rasch measurement is preferable to factor analysis for reducing complex data matrices to unidimensional variables. The two methods: (a) address the same kind of data, but with different interpretations of numerical status; (b) use the same estimation methods, but with different measurement models; and (c) solve the same problems, but with substantially different utility. Factor analysis is faulted for mistaking ordinally labeled stochastic observations for linear measures and for failing to construct linear measurement. The motivation and mathematical basis for Rasch measurement are introduced. How to use Rasch measurement to replace factor analysis is developed for a dichotomy and demonstrated for a rating scale.