extended · conference_paper · 1993

Constructing Linear Measures from Counts of Qualitative Observations.

John M. Linacre; Benjamin D. Wright

Disorder and linearity are essential to science, but empirically derived laws indicate that counts do reflect underlying structure and can support inference. Starting from the premise that a linear structure underlies data, G. Rasch deduced that the necessary and sufficient mechanism to convert from counts to linear measures is the logistic ogive. Because linearity, and not mere numerosity, is what nearly all widely used statistical procedures assume of their data, Rasch theory enables the construction of linear measures from ordinal counts. Three variants of the Rasch model are presented for the following items: (1) dichotomies; (2) Poisson counts; and (3) rating scales. The need for data to cooperate in the construction of measures motivates the assessment and selection of useful data by means of quality control fit statistics. Rasch measurement is successfully used in many fields wher...