### Frank Baker's "Basics of Item Response Theory"

Dennis Roberts writes: "ericae.net/irt/baker/ is a link to the full text of Frank Baker's classic little book on Basics of Item Response Theory (1985) ... with his old software included! This is provided by the ERIC Clearinghouse on Assessment and Evaluation."

The complete text of the revised and updated 2001 edition can be studied one screen at a time, or the entire book can be downloaded as one pdf file.

This book views the "Rasch or One-Parameter, Logistic Model" as a special case of Birnbaum's 3-PL model. Here is what is stated on page 25:

"The next model of interest was first published by the Danish mathematician Georg Rasch in the 1960s. Rasch approached the analysis of test data from a probability theory point of view. Although he started from a very different frame of reference, the resultant item characteristic curve model was a logistic model. ... Under this model, the discrimination parameter of the two-parameter logistic model is fixed at a value of a = 1.0 for all items; only the difficulty parameter can take on different values. Because of this, the Rasch model is often referred to as the one-parameter logistic model.

"The equation for the Rasch model is given by the following:

"where: b is the difficulty parameter and θ is the ability level.

"It should be noted that a discrimination parameter ["1"] was used in [the] equation, but because it always has a value of 1.0, it usually is not shown in the formula."

[Thus Baker's presentation of the Rasch model follows IRT conventions, but somewhat idiosyncratically.]

Frank Baker - Basics of Item Response Theory. Baker F. … 16:1 p.869

Frank Baker - Basics of Item Response Theory. Baker F. … Rasch Measurement Transactions, 2002, 16:1 p.869

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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