The Theory and Practice of Item Response Theory
Item response theory (IRT) is a latent variable modeling approach used to minimize bias and optimize the measurement power of educational and psychological tests and other psychometric applications.Designed for researchers, psychometric professionals, and advanced students, this book clearly presents both the "how-to" and the "why" of IRT. It describes simple and more complex IRT models and shows how they are applied with the help of widely available software packages. Chapters follow a consistent format and build sequentially, taking the reader from model development through the fit analysis and interpretation phases that one would perform in practice. The use of common empirical data sets across the chapters facilitates understanding of the various models and how they relate to one another.
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Conceptual Development of the TwoParameter Model
Metric Transformation 2PL Model
Information and Relative Efficiency
The ThreeParameter Model
Rasch Models for Ordered Polytomous Data
NonRasch Models for Ordered Polytomous Data
Models for Nominal Polytomous Data
Models for Multidimensional Data
11 Linking and Equating
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ˆ θ ˆδ ˆθ 2PL model analysis approach assumption BIGSTEPS BILOG category score Chapter characteristic function coefficient command file conditional independence Condoms continuum convergence correlation corresponding dichotomous discrimination parameter Equation examination example Figure focal group GR model indicates individual’s individuals INFIT information function instrument IRFs IRT model item discrimination item information item location item parameter estimates item response item’s iterations JMLE labeled latent class latent variable likelihood function location parameters log likelihood logistic mathematics maximum measurement metric MMLE model calibration model–data fit monotonically nonincreasing multidimensional MULTILOG NOHARM normal ogive normally distributed number of items observed score obtain ORFs output partial credit PC model person location estimates polytomous prior distribution probability proficiency Rasch model regression response categories response pattern response vector result sample scale slope specifies standard error sufficient statistic Table tion total information transition locations two-parameter unidimensional values