Bayesian Analysis of Item Response Theory Models Using SAS®

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Assessment has played and continues to play an integral role in society and in a culture of inquiry.
Accordingly, numerous instruments have been developed over the years to measure many different
characteristics of individuals in the educational, psychological, health, social, and behavioral sciences.
These instruments have been used to measure the status or level of different characteristics in individuals,
as well as to capture differences in these characteristics across individuals.
To support the development of instruments and measure characteristics in individuals, test theories have
been used to describe how inferences, predictions, or estimates of a particular characteristic, trait, or ability
of a person may be made from responses to items. Test theories such as classical test theory (CTT) and
item response theory (IRT) provide models for explaining test performance in relation to variables that are
assumed to influence behavior. They provide methods for selecting items, evaluating tests or scales,
obtaining scores, and quantifying sources of errors in the measurement process. In the early decades of the
21st century, psychometricians have favored IRT, as opposed to CTT, in scale development and assessment
applications.
IRT models consist of a family of mathematical models that predict item performance by using parameters
that characterize both the items in an instrument and the respondents. Although numerous methods for
estimating the parameters of IRT models exist, interest in estimating the parameters using Bayesian
methods has grown tremendously. In part, this growth is due to the appeal of the Bayesian paradigm among
psychometricians and statisticians, as well as to the advantages of these methods with small sample sizes,
more complex or highly parameterized models (such as multidimensional IRT models), and interest in
simultaneous estimation of item and person parameters. In contrast to traditional approaches for estimating
model parameters, a Bayesian paradigm considers model parameters to be random variables and uses Bayes
theorem to obtain distributions for the model parameters.
Recently, routines have become available in the SAS system software to implement general Bayesian
analyses (PROC MCMC). Use of the SAS system for Bayesian analysis of IRT models has several
significant advantages over other available programs: (1) It is commonly used by researchers across
disciplines; (2) it provides a robust programming language that extends the capability of the program—in
particular, the capability for model checking; and (3) it shows increased performance and efficiency
through the use of parallel processing. The purpose of this book is to illustrate Bayesian estimation and
evaluation of a variety of IRT models that are of interest to psychometricians, scale developers, and
practitioners responsible for implementing assessment programs.

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关键词：Bayesian response Analysis Analysi alysis