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\title{Rasch Measurement Theory Analysis in R: Illustrations and
Practical Guidance for Researchers and Practitioners}
\author{Stefanie A. Wind \& Cheng Hua}
\date{2021-10-22}

\begin{document}
\maketitle

\hypertarget{introduction}{%
\section{Introduction}\label{introduction}}

The purpose of this book is to illustrate techniques for conducting
Rasch measurement theory (\protect\hyperlink{ref-Rasch_ori}{Rasch 1960})
analyses using existing R packages. The book includes some background
information about Rasch models, and the primary objective is to
demonstrate how to apply the models to data using R packages and how to
interpret the results.

The primary audience for this book is graduate students or professionals
who are familiar with Rasch measurement theory at a basic level, and who
want to use the R software program (\protect\hyperlink{ref-R_base}{R
Core Team 2021}) to conduct their Rasch analyses. We provide a brief
overview of several key features of Rasch measurement theory in this
chapter, and we provide descriptions of basic characteristics of the
models and analytic techniques in each of the following chapters.
Accordingly, we encourage readers who are new to Rasch measurement
theory to use this book as a supplement to other excellent introductory
texts on the subject that include a detailed theoretical and statistical
introduction to Rasch measurement. For example, interested readers may
find the following texts useful to begin learning about Rasch
measurement theory:

(\protect\hyperlink{ref-A_Course}{Andrich and Marais 2019})

\begin{quote}
Andrich, David, and Ida Marais. 2019. \emph{A Course in Rasch
Measurement Theory: Measuring in the Educational, Social and Health
Sciences.} Singapore: Springer.
\end{quote}

(\protect\hyperlink{ref-Applying_RM2019}{Bond, Yan, and Heene 2019})

\begin{quote}
Bond, Trevor G., Zi Yan, and Moritz Heene. 2019. \emph{Applying the
Rasch Model: Fundamental Measurement in the Human Sciences (4th Ed.)}.
New York: Routledge, Taylor \& Francis Group.
\end{quote}

(\protect\hyperlink{ref-RM_measurement}{Engelhard and Wang 2020})

\begin{quote}
Engelhard, George, and Jue Wang. \emph{Rasch Models for solving
measurement problems: Invariant Measurement in the Social Sciences.}
Vol.187. SAGE, 2020.
\url{https://us.sagepub.com/en-us/nam/rasch-models-for-solving-measurement-problems/book267292}
\end{quote}

This book also assumes a basic working knowledge of the R software and
programming language. To use this book, readers will need to know how to
run existing code in R or R Studio, and how to make basic edits to
existing code in order to adapt it for use with their own data. Readers
who are new to R may find the following resources helpful for learning
how to use this program:

\begin{itemize}
\item
  \href{https://libguides.library.kent.edu/statconsulting/r}{What is R
  \& R Studio} Visit:
  \url{https://libguides.library.kent.edu/statconsulting/r}
\item
  \href{https://rstudio-education.github.io/hopr/starting.html}{Install
  R \& R-Studio} Visit:
  \url{https://rstudio-education.github.io/hopr/starting.html}
\item
  \href{https://www.statmethods.net/r-tutorial/index.html}{R Tutorial
  for beginners} Visit:
  \url{https://rstudio-education.github.io/hopr/starting.html}
\end{itemize}

In addition, readers should note that our descriptions of the R code
generally assume that the analyses are being conducted in
\href{https://rstudio.com/}{R Studio}. However, all of the R code will
work in both R and R Studio.

\hypertarget{overview-of-rasch-measurement-theory}{%
\subsection{Overview of Rasch Measurement
Theory}\label{overview-of-rasch-measurement-theory}}

Georg Rasch was a Danish psychometrician who introduced a theory and
approach to social science measurement in his classic text entitled
\emph{Probabilistic Models for Some Intelligence and Attainment Tests}
(\protect\hyperlink{ref-Rasch_ori}{Rasch 1960}). This approach to
measurement involves transforming ordinal item responses, such as the
data that are collected in a multiple-choice educational assessment of
middle school students' understanding of engineering design
(\protect\hyperlink{ref-Develop_EDPA}{Alemdar et al. 2017}), a survey
designed to measure self-efficacy for making career decisions
(\protect\hyperlink{ref-apsy_eval}{Nam et al. 2011}), or a diagnostic
scale used to identify individuals with depression
(\protect\hyperlink{ref-RMA_depression}{Shea, Tennant, and Pallant
2009}), to interval-level measures for examinees and items. Now called
Rasch measurement theory, this approach is based on principles and
requirements that reflect measurement in the physical sciences.

Chief among the defining features of Rasch measurement theory is the
emphasis on \emph{invariance} in measurement. In the context of Rasch
measurement theory, invariance occurs when the following properties are
observed in item response data
(\protect\hyperlink{ref-General_laws}{Rasch 1961}):

• The comparison between two stimuli should be independent of which
particular individuals were instrumental for the comparison;

• and it should also be independent of which stimuli within the
considered class were or might also have been compared.

• Symmetrically, a comparison between two individuals should be
independent of which particular stimuli with the class considered were
instrumental for the comparison;

• and it should also be independent of which other individuals were also
compared on the same or on some other occasion.

Rasch used the term \emph{specific objectivity}
(\protect\hyperlink{ref-Spec_objectivty}{Rasch 1977a}) to describe the
importance of identifying specific situations in which the requirements
for invariant measurement are approximated. In emphasizing invariance,
Rasch noted that meaningful interpretation and use of social science
measurement instruments is not possible unless invariance is
approximated.

Rather than assuming that data will adhere perfectly to the model
requirements, researchers who use Rasch models do so in order to
identify deviations from these requirements when they occur. Information
about departures from model requirements can help analysts identify
areas for additional research, including qualitative investigations of
persons and items, as well as guidance for improving the quality of a
measurement procedure. This perspective in which the \emph{measurement
theory} (i.e., the model) is emphasized as a guide for understanding the
quality of the data by comparing it to strict requirements, is a key
distinguishing feature between Rasch measurement theory and other item
response theory (IRT) approaches. In typical IRT analyses, analysts
attempt to identify a model that is the most accurate representation of
the characteristics of the \emph{data}
(\protect\hyperlink{ref-IRT_psy}{Embretson and Reise 2000}). For
example, many researchers select the three-parameter logistic model
(\protect\hyperlink{ref-LTM}{Birnbaum 1968}) when analyzing responses to
multiple-choice educational assessments because the model directly
incorporates instances of guessing and differences in item
discrimination. However, researchers guided by a Rasch perspective would
instead use the Rasch model to identify unexpected observations that
could alert them to potential guessing and inconsistent item ordering
over examinee achievement levels (as reflected by differences in item
discrimination). These unexpected observations could then lead to
additional exploration and the improvement of the assessment procedure.
Although there are many situations in which reproducing the
characteristics of item response data may be useful or necessary, the
general perspective that characterizes Rasch measurement theory is that
the theory (i.e., the model) provides a framework for evaluating data
according to its adherence to fundamental measurement properties. Rasch
measurement theory scholars argue that evidence of adherence to model
requirements is necessary before data can be used to make inferences
about persons and items (e.g., in statistical analyses). As Bond and Fox
(\protect\hyperlink{ref-Applying_RM2019}{Bond, Yan, and Heene 2019})
noted, ``researchers should spend more time investigating their scales
than investigating with their scales''.

In addition to providing useful information about adherence to
fundamental measurement properties, Rasch models have several other
theoretical and practical features that have contributed to their
widespread popularity across disciplines in the social, behavioral, and
health sciences (please see (\protect\hyperlink{ref-Review_RM1977}{Rasch
1977b}) for a review). (\protect\hyperlink{ref-Overview_RM}{Wright and
Mok 2004}) summarized the key theoretical and practical features of the
Rasch measurement approach as follows:

In order to construct inference from observation, the measurement model
must: (a) produce linear measures, (b) overcome missing data, (c) give
estimates of precision, (d) have devices for detecting misfit, (e) the
parameters of the object being measured and of the measurement
instrument must be separable. Only the family of Rasch measurement
models solve these problems. (p.~4)

To help researchers take advantage of these useful features in a
practical way, our book provides an overview of several key models
within the family of Rasch models, offers basic guidance on the
estimation of the models using available R packages, and provides
suggestions and advice for interpreting the results from the analyses.

\hypertarget{online-resources}{%
\subsection{Online Resources}\label{online-resources}}

This book includes several supplemental resources that are available
online, including copies of the R code, example data sets, and data sets
for the challenge exercises at the end of some of the chapters. All of
the materials used in this book including the R software, R packages,
and data sets, are free to download. The following table provides
details about how to download all the relevant learning materials.

\begin{longtable}[]{@{}llc@{}}
\toprule
Title & Version & Download Link \\
\midrule
\endhead
\href{https://cran.r-project.org/src/base/R-4/}{R Programming Language}
& 4.0.3 (latest) & cran.r-project.org \\
\href{https://rstudio.com/products/rstudio/download/}{R Studio} & 1.3 &
rstudio.com \\
\href{https://bookdown.org/connect/\#/apps/5286/access/1060}{Rasch Book
Online Version} & Beta 0.2 & {[}{]}Need Final Address \\
\href{https://github.com/huacheng1985/TheRaschBook}{Source Code for this
Book} & Github & {[}{]}Need Final Address \\
Data set & Beta & See in Each Chapter \\
\bottomrule
\end{longtable}

Table 1.1 Online Resources

\hypertarget{refs}{}
\begin{CSLReferences}{1}{0}
\leavevmode\vadjust pre{\hypertarget{ref-Develop_EDPA}{}}%
Alemdar, Meltem, Jeremy A.Lingle, Roxanne Moore, and Stefanie A. Wind.
2017. {``Developing an Engineering Design Process Assessment Using
Think-Aloud Interviews.''} \emph{International Journal of Engineering
Education} 33 (441-452).

\leavevmode\vadjust pre{\hypertarget{ref-A_Course}{}}%
Andrich, David, and Ida Marais. 2019. \emph{A Course in Rasch
Measurement Theory: Measuring in the Educational, Social and Health
Sciences}. Singapore: Springer.

\leavevmode\vadjust pre{\hypertarget{ref-LTM}{}}%
Birnbaum, Allan. 1968. {``Some Latent Trait Models and Their Use in
Inferring an Examinee's Ability.''} In, 397--479. Statistical Theories
of Mental Test Scores. Addison-Wesley,Menlo Park.

\leavevmode\vadjust pre{\hypertarget{ref-Applying_RM2019}{}}%
Bond, Trevor, Zi Yan, and Moritz Heene. 2019. \emph{Applying the Rasch
Model: Fundamental Measurement in the Human Sciences}. 4th Edition. New
York: Routledge.

\leavevmode\vadjust pre{\hypertarget{ref-IRT_psy}{}}%
Embretson, Susan E., and Seteven P. Reise. 2000. \emph{Item Response
Theory for Psychologists}. \emph{Danish Yearbook of Psychology}.
Lawrence Erlbaum Associates.

\leavevmode\vadjust pre{\hypertarget{ref-RM_measurement}{}}%
Engelhard, George, and Jue Wang. 2020. \emph{Rasch Models for Solving
Measurement Problems: Invariant Measurement in the Social Sciences}. 4th
Edition. Vol. 187. SAGE.
\url{https://us.sagepub.com/en-us/nam/rasch-models-for-solving-measurement-problems/book267292}.

\leavevmode\vadjust pre{\hypertarget{ref-apsy_eval}{}}%
Nam, Suk, Eunjoo Kyung, Sang Min Lee, Sang Hee Lee, and Hyunsoo Seol.
2011. {``A Psychometric Evaluation of the Career Decision Self-Efficacy
Scale with Korean Students: A Rasch Model Spproach.''} \emph{Journal of
Career Development}.
https://doi.org/\url{https://doi.org/10.1177/0894845310371374}.

\leavevmode\vadjust pre{\hypertarget{ref-R_base}{}}%
R Core Team. 2021. \emph{R: A Language and Environment for Statistical
Computing}. Vienna, Austria: R Foundation for Statistical Computing.
\url{https://www.R-project.org/}.

\leavevmode\vadjust pre{\hypertarget{ref-Rasch_ori}{}}%
Rasch, Georg. 1960. \emph{Probabilistic Models for Some Intelligence and
Achievement Tests}. Expanded Edition, 1980. Vienna, Austria: University
of Chicago Press.

\leavevmode\vadjust pre{\hypertarget{ref-General_laws}{}}%
---------. 1961. {``Proceedings of the IV Berkeley Symposium on
Mathematical Statistics and Probability.''} In \emph{On General Laws and
the Meaning of Measurement in Psychology}. Vol. 4.

\leavevmode\vadjust pre{\hypertarget{ref-Spec_objectivty}{}}%
---------. 1977a. {``On Specific Objectivty: An Attempt at Formalizing
the Request for Generality and Validity of Scientific Statements.''}
\emph{Danish Yearbook of Psychology} 14 (58-94).

\leavevmode\vadjust pre{\hypertarget{ref-Review_RM1977}{}}%
---------. 1977b. {``On Specific Objectivty: An Attempt at Formalizing
the Request for Generality and Validity of Scientific Statements.''}
\emph{Danish Yearbook of Psychology} 14 (58-94).

\leavevmode\vadjust pre{\hypertarget{ref-RMA_depression}{}}%
Shea, Tracy L., Alan Tennant, and Julie F. Pallant. 2009. {``Rasch Model
Analysis of the Depression, Anxiety and Stress Scales (DASS).''}
\emph{BMC Psychiatry} 9 (21).
https://doi.org/\url{https://doi.org/10.1186/1471-244X-9-21}.

\leavevmode\vadjust pre{\hypertarget{ref-Overview_RM}{}}%
Wright, Benjamin D., and Magdalena Mo Ching Mok. 2004. {``An Overview of
the Family of Rasch Measurement Models.''} In \emph{Introduction to
Rasch Measurement}, edited by Everett V. Smith and Richard M. Smith,
1--24. JAM Press.

\end{CSLReferences}

\end{document}