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\begin{document}
\begin{titlepage}
\linespacing{1}
\title{Psychometrics: From Practice to Theory and Back}
\author{\textit{15 Years of Nonparametric Multidimensional IRT,\\
DIF/Test Equity, and Skills Diagnostic Assessment}}
\author{William Stout}
\markboth{Psychometrika}{William Stout}
\affil{Department of Statistics, University of Illinois\break and\break Educational Testing Service}
\vspace{\fill}
\begin{quote}
\fontsize{8}{9}\selectfont \textit{This paper was originally
published in the December 2002 issue of \textit{Psychometrika}
(Volume 67, Number 4). It is republished here to demonstrate the
appearance of a paper that is prepared using the Pmetrika LaTeX
Style File Package for Psychometrika Authors (Version 2b1)
published by the Psychometric Society. A publication quality copy
of William Stout's article can be obtained online at
http://www.psychometricsociety.org\break /ARTICLEstout2002.pdf.
The Pmetrika LaTeX Style File Package for Psychometrika Authors
was designed and prepared by Tim Null, and it was based on
original work done by Don Deland of Integre Technical Publishing.
The package can be downloaded at
http://www.psychometricsociety.org. If you have questions about
the package you can contact Tim Null at tim@timnull.com.}
\end{quote}
\vspace{\fill}
\linespacing{1}\fontsize{8}{10}\selectfont
\textit{This aricle is based on the Presidential Address William
Stout gave on June 23, 2002 at the 67th Annual Meeting of the
Psychometric Society held in Chapel Hill, North Carolina.
---Editor}\vskip2pt
I wish to especially thank Sarah Hartz and Louis Roussos for their
suggestions that helped shape this paper. I wish to thank all my
former Ph.D. students: Without their contributions, the content of
this paper would have been vastly different and much less
interesting!\vskip2pt
Requests for reprints should be sent to William Stout, Department
of Statistics, University of Illinois, 725 S. Wright Street,
Champaign IL 61820. E-Mail: stout@stat.uiuc.edu\vskip2pt
\textsf{Dedication: I want to dedicate this paper to my wife,
Barbara Meihoefer, who was lost to illness in this year of my
presidency. For, in addition to all the wonderful things she meant
to me personally and the enormous support she gave concerning my
career, she truly enjoyed and greatly appreciated my psychometric
colleagues and indeed found psychometrics an important and
fascinating intellectual endeavor, in particular finding the
skills diagnosis area exciting and important: She often took time
from her career as a business manager and entrepreneur to attend
psychometric meetings with me and to discuss research projects
with my colleagues and me. She would have enjoyed this
paper.---William Stout}
\end{titlepage}\vspace*{24pt}
\linespacing{1}
%\RepeatTitle{Psychometrics: From Practice to Theory and Back}
\begin{center}\vskip3pt
\vspace{32pt}
Abstract\vskip3pt
\end{center}
\begin{abstract}
The paper surveys 15 years of progress in three psychometric
research areas: latent dimensionality structure, test fairness,
and skills diagnosis of educational tests. It is proposed that one
effective model for selecting and carrying out research is to
chose one's research questions from practical challenges facing
educational testing, then bring to bear sophisticated probability
modeling and statistical analyses to solve these questions, and
finally to make effectiveness of the research answers in meeting
the educational testing challenges be the ultimate criterion for
judging the value of the research. The problem-solving power and
the joy of working with a dedicated, focused, and collegial group
of colleagues is emphasized. Finally, it is suggested that the
summative assessment testing paradigm that has driven test
measurement research for over half a century is giving way to a
new paradigm that in addition embraces skills level formative
assessment, opening up a plethora of challenging, exciting, and
societally important research problems for psychometricians.
\begin{keywords}
nonparametric IRT, NIRT, latent unidimensionality, latent
multidimensionality, essential unidimensionality, monotone locally
independent unidimensional IRT model, MLI1, item pair conditional
covariances, DIMTEST, HCA/CCPROX, DETECT, CONCOV, Mokken scaling,
generalized compensatory model, approximate simple structure, DIF,
differential item functioning, differential bundle functioning
DBF, valid subtest, multidimensional model for DIF, MMD, SIBTEST,
MultiSIB, Mantel-Haenszel, PolySIB, CrossingSIB, skills diagnosis,
formative assessment, Unified Model, reparameterized Bayes Unified
Model, MCMC, evidence centered design, ECD, PSAT Score Report
Plus.
\end{keywords}
\end{abstract}
\vspace{\fill}\newpage
\section{Introduction}
\section{Nonparametric Latent Structure Assessment}
\subsection{Unidimensionality from the Weak LI Conditional Covariance Perspective}
\subsection{Foundational Issues Facilitated by Infinite Test Length Unidimensional MLI1 Modeling}
\subsection{Interpreting Conditional Covariances Geometrically\break to Assess Latent Multidimensional Structure}
\subsection{NIRT-Based Statistical Procedures, Emphasizing Conditional Covariances}
\begin{figure}[h]
%\centerline{\includegraphics{figure03.eps}}
\caption{Projection of item discrimination vectors onto $V_{\theta_T}$ hyperplance for a six item three-dimensional approximate sample structure.}
\end{figure}
\section{Test Fairness}
\subsection{Multidimensional Model for DIF (MMD)}
\subsection{Model-Based Parameterization of the amount of DIF in Various Settings}
\subsection{MMD- Inspired DIF Statistical Procedures}
\begin{figure}[h]
%\centerline{\includegraphics{figure04.eps}}
\caption{Comparison of $\Theta_F$ and $\Theta_R $ distribution with $\Theta_F \vert X_V = k$ and $\Theta_R \vert X_V = k$ distributions.}
\end{figure}
\subsection{Implementation of DIF/DBF Procedures}
\begin{figure}[h]
%\centerline{\includegraphics{figure05.eps}}
\caption{Item discrimination vectors of a 22 item validity sector.}
\end{figure}
\begin{figure}[h]
%\centerline{\includegraphics{figure06.eps}}
\caption{Panel index versus bundle DBF $\hat {\beta}$/item.}
\end{figure}
\section{Formative Assessment Skills Diagnosis: A New Test Paradigm}
\subsection{A Brief Survey of Psychometric Skills Diagnostic Models}
\begin{figure}[h]
%\centerline{\includegraphics[width=254pt]{/figure07.eps}}
\caption{North Carolina End-of-Grade Math Skills Test Subscores.}
\end{figure}
\begin{figure}[h]
%\centerline{\includegraphics{figs/fig08.eps}}
\caption{PSAT Score Report \textit{Plus} Skills Mastery Reporting.}
\end{figure}
\subsection{The Unified Model and Generalizations Making it Useful}
\subsection{Application of the Unified Model to PSAT Data}
\subsection{Skills Diagnosis: The New Paradigm?}
\section{Dimensionality, Equity, and Diagnostic Software}
\section{Concluding Remarks}
\vspace{\fill}\clearpage
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\end{thebibliography}
\vspace{\fill}
%\vfill\eject
\end{document}
```

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