# Department of Statistics

## STAT 778

778—Item Response Theory. [=EDRM 828] (3) (Prereq: EDRM 711 or PSYC 710 or STAT 701 or STAT 704) Statistical models for item response theory, Rasch and other models for binary and polytomous data, and applications. Use of statistical software.

Usually Offered: Spring Semesters, Even years

Purpose: Item response theory (IRT) is the class of statistical methods for analyzing large scale standardized tests and instruments in education, psychology, and public health. Upon completion of the course the students will be familiar with the major concepts and theoretical issues in IRT. They will possess the needed technical knowledge to directly consult the more applied research journals in the field. They will also have the background to continue their studies in a reading course preparing them to utilize the more theoretical journals in the field and to conduct original research.

Current Textbook: Selected journal articles.

 Topics Covered Time Basics of Testing: Process of Measurement, Introduction to Validity*, Classical Test Theory, Reliability, Classical Item Analysis 1.5 weeks Dichotomous Item Response Theory Models: Normal Ogive Model; Invariance; Rasch, 2PL, and 3PL models; Properties of the Monotone Homogeneity Models; Issues in Model Selection 1.5 weeks Estimation of Item Response Theory Models: Overview of Maximum Likelihood* and Bayesian Statistics; Introduction to the EM and Bayes Modal Estimation, Markov chain Monte Carlo, and Metropolis-Hastings Robbins-Monro; Item Information; Implementation using Standard Software 3 weeks Model Fit: Graphical Checks, Chi-square Approaches, Bayesian Methods including Posterior Predictive Model Checking 1 week Multidimensional Models and Dimensionality Assessment: Compensatory, Non-Compensatory, and Variable Compensation Models; Testlet and other Restrictions of the Compensatory Model; Conditional Covariance Based Dimensionality Assessment and Related Procedures; Other Dimensionality Assessment Methods; Mokken Scaling 1.5 weeks Polytomous Item Response Theory Models: Partial Credit, Graded Response, and Continuation Ratio Models; Taxonomy of Polytomous Models; Generalized Graded Unfolding Model 1 week Introduction to Differential Item functioning, Bias, and Impact 0.5 weeks Introduction to Test Construction and Computer Adaptive Testing 0.5 weeks Introduction to Linking, Equating, and Scaling 1.5 weeks Introduction to Diagnostic Classification Models 0.5 weeks Introduction to IRT Model Building and Relationship to the GLMM Framework 0.5 weeks Introduction to Nonparametric Item Response Theory 0.5 weeks * Three extra recorded lectures providing an overview on validity, the needed background on maximum likelihood, and an overview of the course project will be given outside of the regular course schedule

The above course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.

Contact Faculty: Brian Habing