Research projects
Interval estimation of item response theory (IRT) scale scores
Dr. Ji Seung Yang and I studied the issue of incorporating estimation error of item parameters into the inference about scale scores. We rephrased IRT scoring as a predictive inference problem, under which various Bayesian, fiducial, and frequentist approaches could be harmonized.
Generalized fiducial inference (GFI) and its application in IRT modeling
GFI is a generalization and advancement of Fisher's fiducial argument, which offers Bayesian-like but prior-free inference for model parameters. In collaborative work with Dr. Jan Hannig, I derived GFI for binary and graded logistic IRT models, and investigated its asymptotic properties and finite-sample performance.
Semiparametric modeling and testing of differential item functioning (DIF)
Semiparametric DIF test
This is a collaborative project with Brooke Magnus and Dr. David Thissen. We developed a semiparametric approach for modeling and testing DIF along a continuous covariate, using the technique of tensor-product regression splines. A permutation test was proposed and evaluated using Monte Carlo simulations.
Item fit diagnostics for IRT models
Item fit heatmap
Researchers who evaluate the fit of IRT models often look at univariate and bivariate marginal residuals to determine how a poorly fitting model can be improved. Dr. Alberto Maydeu-Olivares and I proposed several piecewise model fit diagnostics with known asymptotic reference distributions, and illustrated their use with both simulated and real data sets.
Patient Reported Outcome Measurement Information System (PROMIS)
PROMIS, funded by the National Institutes of Health (NIH), is a system of reliable, valid, and flexible assessment tools that measure patient-reported health status. For more information, please visit
Yang Liu Ph.D.
Assistant Professor
Psychological Sciences
School of Social Sciences, Humanities and Arts
University of California, Merced
5200 N. Lake Road
Merced, CA 95343

Office: SSM 312B
Lab: SSM 366

Last updated: 12/17/2016
Yang Liu is currently an assistant professor in quantitative psychology at University of California, Merced. His research concentrates on the development of statistical methods for analyzing item response data, as well as the adaptation of measurement modeling to public-health and educational applications.
[ Curriculum Vitae | Preprints and presentations ]
PSY 10: Analysis of Psychological Data
PSY 10 is a lower-division undergraduate level course on non-calculus-based statistics. The topics include descriptive statistics, sampling distribution, confidence intervals, hypothesis testing, and simple linear regression.
[ Syllabus ]
PSY 212: Item Response Theory
PSY 212 is a graduate level course on IRT, developed in collaboration with my colleague Dr. Ji Seung Yang who is currently an assistant professor at University of Maryland, College Park. The topics include the basics of IRT models, their estimation, model fit assessment, and applications.
[ Syllabus ]
Sample Code
Fortran code for fiducial estimation of logistic graded response models. The code was compiled with gfortran 4.8.4 (using the makefile provided in the archive); it also requires libgfortran and liblapack. An example data set (lsat7.dat) and the input file (lsat7.conf, in the format of the standard fortran 2003 namelist) are also included. For a detailed description of the sampling algorithm, please refer to:
Liu, Y. & Hannig, J. (2016). Generalized fiducial inference for logistic graded response models. Manuscript under review.
R code for calculating bivariate diagnostics for unidimensional 2-parameter logistic (2PL) and graded response models using Mplus output. For more details, please refer to:
Liu, Y., & Maydeu-Olivares, A. (2014). Identifying the source of misfit in item response theory models. Multivariate Behavioral Research, 49(4), 354-371.
R code for calculating univariate and bivariate diagnostics for unidimensional 2PL and graded response models using the IRTPRO "-prm.txt" file. For more details, please refer to:
Maydeu-Olivares, A., & Liu, Y. (2015). Item diagnostics in multivariate discrete data. Psychological methods, 20(2), 276-292.
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UC-Merced Psychological Sciences
UNC-CH Quantitative Psychology
UNC-CH Department of Statistics and Operations Research
Psychometric Society
National Council of Measurement in Education
Society of Multivariate Experimental Psychology
UCLA Statistical Computing Resources
Wolfram Alpha: Computational Engine
Comprehensive R Archive Network
Netlib Repository
C++ Resourses
Comprehensive TeX Archive Network