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Understanding Behavior: From Neurons to Societies

Quantitative Methods, Measurement, and Statistics

Quantitative Faculty

Sarah Depaoli
Fan Jia

Keke Lai
Jack Vevea
Haiyan Liu 
Ren Liu 
Emeritus and Founding Faculty: William Shadish (Academic Website)

Quantitative program

Quantitative psychologists create the methods used to gather data and the statistics used to analyze them. 

Quantitative psychology is central to all aspects of psychology: science, education, public interest and practice. This essential role of quantitative psychology is reflected in the fact that Division 5 - Evaluation, Measurement, and Statistics - is one of the Charter Divisions of the APA.

Quantitative psychology includes research and development in a number of broad areas: measurement, research design and statistical analysis (see Aiken, West, Sechrest & Reno, 1990), as well as mathematical and statistical modeling of psychological processes.

Within each area, quantitative psychologists develop new methodologies and evaluate existing methodologies to examine their behavior under conditions that exist in psychological data (e.g., with small samples). This work supports the substantive research of all areas within psychology.

At UC Merced, Psychological Sciences faculty members with interests in quantitative psychology have strengths in a wide array of topics, including Bayesian statistics, experimental and quasi-experimental design, meta-analysis, propensity score analysis, psychometric theory, structural equation modeling, hierarchical linear modeling, item response theory, longitudinal statistical modeling, sample size planning and statistics that are robust to violations of assumption.

Courses in these and related areas are available. The faculty members range in interests from the applied statistics to basic mathematical statistics. 


In addition to the core coursework, students interested in quantitative psychology are encouraged to take the following courses:

  • PSY 202c: Multivariate Statistics
  • PSY 203: Multilevel Modeling
  • PSY 205: Measurement Theory and Psychometrics
  • PSY 206: Quantitative Methods for Reviewing Research (Research Synthesis/Meta-Analysis)
  • PSY 207: Structural Equation Modeling
  • PSY 209: Longitudinal Data Analysis and Bayesian Extensions
  • PSY 210: Item Response Theory
  • PSY 213: Mathematical Toolbox for Quantitative Psychology
  • PSY 215: Essential Mathematics for Quantitative Social Research
  • PSY 290: Statistical Computing
  • PSY 290: Advanced Meta-Analysis
  • PSY 290: Bayesian Statistics
  • PSY 290: Missing Data Analysis

Additional specialized courses will be offered within this area. Students should work with their faculty mentors to select appropriate courses that can provide the best foundations for their research. This may include taking courses in other specialties within Psychological Sciences and courses offered by other programs or by other UC campuses offering courses in quantitative methods.

Students who are interested in quantitative psychology can also take substantive psychology courses in another area of psychology (e.g., developmental, health). This serves two purposes. First, it ensures a minimal level of contact with the field of psychology, commensurate with getting a doctorate in psychology. Second, it can increase the marketability of quantitative psychologists by demonstrating the ability to talk to faculty members in substantive areas such as developmental psychology or health psychology.

Representative Publications for Quantitative Faculty

Bold font indicates Quantitative Psychology Faculty Member.

  • Chen, P., Wu, W., Brandt, H., Jia, F. (2020). Addressing missing data in backward specification search in measurement invariance testing with Likert scale variables: A Comparison of Two Approaches. Behavior Research Methods. doi:10.3758/s13428-020-01415-2
  • Chen, P. Y., Wu, W., Garnier-Villarreal, M., Kite, B. A., & Jia, F. (2020). Testing measurement invariance with ordinal missing data: A comparison of estimators and missing data techniques. Multivariate Behavioral Research, 55(1), 87-101.
  • Cheng, Y., & Liu. H. (2016). A short note on the maximal point-biserial correlation under non-normality. British Journal of Mathematical and Statistical Psychology, 69(3), 344-351.
  • Citkowicz, M., & Vevea, J.L. (2017). A parsimonious weight function for modeling publication bias. Psychological Methods, 22, 28-41.
  • Coburn, K.M., & Vevea, J.L. (2015). Publication bias as a function of study characteristics. Psychological Methods, 20 310-30.
  • Depaoli, S. (2014). The impact of inaccurate “informative” priors for growth parameters in Bayesian growth mixture modeling. Structural Equation Modeling, 21, 239-252.
  • Depaoli, S. (2013). Mixture class recovery in GMM under varying degrees of class separation: Frequentist versus Bayesian estimation. Psychological Methods, 18, 186-219.
  • Depaoli, S. (2012). The ability for posterior predictive checking to identify model mis-specification in Bayesian growth mixture modeling. Structural Equation Modeling, 19, 534-560.
  • Depaoli, S. (2012). Measurement and structural model class separation in mixture-CFA: ML/EM versus MCMC. Structural Equation Modeling, 19, 178-203
  • Depaoli, S., and Clifton, J. (2015). A Bayesian approach to multilevel structural equation modeling with continuous and dichotomous outcomes. Structural Equation Modeling, 22, 327-351.
  • Depaoli, S., Lai, K, and Yang, Y. (2020). Bayesian model averaging as an alternative to model selection for multilevel models. Multivariate Behavioral Research. Online advanced publication
  • Depaoli, S., Rus, H., Clifton, J., van de Schoot, R., and Tiemensma, J. (2017). An introduction to Bayesian statistics in health psychology. Health Psychology Review, 11, 248-264.
  • Depaoli, S., and van de Schoot, R. (2017). Improving transparency and replication in Bayesian statistics: The WAMBS-checklist. Psychological Methods, 22, 240-261.
  • Depaoli, S., Winter, S. D., Lai, K., & Guerra-Peña, K. (2019). Implementing continuous non-normal skewed distributions in latent growth mixture modeling: An assessment of specification errors and class enumeration. Multivariate Behavioral Research, 54, 795-821.
  • Depaoli, S., Yang, Y., and Felt, J. (2017). Using Bayesian statistics to model uncertainty in mixture models: A sensitivity analysis of priors. Structural Equation Modeling: A Multidisciplinary Journal, 24, 198-215.
  • Jia, F., & Wu, W. (2019). Evaluating methods for handling missing ordinal data in structural equation modeling. Behavior Research Methods, 51(5), 2337-2355.
  • Jia, F., Moore, E. W. G., Kinai, R., Crowe, K. S., Schoemann, A. M., & Little, T. D. (2014). Planned missing data design with small sample size: How small is too small? International Journal of Behavioral Development, 38(5), 435-452.
  • Lai, K. (in press). Using information criteria under missing data: Full information maximum likelihood versus two-stage estimation. Structural Equation Modeling.
  • Lai, K. (2020). Correct estimation methods for RMSEA under missing data. Structural Equation Modeling. Advance online publication.
  • Lai, K. (2020) Confidence interval for RMSEA or CFI difference between nonnested models. Structural Equation Modeling, 27, 16-32.
  • Lai, K. (2019). Correct point estimator and confidence interval for RMSEA given categorical data. Structural Equation Modeling. Advance online publication.
  • Lai, K. (2019). Creating misspecified models in moment structure analysis. Psychometrika, 84, 781-801.
  • Lai, K. (2019). More robust standard error and confidence interval for SEM parameters given incorrect model and nonnormal data. Structural Equation Modeling, 26, 260-279.
  • Lai, K., Green, S. B., & Levy, R. (2017). Graphical displays for understanding SEM model similarity. Structural Equation Modeling, 24, 803-818.
  • Lai, K., & Green, S. B. (2016). The problem with having two watches: Assessment of fit when RMSEA and CFI disagree. Multivariate Behavioral Research, 51, 220-239.
  • Liu, H., Jin, I. H., & Zhang, Z. (2018). Structural Equation Modeling of Social Networks: Specification, Estimation, and Application. Multivariate Behavioral Research.
  • Liu, H., & Zhang, Z. (2017). Logistic regression with misclassification in binary outcome variables: a method and software. Behaviormetrika, 44(2), 447-476.
  • Liu, H., Zhang, Z, & Grimm, K. J. (2016). Comparison of Inverse Wishart and Separation-Strategy Priors for Bayesian Estimation of Covariance Parameter Matrix in Growth Curve Analysis. Structural Equation Modeling: A Multidisciplinary Journal, 23 (3), 354-367.
  • Liu, R., & Liu, H. (2020). Nested diagnostic classification models for multiple-choice items. British Journal of Mathematical and Statistical Psychology.
  • Liu, R. (2019). Addressing score comparability in diagnostic classification models: An observed-score equating approach. Behaviormetrika.
  • Liu, R., & Jiang, Z. (2019). A general diagnostic classification model for rating scales. Behavior Research Methods.
  • Liu, R., & Jiang, Z. (2018). Diagnostic classification models for ordinal item responses. Frontiers in Psychology - Quantitative Psychology and Measurement, 9, 2512.
  • Liu, R., Qian, H., Luo, X., & Woo, A. (2018). Relative diagnostic profile: a subscore reporting framework. Educational and Psychological Measurement, 78(6), 1072–1088.
  • Liu, R. (2018). Misspecification of attribute structure in diagnostic measurement. Educational and Psychological Measurement, 78(4), 605-634.
  • Liu, R., Huggins-Manley, A. C., & Bulut, O. (2018). Retrofitting diagnostic classification models to responses from IRT-based assessment forms. Educational and Psychological Measurement, 78(3), 357-383.
  • Liu, R., Huggins-Manley, A. C., & Bradshaw, L. (2017). The impact of Q-matrix designs on diagnostic classification accuracy in the presence of attribute hierarchies. Educational and Psychological Measurement. 77(2), 220240.
  • Qu, W., Liu, H., & Zhang, Z. (2020). A method of generating multivariate non-normal random numbers with desired multivariate skewness and kurtosis. Behavior Research Methods, 52, 939-946.
  • Rhemtulla, M., Jia, F., Wu, W., & Little, T. D. (2014). Planned missing designs to optimize the efficiency of latent growth parameter estimates. International Journal of Behavioral Development, 38(5), 423-434.
  • Shadish, W. R., Cook, T. D., & Cambell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Houghton Mifflin.
  • Shadish, W. R., Cook, T. D., & Leviton, L. C. (1991). Foundations of program evaluation: Theories of practice. Sage.
  • Shadish, W. R., Clark, M. H., Steiner, P. M. (2008). Can nonrandomized experiments yield accurate answers? A randomized experiment comparing random and nonrandom assignments. Journal of the American Statistical Association, 103, 1334-1344.
  • Shadish, W. R., & Haddock, C. K. (2009). Combining estimates of effect size. Russell Sage Foundation.
  • Shadish, W. R., Navarro, A. M., & Phillips, M. G. (2000). The effects of psychological therapies under clinically representative conditions: A meta-analysis. Psychological Bulletin, 126,  512.
  • Wu, W., & Jia, F. (2013). A new procedure to test mediation with missing data through nonparametric bootstrapping and multiple imputation. Multivariate Behavioral Research, 48(5), 663-691.
  • Wu, W., Jia, F., & Enders, C. (2015). A comparison of imputation strategies for ordinal missing data on Likert scale variables. Multivariate Behavioral Research, 50(5), 484-503. Research.
  • Wu, W., Jia, F., Kinai, R., & Little, T. D. (2017). Optimal number and allocation of data collection points for linear spline growth curve modeling: a search for efficient designs. International Journal of Behavioral Development, 41(4), 550-558.
  • Wu, W., Jia, F., Rhemtulla, M., & Little, T. D. (2016). Search for efficient complete and planned missing data designs for analysis of change. Behavior Research Methods, 48(3), 1047-1061.
  • Vevea, J.L. & Coburn, K.M. (2019). Publication Bias. In Valentine, J., Cooper, H., & Hedges, L.V., The Handbook of Research Synthesis and Meta-Analysis (3rd Edition). New York: Russel Sage Foundation.
  • Vevea, J.L., & Hedges, L.V. (1995). A general linear model for estimating effect size in the presence of publication bias. Psychometrika, 60, 419-435.
  • Vevea, J.L. & Woods, C.M. (2005). Publication bias in research synthesis: Sensitivity analysis using a priori weight functions. Psychological Methods, 10, 428-443.
  • Zhang, Z., Jiang, K., Liu, H., & In-Sue Oh. (2017). Bayesian meta-analysis of correlation coefficients through power prior. Communications in Statistics-Theory and Methods, 46, 11988-12007.