This course aims to introduce advanced statistical methods and statistical models which are used in psychometrics and data analysis of psychological, sociological and educational data. Students will learn different approaches to latent variables analysis, such as Confirmatory Factor Analysis (CFA) and some models within Item Response Theory (IRT) framework such as bifactor IRT models etc. Topics of structural equation modelling, analysis of mediated and moderated relations between latent variables will be also introduced. Course continues with discussion of generalized linear models and extension of this models – generalized linear mixed effects models (GLMM). Different types of GLMM, their assumptions and application in social data analysis will be reviewed. At the end of the course some models with discrete latent variables (Latent Class Analysis, Cognitive Diagnostic Models) will be discussed. During the course students learn to select, apply and discuss the results of statistical models appropriate for addressing a given research problem.
Prerequisites:
1) Basic knowledge of statistics (especially regression analysis and factor analysis)
2) Basic knowledge of Item Response Theory (recommended, but now required)
3) Experience of working with base R.
Learning Objectives
To familiarize students with Generalized Linear Mixed Models (GLMM) when the individuals are clustered (e.g., students belonging to different schools), introduce the idea of fixed-effects and random-effects terms in models.
To familiarize students with Confirmatory Factor Analysis (CFA) Structural Equation Modeling (SEM) paradigm, to demonstrate the concepts of moderation and mediation in SEM.
To familiarize students with special chapters of individual differences modeling in social sciences: Measurement Invariance (MI) and Differential Item Functioning (DIF) analysis, Latent Class Analysis, Latent Profile Analysis, Cognitive Diagnostic Modeling.
To illustrate students how they can use R software to perform GLMM, CFA and SEM analysis.
Expected Learning Outcomes
Capable of GLM application and interpretation; correctly selects the link function; realizes the main fallacies for GLM.
Capable of calibrating IRT Rasch models and explanatory IRT models in the GLMM framework; capable of utilizing the full potential of GLMM in applied research
Capable of calibrating, selecting, improving model quality, and interpreting CFA models
Capable of calibrating, re-norming and interpreting parameters of IRT models in CFA parametrization
Capable of conducting path analysis, including mediation and moderation
Capable of conducting latent class and latent profile analysis, cognitive diagnostic modeling, and mixture IRT analyses
Capable of estimation, selection and interpretation of LMM and various GLMM: random intercept, random slope models and their special cases.
Capable of calibrating, selecting and interpreting unidimensional, multidimensional, second-order and bifactor CFA models.
Capable of performing measurement invariance analyses for different types of data and compare the fit of nested models
Course Contents
Introduction into GLM
Generalized Linear Mixed effects Models (GLMM) – the extension of GLM.
Item Response Theory (IRT) as a special case of GLMM. Explanatory IRT models.
Confirmatory Factor Analysis (CFA) and Structural Equation Modeling (SEM)
Relations between IRT and CFA
Second order and bifactor models
Measurement invariance (MI) and Differential Item Functioning (DIF)
Path analysis and SEM
Categorical and ordinal latent variables
Assessment Elements
Homework on GLMM
Homework on random-intercept fixed-slope and random-intercept random-slope GLMMs.
Homework on explanatory IRT and GLMM
Homework on random-intercept fixed-slope, random-intercept random-slope GLMMs and explanatory IRT models.
Homework on CFA and IRT
Homework on CFA and IRT models.
Homework on MI/DIF analysis
Conduct the correct MI/DIF analysis according to the specified task.
Homework on Bayesian statistics
Prepare presentation on Bayesian statistics according to the specified topic.
The final exam
The final exam.
Interim Assessment
2022/2023 2nd module
0.12 * Homework on CFA and IRT + 0.12 * Homework on Bayesian statistics + 0.12 * Homework on explanatory IRT and GLMM + 0.12 * Homework on GLMM + 0.12 * Homework on MI/DIF analysis + 0.4 * The final exam
Bibliography
Recommended Core Bibliography
Applied latent class analysis, , 2002
Applied latent class analysis, , 2009
Applied regression analysis and generalized linear models, Fox, J., 2008
Confirmatory factor analysis for applied research, Brown, T. A., 2006
Explanatory item response models: a generalized linear and nonlinear approach. (2005). Journal of Educational Measurement, 42(3), 303–307. https://doi.org/10.1111/j.1745-3984.2005.00016.x
Hierarchical linear models : applications and data analysis methods, Raudenbush, S. W., 2002
Latent class analysis of survey error, Biemer, P. P., 2011
Latent class analysis, McCutcheon, A. L., 1987
Multilevel analysis : techniques and applications, Hox, J., 2002
New developments and techniques in structural equation modeling, Marcoulides, G. A., 2001
Principles and practice of structural equation modeling, Kline, R. B., 2011
Structural equation modeling : applications using Mplus, Wang, J., 2012
Structural equation modeling : foundations and extensions, Kaplan, D., 2000
Structural equation modeling : foundations and extensions, Kaplan, D., 2009
Recommended Additional Bibliography
Alan Huebner. (2010). An Overview of Recent Developments in Cognitive Diagnostic Computer Adaptive Assessments. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.C5E4E435
Berlin, K. S., Parra, G. R., & Williams, N. A. (2014). An introduction to latent variable mixture modeling (part 2): longitudinal latent class growth analysis and growth mixture models. Journal Of Pediatric Psychology, 39(2), 188–203. https://doi.org/10.1093/jpepsy/jst085
Berlin, K. S., Williams, N. A., & Parra, G. R. (2014). An introduction to latent variable mixture modeling (part 1): overview and cross-sectional latent class and latent profile analyses. Journal Of Pediatric Psychology, 39(2), 174–187. https://doi.org/10.1093/jpepsy/jst084
Tony Jung, & K. A. S. Wickrama. (n.d.). Social and Personality Psychology Compass 2/1 (2008): 302–317, 10.1111/j.1751-9004.2007.00054.x An Introduction to Latent Class Growth Analysis and Growth Mixture Modeling. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.9601523B
Xiuyun Wu, Richard Sawatzky, Wilma Hopman, Nancy Mayo, Tolulope T. Sajobi, Juxin Liu, Jerilynn Prior, Alexandra Papaioannou, Robert G. Josse, Tanveer Towheed, K. Shawn Davison, & Lisa M. Lix. (2017). Latent variable mixture models to test for differential item functioning: a population-based analysis. Health and Quality of Life Outcomes, 15(1), 1–13. https://doi.org/10.1186/s12955-017-0674-0
Instructors
Kuzmina, Yulia
Uglanova, Irina
Course Syllabus
Abstract
Learning Objectives
Expected Learning Outcomes
Course Contents
Assessment Elements
Interim Assessment
Bibliography
Recommended Core Bibliography
Recommended Additional Bibliography
Authors