Master
2024/2025
Psychometrics and Statistics II
Type:
Elective course (Science of Learning and Assessment)
Area of studies:
Psychology
Delivered by:
Department of Educational Programmes
Where:
Institute of Education
When:
2 year, 1-3 module
Mode of studies:
offline
Open to:
students of all HSE University campuses
Master’s programme:
Science of Learning and Assessment
Language:
English
ECTS credits:
6
Course Syllabus
Abstract
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
Interim Assessment
- 2024/2025 3rd module0.4 * Exam + 0.24 * Final Test + 0.12 * R Exercises + 0.24 * Written homework
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
- Handbook of structural equation modeling, , 2012
- Hannah Frick, Carolin Strobl, Fredrich Leisch, & Achim Zeileis. (2012). Flexible Rasch Mixture Models with Package psychomix.
- 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