STSP: Statistical Modeling of Complex Data (7 ECTS)

    Course Code: 
    6248
    Semester: 
    8th
    Elective Courses
    Διδάσκων: 

    KOSMIDIS IOANNIS

    The course focuses on modern statistical modeling methods beyond classical linear models. Emphasis is placed on model formulation, parameter estimation, hypothesis testing, model diagnosis and evaluation, as well as the interpretation and communication of results. The aim is to develop critical thinking about model assumptions, data structure, and the adequacy of statistical conclusions, with applications to real-world data using statistical software.

    • Principles of Statistical Modeling: Statistical models as data-generating mechanisms; likelihood function and identifiability; the logic of modeling and algorithms (model-based vs. algorithmic thinking); interpretation versus prediction; goodness of fit versus predictive performance and cross-validation; bias–variance trade-off; overfitting.

    • Generalized Linear Models (GLMs) and Extensions: Review of generalized linear models (exponential family of distributions and link functions); models for binary data (logistic regression); models for count data (Poisson regression); overdispersion in count models; hurdle and zero-inflated models; models for positive continuous data (log-normal, Gamma, and inverse Gamma models); models for proportions using Beta regression models; multinomial models; ordinal multinomial regression.

    • Linear Mixed-Effects Models (LMMs): Random effects and hierarchical structure; random intercepts; LMMs as extensions of linear models with random effects; random-intercept models: interpretation, within-group/within-subject correlation, variance components; predictions and shrinkage; Best Linear Unbiased Predictions (BLUPs); random-slope models and covariance structures (random slopes: individual trajectories and heterogeneity in rates of change; fixed and random effects: the meaning of the “average” trend and “individual deviation”; selection of the random-effects structure).

    • Estimation and Inference in Linear Mixed-Effects Models: Estimation by Maximum Likelihood and Restricted Maximum Likelihood (ML and REML)—what is estimated and when each method is preferred; model testing and comparison (Likelihood Ratio Test, LRT, including considerations for tests at the boundary of the parameter space, as well as AIC/BIC criteria); interpretation of coefficients and quantification of uncertainty.

    • Overview of Generalized Linear Mixed-Effects Models (GLMMs) and Logistic Regression with a Random Intercept: Link functions; non-normal distributions; conditional likelihood; logistic regression with a random intercept: interpretation of random heterogeneity in probabilities/odds; computational methods: Laplace approximation/adaptive quadrature; comparison with “ordinary” logistic regression.

    • Longitudinal and Repeated-Measures Data: Correlated observations; random intercepts and slopes; marginal versus conditional models; introduction to Generalized Estimating Equations (GEE).

    • Models with Latent Variables: Measurement error models; generalized factor analysis models with latent variables; introduction to Item Response Theory (IRT) models; identifiability issues; psychometric models.

    • Missing Data: Missing at random (MAR); missing not at random (MNAR); imputation methods and the MICE approach.

    • Case Studies: Comprehensive data analyses; applications to economic, social, and medical data; critical evaluation of models and scientific conclusions.

    Recommended Reading

    • Faraway J.J (2006).  Extending the Linear Model with R. Chapman & Hall/CRC Taylor & Francis Group.
    • Wood, S.N. (2017). Generalized Additive Models: An Introduction with R, Second Edition (2nd ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9781315370279
    • Moustaki, I., Steele, F., Chen, Y., & Bartholomew, D. (2026). Analysis of Multivariate Social Science Data: Statistical Machine Learning Methods (3rd ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9781003483342 
    • van Buuren, S. (2018). Flexible Imputation of Missing Data, Second Edition (2nd ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9780429492259
    • Pinheiro, José C., and Douglas M. Bates. Mixed-effects models in S and S-PLUS. New York, NY: Springer New York, 2000.
    • Hambleton, Ronald K., Hariharan Swaminathan, and H. Jane Rogers. Fundamentals of item response theory. Vol. 2. Sage, 1991.
    • Hagenaars, Jacques A., and Allan L. McCutcheon, eds. Applied latent class analysis. Cambridge University Press, 2002.