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Hierarchical models, spring 2008


dos. Mervi Eerola


10 op


Advanced studies.


Basic course on linear models, preferably also generalized linear models. Basis courses in statistics are sufficient to understand the interpretation and use of the models, but not the theoretical aspects.


Period IV, first lecture Wed 12.3. The language of the course is English, unless all participants understand Finnish.
Lectures: Wed 14-16, B120, Thu 14-16, B120

Course status

Optional course for undergraduates or graduates in statistics, especially in biometry, psychometry or econometry.
Part of the course is suitable also for researchers applying hierarchical models and needing to understand the
methodological background and interpretation of these models.

Outline of the course

The course emphasises the general theory of hierarchical modelling and the role of latent variables in it. Many models, which are
widely used in biometry, psychometry and econometry, can be classified as special cases of the general theory. Examples are
generalized linear mixed models, panel analysis, latent class models, item response models and structural equation models.
Common to all of them is dependence among the obervations, which is modelled with latent variables.

The following themes will be covered:
1. Why hierarchical modelling?
2. Modelling dependent data; Recap of GLM and GLMM; Modelling of latent responses
3. Classical latent variable models
4. Theoretical framework for latent variable hierarchical models
5. Identifiability and model equivalence
6. Estimation; likelihood inference vs Bayesian inference
7. Predicting the value of the latent variables
8. Model comparison and diagnostics

The theory is illustrated by real-life examples analysed by modules of R, or by gllamm, a free additional program for analysing
hierarchical models in Stata.


The contents and hours of practicals will be decided in the beginning of the course. The BSCW web environment is used to
distribute practicals and other course material.


The course is based on the following books:

Skrondal, A. and Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal and structural equation
models. Boca Raton, FL: Chapman & Hall/ CRC Press
Demidenko, E. (2004). Mixed models; theory and applications. Hoboken, NJ: Wiley.
Gelman, A. and Hill, J. (2006). Data Analysis using Regression and Multilevel/Hierarchical Models. Cambridge University Press.

Additional course material will be provided.

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