28477 - Statistical Models (A. C.)

Learning outcomes

Students will learn the basic notions to define statistical models.

In particular, students will be able to:

• estimate parameters, test hypotesis about them and build confidence intervals for generalized linear models,
• choose the most suitable model for the specific problem at hand,
• define a latent variable model, estimate and interpret its parameters.

Course contents

• Statistical models: introduction.
• Revision of linear regression models.
• Generalized linear models. Exponential families, linear predictor, link functions. Maximum likelihood estimators. Goodness of fit: the deviance of a model. Residual analysis. Inference on the parameters: likelihood ratio statistic.
• Poisson regression for count data.
• Logistic regression for binary, multinomial and ordered data.
• Linear mixed models: basic concepts. Fixed and random effects. Variance-covariance matrix structures. maximum likelihood and restricted maximum likelihood estimators. Residual analysis. Goodness of fit of a linear mixed model. Inference about the parameters: confidence intervals and hypothesis testing.
• latent variable models: basic concepts. Factor analysis as a model with continuous latent variables. Gaussian mixtures as a model with nominal latent variables.

Readings/Bibliography

Dobson, A. J. (2002) An Introduction to Generalized Linear Models. Second Edition. Chapman & Hall/CRC.

West, B. T., Welch, K. B. and Galecki, A. T. (2007) Linear Mixed Models. A Practical Guide Using Statistical Software. Chapman & Hall/CRC.

Everitt, B. S., Hothorn, T. (2006) A Handbook of Statistical Analysis Using R. Chapman & Hall/CRC.

Handsouts.

Azzalini, A. (2001) Inferenza Statistica. Una Presentazione Basata sul Concetto di Verosimiglianza. Seconda Edizione. Springer-Verlag.

 

Teaching methods

Lectures

tutorial sessions in computer laboratory

Assessment methods

Written exam

Oral exam (optional)

Office hours

See the website of Giuliano Galimberti