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.

Course contents

PART 1 - common for all students (Prof. Giuliano Galimberti

• 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 categorical data.

PART 2 - for students from Modelli Statistici C.A. (Prof. Giuliano Galimberti)

• 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.

PART 2 - for students from Modelli Statistici per le scienze biologiche e sociali (Dott.ssa Linda Altieri)

• 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.
• Case studiies

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. ferenza Statistica. Una Presentazione Basata sul Concetto di Verosimiglianza. Seconda Edizione. Springer-Verlag.

Teaching methods

Lectures

Tutorial sessions in computer laboratory

Assessment methods

Modelli statistici C.A.

Written exam 
Oral exam (optional)

Modelli statistici per le scienze biologiche e sociali

Written exam
Oral exam

Final Mark: 2/3 written mark + 1/3 oral mark (if both are larger or equal than 18/30)

 

Office hours

See the website of Giuliano Galimberti