B027526 - ADVANCED STATISTICAL MODELS – MOD. B

Italian

The course is dividend in two modules. Module A (6 credits) covers the theory and application of the linear regression model and of binary response models. Module B (6 credits) deals with generalized linear models for ordinal and nominal responses and for counts; quantile regression; multilevel linear models.
The models are exploited for the analysis of real data using Stata, with particular attention to the choice of the model and interpretation of the results.

- Fahrmeir, L., Kneib, T., Lang, S., Marx, B. (2021). Regression. Models, Methods and Applications. Springer.
- slides of the teachers

Knowledge of the properties and potentialities of the main statistical models. Ability to select the most appropriate model depending on the research aims and the available data. Ability to estimate the selected model, to evaluate the model adequacy and to interpret the results. Ability to write a short report on the analysis.

Basic knowledge of calculus, matrix algebra, probability and statistical inference.
Compulsory prerequisite exam: "Statistical Inference and computational methods".

Classroom lessons and lab activities.

The exam consists of a written test with questions about theory and exercises. Exercises require the elaboration (using a pocket calculator) of the results derived from the application of statistical models, discussing the specification choices and providing relevant interpretations. During the course individual homeworks are assigned (to be performed using data analysis software) that may contribute to the final mark as established in the Moodle page of the course. The oral exam is optional or compulsory on the basis of the rules reported in the Moodle page of the course.

Module A
1. The linear regression model: a review with applications
1.1. Simple linear regression
1.2. Multiple Linear regression
1.3. Non linear functions
1.4. Interactions
1.5. Estimation
1.6. Inference
1.7. Model selection
1.8. Diagnostics
2. Binary responses and logistic regression
2.1 Estimation and inference
2.2. Goodness of fit and model choice
2.3 Prediction and ROC curve

Module B
3 .Theory of generalised linear models
3.1. exponential family
3.2. generalised linear models
3.3. estimation
3.4. inference
4. Models for categorical responses
4.1. Ordinal responses
4.2 Nominal responses
5. Models for counts and Poisson regression
6. Multilevel models
7. Quantile Regression