Advanced statistical models

Aims: To introduce advanced modelling strategies for independent data or data characterized by spatial or temporal dependence including model selection, inference, prediction.
Learning outcomes: At the end of the course the students will have an appreciation of the different modelling strategies for data characterized by various kinds of dependencies and will be able to deal with estimation issues, to perform model selection and to apply the models to real data situations.

Course content

Module 1. Generalized linear (GLM) and latent variable models (GLLVM) (Prof. S. Cagnone)

- GLM:

• Introduction to GLM
• Model Specification
• Inference
• Extentions and Applications

- GLLVM:

• Introduction to GLLVM
• Model specification for continuous and categorical data
• Inference
• Applications

Module 2. Models for panel data (Prof. L. Trapin)
- Large N, Small T:

• Static panels: pooled, fixed effect, random effect estimators
• Dynamic panels: endogeneity, IV, and gmm estimators

- Large N, Large T:

• Interactive fixed effect estimators
• Grouped panels

- Nonlinear panels

Module 3. Advanced time series analysis: Time-varying-parameter models (Prof. A. Luati)

• Nonlinear non-Gaussian models
• Maximum likelihood estimation
• Asymptotic theory

Module 4. Specification and Inference for models with cross-sectional (spatial) dependence (Prof. A. G. Billè)
- Introduction to Random Fields:

• Markovian Random Fields (CAR models) vs Non-Markovian Random Fields (SAR models)
• Definition and types of weighting matrices
• The concept of Spillover effects
• Endogeneity issues

- Cliff-Ord's types of models and their extensions to panel data:

• Main assumptions
• Frequentist estimation procedures
• Definition of spatial marginal effects
• Testing

- Spatial discrete choices and limited dependent variable models:

• The utility theory behind
• Main assumptions
• Frequentist estimation procedures
• Definition of spatial marginal effects