Lecturer

prof. aggr. Laura Rizzi laura.rizzi@uniud.it

Credits

6 CFU

Department

Department of Economics and Statistics

Aims: (GLM + LMM = GLMM)

This course is devoted to the description of econometric and statistical tools which allow complex contexts modelling. The course structure may be described by the expression “GLM + LMM = GLM”, because lessons will start treating generalized linear models (GLM) and linear mixed models (LMM), then linear generalized mixed models will be described (GLMM).

Linear generalized models (GLM) represent a flexible generalization of linear regression as they allow the analysis of whichever response variable with distribution belonging to the exponential family. The GLM approach represents a unified context for different statistical models, the linear model included.

Linear mixed models (LMM) represent an extension of linear models which allows to describe complex data with jerarchical structures affecting the observations independence, throught the inclusion of mixed effects inside the model formulation. Many fields of analysis, in fact, present data with jerarchical structures, longitudinal dimension or repeated measures which make observations not independent.

Finally, if mixed effects have to be considered in generalized linear models formulation, the statistical econometric tools usefull in this situations relate to the generalized linear mixed models context: GLMM.

This course requires a good knowledge of base econometric methods and statistical inference, together with a good level of english language comprehension.

Programme

1. GLM - generalized linear models;

a. Continue responses

b. Binary and categorical responses

c. Count responses

d. Inference and estimation

1. LMM – Linear mixed models

a. Jerarchical data structures

b. Longitudinal data

c. Mixed effects treatment

1. GLMM – generalized linear mixed models

a. GLMM with continuous response

b. GLMM with binaryresponse

c. GLMM with categorical response

d. GLMM with count response

References and material

Slides presented during the course, together with other material, will be available on the teacher web page. Some book of interest are the following:

1. Dobson, A.J.; Barnett, A.G. (2008). Introduction to Generalized Linear Models (3rd ed.). Boca Raton, FL: Chapman and Hall/CRC. ISBN 1584881658.
2. McCullagh, Peter; Nelder, John (1989). Generalized Linear Models, Second Edition. Boca Raton: Chapman and Hall/CRC. ISBN 0-412-31760-5.
3. Jiming Jiang. (2007) Linear and generalized linear mixed models and their applications (Springer Series in Statistics); ISBN-13: 9780387479415; ISBN: 0387479414