Advanced Statistical Models in Science and Engineering

Code:

M4015

Acronym:

M4015

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2017/2018 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ENM	12	Official Study Plan since 2013-2014	1	-	6	56	162

Teaching language

Portuguese

Objectives

To provide the students with advanced regression techniques for Gaussian, binomial and Poisson regressions, especially designed for repeated measures and longitudinal data.

Learning outcomes and competences

At the end of the course, the students are expected to:

1. correctly identify scenarios of repeated measurements and/or longitudinal data.


2. understand and perform (Gaussian) linear regression analysis within those contexts, using either mixed effects models or the generalized least squares method.


3. understand and perform generalized linear models (in particular, the binomial logistic model and the Poisson model) with mixed effects.


4. correctly interpret and criticize the results obtained from the application of the above models. 

Working method

Presencial

Program

1.Generalized least squares method.

2. (Gaussian) linear regression with mixed effects.

3. Generalized linear models with mixed-effects (binomial logistic and Poisson models). Generalizing estimating equations. 

Fot the above mentioned methodologies, the theoretical descriptions and methods for estimation of parameters will be given in detail as well as the correspondent instructions in R.

Mandatory literature

José Pinheiro e Douglas Bates; Mixed Effects Models in S and S Plus , Springer, 2000. ISBN: ISBN-13: 978-1475781441
Fitzmaurice Garrett M. 1962-; Applied longitudinal analysis. ISBN: 978-0-470-38027-7

Complementary Bibliography

Zuur Alain F., ed. lit. 340; Mixed effects models and extensions in ecology with R. ISBN: 978-1-4419-2764-4
Diggle Peter J.; Analysis of longitudinal data. ISBN: 0-19-852284-3

Teaching methods and learning activities

The classes will be simultaneously theoretical and practical with several examples of application and always making use of available statistical programing. The used software will be the free programing language R. Basic principles and careful modelling will be emphasized.

The teaching methodologies will be adjusted so that students will be able to integrate the objectives of the curricular unit.

Software

R

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	33,30
Trabalho escrito	66,70
Total:	100,00

Calculation formula of final grade

The evaluation will be distributed with a final examination. During the semester, the students will be required to write, hand on and orally present two reports. There will be a final examination.
The final mark will correspond to the average of the classifications obtained in the examination and in the reports.
The mark obtained in the written reports cannot be improved and will only be valid for that scholar year.

Classification improvement

The mark obtained in the written reports cannot be improved and will only be valid for that scholar year.