Advanced Statistical Models in Science and Engineering

Code:

M4015

Acronym:

M4015

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 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	6	Official Study Plan since 2013-2014	1	-	6	56	162
			2

Teaching language

Suitable for English-speaking students

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 regression marginal models (using generalized estimating equations) for discrete longitudinal responses


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


5. 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. Marginal regression models for longitudinal discrete responses (using GEE - Generalized Estimating Equations)

4. Generalized linear mixed models (binomial logistic and Poisson models). 

Fot the above mentioned methodologies, the theoretical description of the model, the process for estimation of the parameters, the process for inference on the model parameters and the methods for evaluation of goodness-of-fit will be detailed. 

All statistical analysis will be performed with 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 making use of R. The didactic exposure process will be carried out in a dynamic way and adjusted to the audience assimilation speed. Students will be encouraged to actively participate in the classes so that the didactic exposure may lead to a dialectic process. 

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

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Attendance to the practical classes is mandatory. The rules of class attendance are those set out in the assessment standards in effect for the academic year 2018/2019, approved by "Conselho Pedagógico".

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 in and orally present two writeen projects. There will be a final examination.
The final mark will correspond to the average of the classifications obtained in the examination and in the written projects as long as the examination mark is at least 6.0 points (out of 20). The student will fail in case the examination mark is below 6.0, regardless of the marks obtained in the written projects. 

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

Classification improvement

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