Linear Models 2
Code: 104861 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| 2503852 Applied Statistics | OB | 3 |
Contact
- Name:
- Coordinació del Grau D'estadística
- Email:
- coordinacio.grau.estadistica@uab.cat
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
Knowledge of descriptive and inferential statistics. A previous course of Linear Models is required.
Objectives and Contextualisation
The objective of the subject is to extend the use of linear combinations of a set of predictors to reduce the uncertainty of a response variable. In particular, we will work on the use of parametric models, beyond the normal law, for the response variable. Also, in this more generic modeling environment, we'll go deeper into how to include information, for example, information about the design of the experiment.
Learning Outcomes
- CM09 (Competence) Assess the suitability of the models with the correct use and interpretation of indicators and graphs.
- CM09 (Competence) Assess the suitability of the models with the correct use and interpretation of indicators and graphs.
- CM10 (Competence) Modify the existing software if required by the statistic model, or create new software, if necessary.
- KM12 (Knowledge) Provide the experimental hypotheses of modelling, considering the technical and ethical implications involved.
- KM12 (Knowledge) Provide the experimental hypotheses of modelling, considering the technical and ethical implications involved.
- KM13 (Knowledge) Detect interactions, co-linearity and importance between explanatory variables.
- SM11 (Skill) Analyse the residuals of a statistical model.
- SM12 (Skill) Interpret the results obtained to formulate conclusions about the experimental hypotheses.
- SM13 (Skill) Compare the degree of adjustment between diverse statistical models.
- SM14 (Skill) Use graphs to visualise the fit and suitability of the model.
Content
1. Subset Selection in Multiple Regression
Best Subset Selection, Stepwise Selection, Optimal model selection according to different criteria.
Shrinkage Methods: Ridge Regression and LASSO regression. Selecting the Tuning Parameter
Dimension Reduction Methods: Partial Least Squares
2. Logistic Regression: The Logistic Model. Estimating the Regression Coefficients. Predictions.
Multiple Logistic Regression and LASSO
3. Rafndom Effects and Mixed effects Models.
4. Moving Beyond Linearity
Break-points in Regression
Splines
Generalized Additive Models
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Computer Practices | 50 | 2 | CM09, CM10, KM12, KM13, SM11, SM12, SM13, SM14, CM09 |
| Theory | 50 | 2 | CM09, CM10, KM12, KM13, SM11, SM12, SM13, SM14, CM09 |
| Type: Supervised | |||
| problems / exercises to solve | 16 | 0.64 | CM09, KM12, KM13, SM11, SM12, SM13, SM14, CM09 |
| Type: Autonomous | |||
| Preparation for the exam | 10 | 0.4 | CM09, KM13, SM11, SM12, SM13, SM14, CM09 |
The course material (theory notes, lists of problems and statements of practice) will be available at the virtual campus, progressively throughout the course.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Final test | 40% | 4 | 0.16 | CM09, KM13, SM11, SM12, SM13, SM14 |
| Partial exam | 30% | 4 | 0.16 | CM09, KM13, SM11, SM12, SM13, SM14 |
| Practices (deliveries or check) | 30% | 16 | 0.64 | CM09, CM10, KM12, KM13, SM11, SM12, SM13, SM14 |
The subject will be assessed with assignments (exercise assignments, problem checks and/or practicals) and 2 exams. To obtain the weighted grade of continuous assessment you must have a minimum of 3/10 in each of the parts.
Students who have opted for the single assessment modality will have to complete an assessment that will consist of a theory exam, a problem test and the delivery of practical reports of the course. Assessment of submissions may require an assessment interview with the teacher. The student's grade will be the weighted average of the three previous activities, where the exam will account for 45% of the grade, the test 45% and the assignments 10%.
If the final grade does not reach 5/10, the student has another opportunity to pass the subject through the remedial exam that will be held on the date set by the degree coordinator. In this test you can recover 70% of the grade corresponding to the theory and the problems. The part of internships is not refundable.
Bibliography
Linear Mixed-Effects Models Using R A Step-by-Step Approach / by Andrzej Gałecki, Tomasz Burzykowski https://bibcercador.uab.cat/permalink/34CSUC_UAB/1eqfv2p/alma991010402935906709
Lee, Y., Nelder, J. and Pawitan, Y. (2006). Generalized Linear Models with Random Effects. Chapman & Hall. London.
John E. Freund, Irwin Miller, Marylees Miller. (2000) Estadística matemática con aplicaciones. Pearson Educación. (existeix castellà)
McCullagh, P. and Nelder, J. (1992). Generalized Linear Models. Chapman & Hall. London.
Daniel Peña; Regresión y diseño de Experimentos, Alianza Editorial (Manuales de Ciencias Sociales), 2002.
Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani; An Introduction to Statistical Learning, Springer texts in Statistics, 2013.
Christopher Hay-Jahans; An R Companion to Linear Statistical Models. Chapman and Hall, 2012.
John Fox and Sandord Weisberg; An R Companion to Applied Regression, 2nd edition, Sage Publications, 2011.
Software
R Core Team. R: A language and environment for statistical computing. R
Foundation for Statistical Computing, Vienna, Austria. URL
https://www.R-project.org/.
Language list
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PLAB) Practical laboratories | 1 | Catalan/Spanish | first semester | afternoon |
| (TE) Theory | 1 | Catalan/Spanish | first semester | afternoon |