Veidlapa Nr. M-3 (8)
Study Course Description
Linear Models
Course Code
SL_112
Branch of Science
Mathematics; Theory of probability and mathematical statistics
ECTS
6.00
Target Audience
Life Science
LQF
Level 7
Study Type And Form
Full-Time; Part-Time
Study Course Implementer
Course Supervisor
Māris Munkevics
Structure Unit Manager
Andrejs Ivanovs
Structural Unit
Statistics Unit
Contacts
14 Baložu street, Riga, statistika@rsu.lv, +371 67060897
About Study Course
Objective
This course gives students the in-depth knowledge of the theory of linear models and provides training for applying the theory to solve practical problems. The software package R will be used for computation and independently prepared data analysis projects.
Preliminary Knowledge
Calculus; Probability.
Learning Outcomes
Knowledge
1.• as a result of completion of a study course, the student is able to demonstrate an in-depth knowledge of the theory behind linear models; • explain the limitations and assumptions of the linear models; • discuss the different parameterisation options in linear models.
Skills
1.Is able to independently: • choose appropriate model for the data and check the model assumptions; • interpret and use (predictions; inference) the estimated model; • perform multiple comparisons and post-hoc tests.
Competences
1.The students will be able to: • solve prediction problems using linear models’ methodology. • use linear models to answer complex what-if questions (Example: what would the average difference between male and female blood pressure be, if the proportion of overweight population would be the same for both genders?). • critically assess the linear models used in scientific publications and the validity of the conclusions made by authors.
Assessment
Individual work
|
Title
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% from total grade
|
Grade
|
|---|---|---|
|
1.
Individual work |
-
|
-
|
|
• Individual work with the course material in preparation to 12 lectures and 12 shorts (1-3 question) Moodle tests after each lecture according to plan.
• Independently prepare 2 data analysis projects.
In order to evaluate the quality of the study course as a whole, the student must fill out the study course evaluation questionnaire on the Student Portal.
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Examination
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Examination |
-
|
-
|
|
Assessment on the 10-point scale according to the RSU Educational Order:
• 2 data analysis projects – 30%.
• 12 homeworks – 20%.
• Final written exam – 50%.
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Study Course Theme Plan
FULL-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Introduction to linear models. Examples: regression, ANOVA. Method of least squares for estimating the model parameters.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Introduction to the software for estimating linear models.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Maximum likelihood method for estimating the parameters, geometric interpretation.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Interpreting model parameters. Interactions.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Linear functions of parameters. T-test for testing hypothesis about parameters, confidence intervals.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Example analysis (data with run-in period/ modelling a breakpoint).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Gauss-Markov theorem, BLUE (best linear unbiased estimator).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Example analysis. Research questions requiring a customised contrast/linear function of parameters.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Prediction of a new observation, prediction interval. Coefficient of determination, R2.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Estimating a growth curve with prediction intervals. Use of polynomials/splines to model non-linear relationship.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
F-test for comparing models.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Comparing models. Different types of tests (type I/type III SS).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Power of a F-test, geometric interpretation of F-test.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Planning of a study. Sample size required to achieve the desired power.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Overparameterised models, different parameterisations.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Example analysis – interpretation of parameters, comparing estimates from differently parameterised models.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Concepts of model building. Mallows Cp criterion, Akaike information criterion (AIC), Bayesian information criterion (BIC), stepwise regression.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Model selection examples. Correct model might not always be the best choice,
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Model assumptions. Theoretical properties of residuals, leverage, standardized residuals.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Analysis of a problematic dataset I.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Model diagnostics, graphs for checking model assumptions. Transformations for treating non-normality and heteroscedasticity. Approximating non-linear relationship with splines or polynomials.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Analysis of a problematic dataset II.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Multiple testing I. Tukey HSD, tests and confidence intervals based on multivariate t-distribution.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Multiple comparisons.
|
Total ECTS (Creditpoints):
6.00
Contact hours:
48 Academic Hours
Final Examination:
Exam (Written)
PART-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Introduction to linear models. Examples: regression, ANOVA. Method of least squares for estimating the model parameters.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Introduction to the software for estimating linear models.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Maximum likelihood method for estimating the parameters, geometric interpretation.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Interpreting model parameters. Interactions.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Linear functions of parameters. T-test for testing hypothesis about parameters, confidence intervals.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Example analysis (data with run-in period/ modelling a breakpoint).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Gauss-Markov theorem, BLUE (best linear unbiased estimator).
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Example analysis. Research questions requiring a customised contrast/linear function of parameters.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Prediction of a new observation, prediction interval. Coefficient of determination, R2.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Estimating a growth curve with prediction intervals. Use of polynomials/splines to model non-linear relationship.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
F-test for comparing models.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Comparing models. Different types of tests (type I/type III SS).
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Power of a F-test, geometric interpretation of F-test.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Planning of a study. Sample size required to achieve the desired power.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Overparameterised models, different parameterisations.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Example analysis – interpretation of parameters, comparing estimates from differently parameterised models.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Concepts of model building. Mallows Cp criterion, Akaike information criterion (AIC), Bayesian information criterion (BIC), stepwise regression.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Model selection examples. Correct model might not always be the best choice,
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Model assumptions. Theoretical properties of residuals, leverage, standardized residuals.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Analysis of a problematic dataset I.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Model diagnostics, graphs for checking model assumptions. Transformations for treating non-normality and heteroscedasticity. Approximating non-linear relationship with splines or polynomials.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Analysis of a problematic dataset II.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Multiple testing I. Tukey HSD, tests and confidence intervals based on multivariate t-distribution.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Multiple comparisons.
|
Total ECTS (Creditpoints):
6.00
Contact hours:
36 Academic Hours
Final Examination:
Exam (Written)
Bibliography
Required Reading
1.
Faraway, J.J. Linear Models with R. Taylor & Francis group, 2014.
2.
Christensen, R. Plane answers to complex questions - the theory of linear models. Springer, 2011.
Additional Reading
1.
Harville, D.A. Matrix Algebra From a Statistician's Perspective. Springer, 2008.
2.
Puntanen, S., Styan, G. and Isotalo, J. Matrix tricks for Linear Statistical Models. Springer, 2011.