Linear Models

Study Course Description

Course Description Statuss:Approved

Course Description Version:5.00

Study Course Accepted:14.03.2024 11:46:46

Study Course Information
Course Code:		SL_112		LQF level:		Level 7
Credit Points:		4.00		ECTS:		6.00
Branch of Science:		Mathematics; Theory of Probability and Mathematical Statistics		Target Audience:		Life Science
Study Course Supervisor
Course Supervisor:		Māris Munkevics
Study Course Implementer
Structural Unit:		Statistics Unit
The Head of Structural Unit:
Contacts:		14 Baložu street, Riga, statistikarsu[pnkts]lv, +371 67060897
Study Course Planning
Full-Time - Semester No.1
Lectures (count)		12	Lecture Length (academic hours)		2	Total Contact Hours of Lectures		24
Classes (count)		12	Class Length (academic hours)		2	Total Contact Hours of Classes		24
Total Contact Hours								48
Part-Time - Semester No.1
Lectures (count)		12	Lecture Length (academic hours)		1	Total Contact Hours of Lectures		12
Classes (count)		12	Class Length (academic hours)		2	Total Contact Hours of Classes		24
Total Contact Hours								36
Study course description
Preliminary Knowledge:
Calculus; Probability.
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.
Topic Layout (Full-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Introduction to linear models. Examples: regression, ANOVA. Method of least squares for estimating the model parameters.			Lectures		1.00	auditorium
2	Introduction to the software for estimating linear models.			Classes		1.00	computer room
3	Maximum likelihood method for estimating the parameters, geometric interpretation.			Lectures		1.00	auditorium
4	Interpreting model parameters. Interactions.			Classes		1.00	computer room
5	Linear functions of parameters. T-test for testing hypothesis about parameters, confidence intervals.			Lectures		1.00	auditorium
6	Example analysis (data with run-in period/ modelling a breakpoint).			Classes		1.00	computer room
7	Gauss-Markov theorem, BLUE (best linear unbiased estimator).			Lectures		1.00	auditorium
8	Example analysis. Research questions requiring a customised contrast/linear function of parameters.			Classes		1.00	computer room
9	Prediction of a new observation, prediction interval. Coefficient of determination, R2.			Lectures		1.00	auditorium
10	Estimating a growth curve with prediction intervals. Use of polynomials/splines to model non-linear relationship.			Classes		1.00	computer room
11	F-test for comparing models.			Lectures		1.00	auditorium
12	Comparing models. Different types of tests (type I/type III SS).			Classes		1.00	computer room
13	Power of a F-test, geometric interpretation of F-test.			Lectures		1.00	auditorium
14	Planning of a study. Sample size required to achieve the desired power.			Classes		1.00	computer room
15	Overparameterised models, different parameterisations.			Lectures		1.00	auditorium
16	Example analysis – interpretation of parameters, comparing estimates from differently parameterised models.			Classes		1.00	computer room
17	Concepts of model building. Mallows Cp criterion, Akaike information criterion (AIC), Bayesian information criterion (BIC), stepwise regression.			Lectures		1.00	auditorium
18	Model selection examples. Correct model might not always be the best choice,			Classes		1.00	computer room
19	Model assumptions. Theoretical properties of residuals, leverage, standardized residuals.			Lectures		1.00	auditorium
20	Analysis of a problematic dataset I.			Classes		1.00	computer room
21	Model diagnostics, graphs for checking model assumptions. Transformations for treating non-normality and heteroscedasticity. Approximating non-linear relationship with splines or polynomials.			Lectures		1.00	auditorium
22	Analysis of a problematic dataset II.			Classes		1.00	computer room
23	Multiple testing I. Tukey HSD, tests and confidence intervals based on multivariate t-distribution.			Lectures		1.00	auditorium
24	Multiple comparisons.			Classes		1.00	computer room
Topic Layout (Part-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Introduction to linear models. Examples: regression, ANOVA. Method of least squares for estimating the model parameters.			Lectures		1.00	auditorium
2	Introduction to the software for estimating linear models.			Classes		1.00	computer room
3	Maximum likelihood method for estimating the parameters, geometric interpretation.			Lectures		1.00	auditorium
4	Interpreting model parameters. Interactions.			Classes		1.00	computer room
5	Linear functions of parameters. T-test for testing hypothesis about parameters, confidence intervals.			Lectures		1.00	auditorium
6	Example analysis (data with run-in period/ modelling a breakpoint).			Classes		1.00	computer room
7	Gauss-Markov theorem, BLUE (best linear unbiased estimator).			Lectures		1.00	auditorium
8	Example analysis. Research questions requiring a customised contrast/linear function of parameters.			Classes		1.00	computer room
9	Prediction of a new observation, prediction interval. Coefficient of determination, R2.			Lectures		1.00	auditorium
10	Estimating a growth curve with prediction intervals. Use of polynomials/splines to model non-linear relationship.			Classes		1.00	computer room
11	F-test for comparing models.			Lectures		1.00	auditorium
12	Comparing models. Different types of tests (type I/type III SS).			Classes		1.00	computer room
13	Power of a F-test, geometric interpretation of F-test.			Lectures		1.00	auditorium
14	Planning of a study. Sample size required to achieve the desired power.			Classes		1.00	computer room
15	Overparameterised models, different parameterisations.			Lectures		1.00	auditorium
16	Example analysis – interpretation of parameters, comparing estimates from differently parameterised models.			Classes		1.00	computer room
17	Concepts of model building. Mallows Cp criterion, Akaike information criterion (AIC), Bayesian information criterion (BIC), stepwise regression.			Lectures		1.00	auditorium
18	Model selection examples. Correct model might not always be the best choice,			Classes		1.00	computer room
19	Model assumptions. Theoretical properties of residuals, leverage, standardized residuals.			Lectures		1.00	auditorium
20	Analysis of a problematic dataset I.			Classes		1.00	computer room
21	Model diagnostics, graphs for checking model assumptions. Transformations for treating non-normality and heteroscedasticity. Approximating non-linear relationship with splines or polynomials.			Lectures		1.00	auditorium
22	Analysis of a problematic dataset II.			Classes		1.00	computer room
23	Multiple testing I. Tukey HSD, tests and confidence intervals based on multivariate t-distribution.			Lectures		1.00	auditorium
24	Multiple comparisons.			Classes		1.00	computer room
Assessment
Unaided 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.
Assessment Criteria:
Assessment on the 10-point scale according to the RSU Educational Order: • 2 data analysis projects – 30%. • 12 homeworks – 20%. • Final written exam – 50%.
Final Examination (Full-Time):		Exam (Written)
Final Examination (Part-Time):		Exam (Written)
Learning Outcomes
Knowledge:		• 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:		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.
Competencies:		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.
Bibliography
No.	Reference
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.