- Credits: 4
- Lectures: 2 lectures weekly, 50 minutes each. Mondays 18:00 - 18:50, Wednesdays 18:00 - 18:50 in classroom P21b
- Instructor: Mgr. Adam Ťápal, M.A.
Course summary:
Factor analysis is ubiquitous in psychology. An idea originally developed by Charles Spearman for the study of human cognitive abilities, factor models constitute an important methodology in many sub-fields of psychological science. Factor analysis is by no means important only to researchers and methodologists – anyone who wishes to be a critical consumer of psychological science should acquire some understanding of it, whether one works with tests, scales, in personnel selection, counselling or clinical environments.
This course is designed to provide a deeper understanding of factor analysis than is usual in broader, general courses of statistical data analysis offered in most psychology programs. Students will learn about the mathematical formulation and the reasoning behind the Common Factor Model, the methods for fitting the model on data and evaluating model fit, common estimation methods and problems related to the model and its use. The course will further cover unrestricted (exploratory) and restricted (confirmatory) factor models as well as software to be used for fitting them, different criteria of analytical rotation, widely used fit indices and special topics such as bi-factor models, group models, classical test theory applications or the differences between factor analysis and principal components analysis
Requirements and relation to other courses:
Students are strongly recommended to have taken at least an elementary course in statistical data analysis. Understanding of multiple linear regression is beneficial, as is at least basic knowledge of R. Students with zero or little previous exposure will be given resources and time to catch up and will be expected to do so. Learning the material in this class will enhance students’ understanding in related courses such as psychometrics or psychological assessment, as well as provide them with skills useful in carrying out their own research.
Mathematics anxiety:
Don’t be afraid of math! It is common among students in social sciences to get scared whenever equations and strange symbols pop up in lecture materials. However, mathematics is in many cases nothing but an abstract language we use to grasp concepts and work with them. The fact that you are a university student means you are very likely to be able to learn and speak this language if you put in a bit of effort. Although we will study mathematical notation and formulas in this course, an ordinary background in high-school math is sufficient, and other topics will be reviewed. If you are worried nonetheless, give the course a shot and be assured you will understand the material if you try.
Course requirements:
- Participation: Regular attendance and participation is monitored. Students are not required to attend every session, but are strongly recommended to do so. More specific participation rules will be laid out during the first class.
- Homework: Three homework assignments will be distributed over the semester. Each assignment constitutes 20% of the final grade. Failing to submit the homework will award the student with zero points.
- Exam: A final take-home exam will be distributed in the last class. The exam constitutes 40% of the final grade. Failing to submit the final exam will result in not passing the course. A short oral discussion of the submitted exam and homework is mandatory part of the exam.
- Grading:
- A >= 92%
- B >= 84%
- C >= 76%
- D >= 68%
- E >= 60%
- F < 60%
- Academic misconduct: Any form of academic misconduct, such as cheating, copying homework or exam, or unauthorized teamwork will not be tolerated. In case of suspicion for academic misconduct, the instructor will notify the disciplinary committee. In other words - please work on the assignments yourselves and only yourselves. The course is not that hard, c'mon.
Course topics:
- Introduction (1-2 classes)
What is factor analysis? Objectives, goals and principles. Definition of used terms. Review of key concepts. Exploratory vs. Confirmatory factor analysis. Brief history of factor analysis - Matrix algebra (1-2 classes, Homework assignment 1)
Scalars, vectors and matrices – what is a vector, what is a matrix? Why bother with vectors and matrices? Basic matrix and vector operations and functions. - The Common Factor Model (1-2 classes)
The fundamental equations of factor analysis. The fundamental theorem of factor analysis. What is the factor model, actually? Mean, covariance and correlation structures. - Fitting the model on data (3-4 classes)
Methods of fitting the model on data. Model identification and rotational indeterminacy. Fitting the model on population and sample correlation matrices. The communality problem. Iterative and non-iterative estimation – Principal Factors Method, Ordinary Least Squares, Maximum Likelihood. Heywood cases. Evaluating model fit - Fitting the unrestricted model with software (1-2 classes)
Fitting the model in CEFA. Concise overview of other selected software. - How many factors do I choose? Is the model any good? (2 classes)
Common rules of thumb and guidelines for choosing the number of factors. Alternative methods - parallel analysis, minimum average partial. Goodness-of-fit tests. Common fit indices. - Rotation (1 class, Homework assignment 2)
The concept of rotation and simple structure. Orthogonal rotations, oblique rotations, target rotation. - Factor scores and sample size in factor analysis (1 class)
How do we (and should we?) obtain factor scores? How big of a sample do I need? - Restricted (confirmatory) factor analysis (3 classes)
Goals and purposes of confirmatory factor analysis. Constraints, restrictions and identification conditions. Parameter matrices. Free and fixed parameters. Path diagrams. Common estimation methods. - Fitting the restricted model with software (1-2 classes)
- Goodness of fit in CFA (2-3 classes, Homework assignment 3)
Methods and processes for evaluating model fit. ommon fit indices. Tests of good fit. Comparing different models. - Special topics
Bi-factor models. Group models. Differences between Principal Components Analysis and Factor analysis. Classical Test Theory Applications.
Resources
- Class notes. Notes for each topic compiled by the instructor will be made available before every class. The class notes will constitute sufficient material for the assignments and exam.
- Broadening literature. Mulaik, S. A. (2009). Foundations of factor analysis, Second Edition. CRC Press. [available from the instructor upon request]