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Psychometrics and SEM


Admission Requirements



This course will provide you with an overview of tools for the analysis of test data. You will learn to understand and apply these tools using statistical software. During the course, you will work on the analysis of empirical data and make exercises about the theory. A more general aim is to enhance your psychometric research skills.
In psychology and education, attributes of individuals are often measured with tests. A test consists of a number of separate items, questions or problems to be solved. The responses are used to obtain a score that indicates the degree to which a person possesses a certain quality, e.g. compulsiveness or spatial intelligence. Behavioral scientists are interested in various aspects of the scores of such tests. In particular you may want to know something about its meaning, reliability, validity, and the best way to obtain such a score. To this end statistical theories for tests and measurements have been developed. In this course you will learn to understand the main test theories and to apply them. Substantive issues are only cursorily discussed; this is primarily an applied statistics course.
The attributes measured with tests are not directly observed but are indirectly measured by test items. Such indirectly measured attributes are called latent variables or, in the context of mental testing, latent traits. Behavioral scientists are interested in the (causal) relations between such latent variables, where relations are usually modeled by regression equations. Structural equation models (sem) allow the researcher to specify a relation structure on a set of directly or indirectly measured variables. The parameters of such sem’s can estimated and the fit of the model tested.
The course has three parts: Part I deals with traditional test theory, Part II with modern test theory, Part III with structural equations models. The first is most often used practice, but the second is more statistically sound and has a usefulness that goes far beyond that of traditional test theory. Some more advanced applications of modern test theory are discussed at the end of the Part II. The final part combines latent variables in a system of regression equations. Both classical and modern measurement models can be integrated into sem’s, but we limit ourselves to the model for continuous observed variables. All computations and simulations will be performed with R.

Course objectives

Provide an overview of tools for the analysis of test data.

Time Table

For the course days, course location and class hours check the Time Table under the
tab “Statsci Students —> Program Schedule” at

Mode of Instruction

Each week there is a lecture about the topic to be studied. Outside the lectures time should be spent on making exercises about the text: questions, derivations, and simulations and analysing empirical data.

Furthermore, students are advised to read the designated text before each meeting.

Method of Assessment

The final grade depends on open-book written exam 100% and three assignments (pass/fail), one for each part of the course. Assignments are completed and submitted at the end of each part.

Course credits will be obtained when the exam is graded by at least a 6, and one passes each of the assignments each simply graded OK (1), not OK (0). The assignments are reports on the analysis of test data with: I classical test theory, II modern test theory, III structural equation models.

Empirical data is provided by the lecturer. You may also analyze your own data if they are appropriate for this course.

Date information about the exam and resit can be found in the Time Table pdf document under the tab “Masters Programme” at The room and building for the exam will be announced on the electronic billboard, to be found at the opposite of the entrance, the content can also be viewed here.

Reading List

  • McDonald R. P. (1999). Test Theory: A Unified Treatment, London: Lawrence Erlbaum.

  • Papers (to be announced during the course).


Enroll in Blackboard for the course materials and course updates.

To be able to obtain a grade and the ECTS for the course, sign up for the (re-)exam in uSis ten calendar days before the actual (re-)exam will take place. Note, the student is expected to participate actively in all activities of the program and therefore uses and registers for the first exam opportunity.

Exchange and Study Abroad students, please see the Prospective students website for information on how to apply.

Contact information

Kelderman [at] fsw [dot] leidenuniv [dot] nl


  • This is an elective course in the Master’s programme of the specialisation Statistical Science for the Life & Behavioural sciences.