## Admission Requirements

Statistics and probability.

## Description

In behavioral sciences, life sciences, and official statistics it is customary to measure properties of individuals rather than populations. Many properties of individual subjects, such as extroversion, verbal intelligence, the quality of life after an eye operation, or the tendency to avoid taxes, cannot be measured directly. These attributes are latent and can only be gauged via the measurement of manifest variables which are contingent upon them. Latent variable models make this possible. This course will provide you with in-depth knowledge of latent variable models, and you will learn to work with them. During the course, you will work on the analysis of empirical and simulated data and make exercises about the theory. Substantive issues are only cursorily discussed; this is primarily an applied statistics course.

In this course, we work mainly with test data, although other data sources, such as capture-recapture data to estimate latent prevalence of attributes, have been analyzed with latent variable models too. A test consists of a number of separate items--- questions to be answered or problems to be solved. The responses to these items are used to obtain a score that approximates the subject's level on a latent variable. Researchers are interested in various aspects of these scores. In particular, one may want to know something about its meaning, reliability, validity, and the best way to obtain them. To this end, latent variable models for tests and item responses have been developed.

An important topic in psychometrics is the study of (causal) relations between these 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 be estimated and the fit of the model tested. SEM’s are frequently used in disciplines like behavioral genetics (twin studies), sociology, and econometrics.

The course has three parts: Part I deals with traditional test theory, Part II with modern test theory and latent-class analysis, 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, such as adaptive testing and equating the scores of different tests, are discussed at the end of 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. All computations and simulations will be performed with R.

## Course objectives

Understand the mathematics of latent variable models and be able to derive some of their properties from basic assumptions. Being able to analyze real empirical data with latent variable models and interpret their outcomes. Some knowlege of reasons why models fail and how to deal with it.

## Timetable

See the Leiden University students' website for the Statistics and Data Science programme ->

## Mode of Instruction

Studying a textbook, following lectures, making exercises. Analyzing empirical data. This work may be done in small groups of two or three students. During practicals lecturers may be consulted.

## Assessment Method

The final grade depends on an open-book written exam. Access to the exam depends on the successful execution of assignments, one for each part of the course. Passing at least 2 out of the 3 assignments is required to be able to take the exam. Assignments are completed and submitted no later than at the end of each part. In the final week, a presentation is given over the material of the whole course. Course credits will be obtained when the exam is graded by at least a 6. The assignments are reports on the analysis of test data with: I classical test theory, II modern test theory, III structural equation models. The exam tests insight into the theory gained by executing exercises and studying the book.

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

## Reading List

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

Computer manuals (to be announced during the course).

## Registration

Enroll in Usis for the course materials and course updates.

If one is eligible to do in the exam, to obtain a grade and the EC 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.

## Contact

Prof.dr. H. Kelderman: h.kelderman@fsw.leidenuniv.nl

Dr. J.D. Karch: j.d.karch@fsw.leidenuniv.nl