# Psychometrics and Structural Equation Modeling

Course
2024-2025

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 and scale 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. Similarly, scale scores attempt to measure some latent dimension (e.g., depression, extraversion). 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. These relations are depicted by vertices in a directed graph and modeled by regression equations. Structural equation models (SEMs) allow the researcher to specify this relation structure on a set of manifest or latent variables. The parameters of such SEMs can be estimated and the fit model fit 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 classical test theory, Part II with modern test theory, item response theory, and factor analysis. 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. Advanced applications of modern test theory, such as adaptive testing, differential item-functioning, and equating the scores of different tests, are discussed at the end of Part II. Part III concerns structural equations models, and extensions of measurement models to questions such as population heterogeneity and change-over-time. These topics 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 knowledge of reasons why models fail and how to deal with it.

## Timetable

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of Instruction

Studying a textbook, following lectures, completing data assignments. 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 two take-home data assignments and a written exam. The final grade will be based on the following three components:

• Graded Take-Home Assignment 1 (individual, specific date will be announced on brightspace, 20% of the final grade)

• Graded Take-Home Assignment 2 (individual, specific date will be announced on brightspace, 20% of the final grade)

• Open-book written exam (individual, 60% of the final grade, the exam needs to be graded with at least a 5.5 to pass the course)

The final grade will be the average of the scores from these three components. To pass the course, your final score must be 5.5 or higher.

Given the breadth of the course across several methodological areas, readings (open-access) will be provided per-topic.

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

• Enrolment for the fall opens in July

• Enrolment for the spring opens in December

Note:

• It is mandatory to enrol for all activities of a course that you are going to follow.

• Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

• Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Hannelies de Jonge: h.de.jonge@fsw.leidenuniv.nl

## Remarks

Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.