85177 - Latent Variable Models

Course Unit Page

Academic Year 2021/2022

Learning outcomes

By the end of the course the student acquires knowledge of multivariate statistical methods based on latent variable models for the analysis of categorical and continuous data. The student is also able to choose the best method to perform multivariate analyses of a given dataset and to interpret the obtained results.

Course contents

Introduction to the latent variable models.

The normal linear factor model: specification, maximum likelihood estimation by the EM algorithm, goodness of fit.

Latent trait model with binary data: specification of logit/normit model and normit/normit model, model estimation by the E-M algorithm, goodness of fit.

Latent trait model with polytomous and ordinal data: specification and parameter interpretation. The underlyng variable approach.

Latent class model with binary data: specification, identifiability, maximum likelihood estimation, goodness of fit.


Bartholomew D., Knott M., Moustaki I (2011), Latent variable models and factor analysis : a unified approach/third ed. Chichester, UK : Wiley.


Bartholomew D., Moustaki I., Steele F., Galbraith J.I. (2002), The Analysis and Interpretation of Multivariate Data for Social Scientists,Chapman and Hall/CRC.

Teaching methods

Lectures and tutorials in R

Assessment methods

The exam consists of a mandatory written exam lasting two hours. It is composed by questions concerning the theoretical aspects and one exercise in R focused on the data analysis and on the interpretion of the results. The final mark is given by the sum of the partial grades given to the exercise and to the theoretical questions and is expressed out of thirty.

During the exam the use of textbooks, notes and computers tools are not allowed.

Teaching tools

Teacher's notes available at the web-site https://virtuale.unibo.it/

Office hours

See the website of Silvia Cagnone