Measurement Models: Topics

The table below outlines the topics covered in the three-day measurement models workshop. Measurement models encompass factor analysis models, item response theory models, and some latent class and latent profile mixture models. Measurement models are important for scale development, intermediate outcomes, errors-in-variables models, etc. Briefly, day 1 introduces the kinds of research questions approached using measurement models; an introduction to Mplus software; using Mplus software; and the importance of workflow; finally, measurement models are introduced. Day 2 introduces Item Response Theory (measurement models for ordinal dependent variables) and Differential Item Functioning (DIF) detection. Day 3 expands the discussion of DIF and introduces special modeling issues and approaches, including models with latent classes, complex sampling weights, and Bayesian data analysis.

Note about 2021 Workshop

Usually, this is a three day workshop 9-4 (we break for an hour for lunch, so about 18 hours). In 2021, we'll do the content below over 4 days 11-3 with a half hour break in the middle (14 hours). The reason for the change is people may be participating from home and from different time zones.

Day 1


  • Workshop Objectives
  • Content Covered in Workshop
  • Resources to Continue Learning After Workshop
  • Broad Overview of Measurement-Related Research Questions

Orientation to General Latent Variable Modeling Framework

  • Path Diagram Notation
  • Perspectives on Latent Variables

Orientation to Mplus

  • Writing a Mplus command file
  • Using Mplus on a PC
  • Using Mplus on a MAC
  • Getting Data into Mplus (Using SAS, SPSS, Stata, R)
  • Workflow and Reproducibility

Factor Analysis

  • Dimensionality
  • Model assumptions
    • Good Practice
    • Bad Practice
  • Exploratory Factor Analysis
  • Model Fit Statistics: Interpretation and Use
  • Confirmatory Factor Analysis (CFA)
  • Bifactor Analysis
  • CFA with Covariates
    • Multiple Indicator, Multiple Cause Models (MIMIC)
    • CFA with Covariates and Direct Effects
    • Model Building Strategies (model fitting, decision logic)

Day 2

Item Response Theory (IRT)

  • Item Response Theory
  • Test and Item Information
  • IRT as a general latent variable model
  • Latent Response Variable Formulation for Categorical Dependent Variables
  • Assumptions of IRT
  • Applications of IRT

Day 3

Differential Item Functioning

  • Uniform Differential Item Functioning
    • Detection with CFA with Covariates
    • Detection with Multiple Group CFA
    • MIMIC Models with categorical dependent variables
  • Non-uniform DIF
    • Multiple Group CFA
    • Multiple Group MIMIC
  • Algorithm for model building with Multiple Group CFA for DIF
    • Using Mplus and DIFFTEST procedure to detect uniform DIF
    • Automating the DIFFTEST procedure to enhance reproducibility and reduce risk of errors
    • Comparison with other methods and software
    • Non-Uniform DIF using a single group approach

Day 4 2021

  • Factor Mixture Models

  • Incorporating Complex Sampling Weights

  • CFA with Bayesian Data Analysis techniques

  • Responsible Conduct of Research

    • Confidentiality

    • Sensitivity

    • Understanding Group Differences Research versus Individual Effects

    • Circularity and Ipsativity in Measurement Research

  • Resources to Continue Learning After Workshop