It’s been a while since measurement invariance alignment has been introduced in 2014, but not that many researchers applied it in practice. Among ~200 citations (as of May 2019) of the original alignment paper there were only a few substantive applications. It is a pity because you can always enjoy more optimistic results with alignment as compared to the conventional (frequentist, exact) measurement invariance techniques. I guess, it’s been happening due to statistical complexity and a lack of simple guidelines. In this post I summarized, in an approachable way, the steps that are necessary to apply alignment procedure. In addition, I provide couple of R functions which automate preparation of Mplus code and extraction of useful information from the outputs.

[November 13, 2020]: The post was updated to make it fully reproducible.

## Contents

Intro

Step 1. Find an acceptable configural invariance model

Step 2. Set up “FREE” alignment model in Mplus

Step 3. Set up “FIXED” alignment model

Step 4. Interpret the “Approximate measurement invariance” output

Step 5. Interpret “FACTOR MEAN COMPARISON” output

Step 6. Interpret “ALIGNMENT OUTPUT” output

Step 7. Checking the reliability of the results with simulation

Example Mplus files

Additional options (Bayesian estimation, estimation fine tuning, extra mean ranking table, fit function contribution, categorical indicators)

Software, including automation in R

Resources