I mentioned in some links to my previous post on factor analysis with ordinal variables that there’s a link between the approach detailed there, and the approach used to construct standardised aptitude and knowledge tests. In some ways the testing example is even simpler than the introductory example. Here are my notes about how it seems to work:1
Footnotes
If anyone has any direct experience of building or working with such tests, and wants to correct or add further nuance to my notes here, please do! I’m just reasoning from first principles here, so expect there are some additional complexities in practice.↩︎