Lets use methods from Item-Response Theory to look at the relation between each item and the latent variable. See here for a walkthrough of the theory.

As discussed in the theory walkthrough, a graded response model is appropreate where we have a polytomous responses (e.g. levels of agreement). We know that most of the variation is explained by the first factor. We’ll first look at the Item Characteristic Curves for each item, then the Item Information Curve accross all items. We’ll impliment the graded response model using the package “ltm”.

Looking at each plot in turn, it appears there is good discriminatory power above the mean of the supposed latent construct (psychological distress). However, many of the items have poor discriminatory power below the mean. As a result, the items don’t allow us to differentiate between people that are have low levels of distress. This isn’t very surprising. Now lets look at the Item Information Curve, across all items.

As we suspected, we get a strong floor effect where none of our items tell us much about those that are at the extreme low end of the latent trait. I am unsure of how much of a problem this is - from a modelling perspective. It appears from Flora & Curran (2004) that robust weighted least squares (which we’re doing) performs well when analysing (ordinal) data with strong floor/ceiling effects.