Dear community,

I wanted to ask if someone knows of examples of items that, after a calibration by means of factor analysis / multidimensional IRT, have resulted in having such a property. That is, an item that has at least two factor loadings (or, equivalently, discrimination parameters), at least one of them positive and another one negative.

Example:

A (hypothetical) instrument for assessing ADHD could have two latent factors / dimensions, each one measuring the predominance of "attention deficit" symptoms, and the other measuring the predominance of "hyperactivity" symptoms. An item could measure in a "positive" sense the attention deficit factor, thus increasing the probability of endorsing it with an increase in the attention deficit symptoms, while measuring in a "negative" sense the hyperactivity factor (decreasing the probability of endorsing it with an increase in the attention deficit symptoms).

A similar example could be put forward e.g. for an instrument that measures e.g. depression/anxiety symptoms.

Examples of items that load on non-substantive factors (e.g. response styles or similar) could also serve my purpose.

Do any examples of such items exist in the wild, that anyone in this community know of? Your help will be much appreciated!

Also, apologies for any imprecisions regarding assessment/clinical conditions. I'm a pure psychometrics guy :)