Help me understand the unidimensionality assumption in test theory (CTT and IRT)

#1
De Ayala (2009) writes:

There is an implicit unidimensionality assumption in CTT. That is, for observed scores to have any meaning they need to represent the sum of responses to items that measure the same thing.
This always made sense to me until recently. In any statement found in a psychological questionnaire, there is semantic overlap between constructs. Heck, we even allow factors to be correlated in obliquely rotaded PCAs and EFAs. As soon as any two factors are correlated, the items cannot be purely unidimensional, right?

Can someone help me understand this better? When do violations against unidimensionality become problematic? I mean, even the big five factors are correlated...
 

spunky

Can't make spagetti
#2
Keep in mind that CTT is old. Like over 100 years old. They were making a lot of assumptions back there to try and make sense of the data they ahve since, most of the time, factor analyses and rotations had to be done by hand. The idea of 'strict unidimensionality', which CTT invokes, is more of a relic of the past. These days we mostly concentrate on what is known as either 'essential unidimensionality' which is basically asking the question "We know these things are not unidimensional. But how much saturation in one dimension can we get away with, while recognizing that other dimensions still exist?"

Or the more modern approaches simply give up on the idea of unidimensionality and work with multidimensional models directly