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I recently came across the definition of unidimensionality (in the context of IRT and internal consistency reliability, specifically Cronbach's alpha). Johnsosn (2007) states that

There is a one-dimensional, unknown quantity associated with each respondent in the sample that describes the individuals propensity to endorse the items in the survey (or exam). Let θv denote the propensity of individual v.

However, i though that unidimensionality was the fact that items in the scale measure the same construct, "the same thing".

What does unidimensionality refer to in this context?

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  • $\begingroup$ The "same thing" is the "one-dimensional, unknown quantity". If the items didn't measure the same thing, and instead measured two different things, then each individual would have a two-dimensional quantity associated with them. It sounds like your confusion is really about whether the interpretation of a construct is attributed to the individual or to the scale, which is a much broader question. $\endgroup$ – Noah May 20 '19 at 23:54
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I think that Johnson's interpretation is more correct. Your statement that

the fact that items in the scale measure the same construct, "the same thing".

isn't inconsistent with Johnson, I think.

Consider depression. I'm not a clinician, but depressive symptoms can be classified into two broad categories.

Affect and cognitive symptoms: sadness, apathy, feeling hopeless, feeling worthless, feeling guilty, suicidal ideation. Somatic: feeling tired, appetite disturbances, sleep disturbances

You might even be able to split the first category into affect (feelings, mood) vs cognitive (thoughts, e.g. I'm worthless, others are better than me, life isn't worth living).

This slide is from my dissertation presentation. Say you have 9 questions on depression (specifically, the PHQ-9 questionnaire). Traditional IRT models are unidimensional. So, your 9 questions have to be adequately represented by this conceptual model:

enter image description here

As opposed to something more like this:

enter image description here

The thing is, I believe that traditional IRT models can be robust to some degree of multidimensionality if the dimensions are strongly correlated. The affective, cognitive, and somatic aspects of depression may be strongly correlated enough in most people that the traditional depression scales work well enough under unidimensional IRT. I have one citation to back this up, but it's in a book chapter.

Reise SP, Cook KF, Moore TM. Evaluating the Impact of Multidimensionality on Unidimensional Item Response Theory Model Parameters. In: Handbook of Item Response Theory Modeling: Applications to Typical Performance Assessment. 1st ed. New York, NY: Routledge; 2015:13-40.

Moreover, you can explicitly model multidimensionality. You may want to google multidimensional IRT or bifactor models for two ways to accomplish this. My second picture is what you'd assume under a multidimensional IRT model. In bifactor models, you'd assume there's one primary trait on which all the items load, and then subsets of the items load on one or more secondary factors, e.g.

enter image description here

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