How is Item Response Theory (IRT) called for continuous response?

Question

I would like to model my problem using something similar to Item Response Theory - but my responses are not binary - they are continuous in [0;1].

How are these models/the research field called?

Does "linear response" mean that you're dealing with a continuous response (or manifest) variable in [0;1]?
Thanks. Could you indicate what is the response variable, precisely? We also need additional information: Do you assume discrete or continuous latent variable(s)? (Some authors, like Bartholomew & Knott, Skrondal & Rabe-Hesketh, or De Boeck, have emphasized the importance of such distinction between latent and manifest variables in the past.)
I'll look at the book. I assume continuous latent variables. I want to model Triathlon finishing time (continuous response variable). There's an athlete who has abilities (swimming, endurance, ...) and item's which have difficulties (route difficulty, climate ...)
B&K book: Table 1.3, p. 11. I would say this has more to do with Factor Analysis, then, but I wonder why response times are bounded in [0;1].

RJ Wirth · Accepted Answer · 2012-11-29 21:52:08Z

up vote 2 down vote accepted

If you have a continuous indicator, then you would use factor analysis. Think of FA as linear regression and IRT it's logistic regression brother.

answered Nov 29 '12 at 21:52

RJ Wirth
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1 Answer