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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?

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Does "linear response" mean that you're dealing with a continuous response (or manifest) variable in [0;1]? –  chl Nov 27 '12 at 15:36
    
Yes, I changed the title;-) –  user1141785 Nov 28 '12 at 9:01
    
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.) –  chl Nov 28 '12 at 13:20
    
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 ...) –  user1141785 Nov 28 '12 at 19:22
    
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]. –  chl Nov 28 '12 at 20:27
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up vote 3 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.

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