Tony LI posted on Friday, June 25, 2010 - 10:32 pm
Dear Linda, Bengt,
I am wondering if Mplus can model an IRT model for continuous item responses ? (reference below)
Mellenbergh, G. J. (1994). A unidimensional latent trait model for continuous item responses. Multivariate Behavioral Research, 29, 223–236.
[Abstract] Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.
I think this is simply latent class analysis and factor analysis where the outcomes are continuous. Both of these models can be estimated in Mplus.
Tony LI posted on Friday, June 25, 2010 - 11:31 pm
Sorry Linda, I made a error-the abstract above is for another paper, the correct one is:
[A general linear latent trait model for continuous item responses is described. The special unidimensional case for continuous item responses is Joreskog's (1971) model of congeneric item responses. In the context of the unidimensional case model for continuous item responses the concepts of item and test information functions, specific objectivity, item bias, and reliability are discussed; also the application of the model to test construction is shown. Finally, the correspondence with latent trait theory for dichotomous item responses is discussed. ]
I just want to let you know about an IRT model proposed by Samejima(1973) for continuous responses. Below are two references about the topic. In addition, the model parameters can be estimated by using a recently released R package "EstCRM".
Ferrando, P.J.(2002). Theoretical and Empirical Comparison between Two Models for Continuous Item Responses. Multivariate Behavioral Research, 37(4), 521-542.
Samejima, F.(1973). Homogeneous Case of the Continuous Response Model. Psychometrika, 38(2), 203-219.
Rich Jones posted on Thursday, May 10, 2012 - 12:31 am
I think this can be approached by taking normalized continuous responses (y falling between 0 and 1, but not inclusive), transforming this to logit (as per Samenjima) or probit, and then going about your usual factor analysis business.
I'd be interested if any of the readers or moderators had any thoughts on that.