Parameterization using MLR for IRT PreviousNext
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 Roy Levy posted on Wednesday, November 22, 2006 - 4:17 pm
I'm running an IRT model using


and fixing the variance of the factor to be 1. I find that I cannot use the PARAMETERIZATION option using this estimator. I am curious about the parameterization of the latent response variable formulation of the IRT model. By requesting TECH1 to see the initial values I see that theta initially is a diagonal matrix with 1's on the diagonal. Am I correct in thinking that the elements of theta are fixed at these values? In other words, is it the case that the residual variances for the latent response variables are fixed at 1 during estimation?

Thank you for your time and attention,
 Bengt O. Muthen posted on Wednesday, November 22, 2006 - 4:32 pm
For general information on IRT in Mplus, see

With the default MLR link of logit, there are no residual variance parameters to be estimated (see also IRT books). You can, however, think of residuals for underlying continuous latent response variables which with logit would have a logistic density for the residual with res var fixed at pi-square/3 (the logistic density variance) - this is the same as a logit formulation (same in logistic regression). The probit link uses res vars fixed at 1.
 Roy Levy posted on Wednesday, November 22, 2006 - 6:20 pm
Thanks for the speedy reply. I understand your response and this addresses my concern, as I was thinking of underlying continuous latent response variables with the logit link. I was thrown off by seeing 1's in the diagonal of theta as initial values. I suppose they have no influence on the estimation.
 Bengt O. Muthen posted on Wednesday, November 22, 2006 - 6:56 pm
That's right in this case.
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