Marginal reliability is based on the true score model (Lord & Novick, 1968) and is an estimate of the overall reliability of a test based on the average conditional standard errors. Often it is close in value to coefficient alpha (and sometimes it may even be identical). Several of the resources I have reviewed on this issue seem to suggest that alpha provides a lower estimate of marginal reliability. The formula used to define marginal reliability is reproduced below:
Thank you. I am familiar with the book but do not remember it discussing marginal reliability with MPlus. I will contact Dr. Raykov directly to see if he has any ideas on this. One final question: how do I pull up a plot of the SEMs in an IRT analysis?
I am sorry if it sounds like I am jumping from one thing to the next but I was told by a reviewer to provide a reliability estimate for my IRT analysis and the only IRT reliability estimate I was familiar with at the time was marginal reliability. In speaking with Dr. Raykov, however, it appears that marginal reliability is not used much any more (and so the plot of the IRT SEMs is no longer relevant). I have found a reference that shows how to calculate composite reliability from IRT data but I need the standardized factor loadings. My new questions are as follows: 1. are the discrimination parameter estimates in an IRT analysis the factor loadings (and if not, what is?). 2. are these estimates standardized and if not, what do I need to do to get standardized estimates?