[Rasch] multidimensional vs two unidimensional models

Swank, Paul R Paul.R.Swank at uth.tmc.edu
Sat May 3 02:49:21 EST 2014

I would guess that the two dimensional model is controlling for the unreliability in the measures whereas when you look at the raw correlations, it is not. Thus the .75 represents correlations between latent constructs whereas .39 is the correlation between manifest or measured variables.

 Dr. Paul R. Swank, Professor 
Health Promotion and Behavioral Sciences
School of Public Health
University of Texas Health Science Center Houston

-----Original Message-----
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Iasonas Lamprianou
Sent: Friday, May 02, 2014 11:37 AM
To: rasch at acer.edu.au
Cc: iasonas at ucy.ac.cy
Subject: Re: [Rasch] multidimensional vs two unidimensional models

Dear friends,

I am running an analysis on a very interesting dataset and I would like to benefit from your experience with multidimensional Rasch models. I am using a Conquest-like implementation in the open-source platform R (the package is called TAM). Essentially, according to the authors, they have moved the Conquest algorithms to R. For all practical intents and purposes of this discussion, we can assume that I use (a flavour of) Conquest. 

I have 22 dichotomous questions and 5000 persons. Twelve of the questions tap on dimension 1 and 10 questions tap on dimension 2. I tried running two independent unidimensional Rasch models with satisfactory results (good fit statistics). I extracted the person estimates from the two analyses and the correlation was r=0.39. It may be important to say that for the second scale there is a very strong floor effect, more than 50% got 0 (I know that this is a problem, but there is nothing I can do at this point). Since I use MML estimation, the software gave some reasonable estimates for those people, but it is likely hat this may have affected the correlation between the two dimensions. However, when I run a two-dimensional Rasch model, where each item taped only on its dimension, the reported correlation of the two latent dimensions as reported by the software was 0.75! But if I extract the two lists of estimates (on the two dimensions), the correlation is 0.39 (the same as the correlation from the two independent analyses). I wonder why is that? Could the effect of the two-dimensional model be so high?

Also, the "EAP reliability" of the second dimension (the one with the high floor effect) is reported to be 0.268 when I run the analysis individually, however, the same statistic becomes 0.449 when I run the multidimensional model (the EAP reliability of the first scale is not increased significantly). 

My questions are: 
(a) is it reasonable for the correlation between the two dimensions to be twice as large (for the two-dimensional model) as the correlation of the estimates of the independent analyses? Or am I doing something wrong? Did anyone have such an experience before? 
(b) why is the EAP reliability increased so much? Does the second dimension "gain" information from the first dimension?

If I run a unidemensional model with all 22 items and compare it with the two-dimensional model (two nested models) I get significant results but not too impressive:
    Model   loglike Deviance Npars      AIC      BIC   Chisq df       p
1 Model 1 -21435.62 42871.25    23 42917.25 43066.63 10.5914     0.00501
2 Model 2 -21430.33 42860.65    25 42910.65 43073.03      NA NA      NA

Would you be tempted to consider the 22 items to be unidimensional since the correlation between the two latent dimensions is reported to be 0.75 and since there is only a modest reduction to the Deviance when I fit the two-diemensional model? 

Thank you for your patience to read this long email. I hope  one of you may have similar experiences to share or comments to send for my questions. 

Have a nice weekend,

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