[Rasch] Rsch and CFA

David Torres Irribarra dti.berkeley at gmail.com
Wed Jun 13 01:58:11 EST 2012


Hi,

Some thoughts on these three points:

1. One way of thinking about this: In regular linear regression you can write the equation with or without error depending on whether you are modeling the observed response y (in that case you write + e_i term) or if you are modeling the expected value of y (in which case you do not write the + e_i term). In the Rasch model, which is a form of logistic regression, you are not modeling the observed response y, you are modeling an expected value (i.e. the log odds of the probability of answering correctly to the item), so in the same sense, you do not write the error term. 

2. I am not sure that there is agreement regarding a causal interpretation about the Rasch model (or any other latent variable model for that matter). For an introductory discussion on this point (from the perspective of someone who favors the causal interpretation) you may want to read the chapter on latent variables and the chapter on validity on 'Measuring the Mind' by Borsboom.

3. I think that the way in which CFA is used vary considerably from field to field. I am not sure I would say that CFA users do not use factor scores.

Regards,

David Torres Irribarra

Sent from my iPad

On Jun 12, 2012, at 7:55 AM, Anthony James <luckyantonio2003 at yahoo.com> wrote:

> Dear colleagues,
> I have some questions on Rasch and other latent trait models.
> Please help clarify things for me.
>  
> 1.      In latent trait models based on CTT there is always an error term in the equations. But in formulations of Rasch and IRT models there is no room for error.  Why? Why don't we assume that in the responses to items error also plays a role?
> 2.      Is there any proof in the Rasch and IRT models to show that observed item responses are CAUSED by the latent variable. I mean is there a proof to establish a causal relationship between observed and latent variables?
> 3.      Why aren’t confirmatory  factor analysis and structural equation modeling used as measurement models in the way IRT models are used. I mean why don’t CFA people base person scores on factor scores from CFA?
>  
> Cheers
> Anthony
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