# [Rasch] Rsch and CFA

Svend Kreiner svkr at sund.ku.dk
Wed Jun 13 07:10:42 EST 2012

```And regarding 2: no there is no proof of a causal relationship. A reciprocal relationship between the latent variable and the items (where items are conditionally independent given the latent variable) is mathematically equvalent to the causal model.

Regarding 3: cfa and sems could easily be used as measurement models. I guess they simply do not care about person measurement.

Cheers Svend
________________________________________
From: rasch-bounces at acer.edu.au [rasch-bounces at acer.edu.au] on behalf of Rense Lange [rense.lange at gmail.com]
Sent: Tuesday, June 12, 2012 8:53 PM
To: rasch at acer.edu.au
Subject: Re: [Rasch] Rsch and CFA

Regarding 1: Sure there is an error term, it follows directly from Rasch models' probabilistic nature. The model gives the probabilities of getting one item correct and from there one can compute the probabilities of getting any number items correct in a set, and from there one can obtain (e.g, via bootstrapping) the likely error in the Rasch measure. Of course Winsteps already told you the answer you will get ...

On Jun 12, 2012, at 9:55 AM, Anthony James wrote:

Dear colleagues,
I have some questions on Rasch and other latent trait models.

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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