[Rasch] local independence

Svend Kreiner svkr at sund.ku.dk
Fri Sep 6 06:31:52 EST 2013

First, PROMIS guys  are not examining EFA residuals. They are examining CFA residuals.

The difference between CFA analysis and IRT and Rasch analysis of local dependence is that we in principle are looking at the partial correlations among items controlled for the latent trait (which would be equal to the correlations of the Rasch residuals if the Rasch model had been a linear model) whereas they are looking at the marginal correlations without control for the latent trait. 

Analysis of partial correlations is better because we know that the partial correlations should be equal to zero under the Rasch/IRT model so that a positive correlation is evidence of positive local dependence.

During CFA analysis, an observed correlation between two items that is larger than the fitted correlation under the CFA model can be taken as evidence of positive local dependence. Of course, many people doing CFA analysis automatically thinks about multidimensionality when they have evidence of local dependence, but that is another story. The same is often the case among Rasch modellers.



From: rasch-bounces at acer.edu.au [rasch-bounces at acer.edu.au] on behalf of Tyner, Callie [callietyner at PHHP.UFL.EDU]
Sent: Thursday, September 05, 2013 6:20 PM
To: rasch at acer.edu.au
Subject: Re: [Rasch] local independence

Thanks Mike for the input

I got the idea to examine EFA residuals from the PROMIS (Reeve, et al., 2007) paper on item calibration  [Reeve, B. B., Hays, R. D., Bjorner, J. B., Cook, K. F., Crane, P. K., Teresi, J. A., … Cella, D. (2007). Psychometric evaluation and calibration of health-related quality of life item banks: Plans for the Patient-Reported Outcomes Measurement Information System (PROMIS). Medical Care, 45(5), S22-S31. doi:10.1097/01.mlr.0000250483.85507.04]

Here the authors give the following methods for assessing items:
II. Evaluate Assumptions of the Item Response Theory (IRT) Model
A. Unidimensionality
     1. Confirmatory Factor Analysis (CFA) using polychoric correlations (one-factor and bi-factor models)
     2. Exploratory Factor Analysis will be performed if CFA shows poor fit
B. Local independence
     1. Examine residual correlation matrix after first factor removed in factor analysis
     2. IRT-based tests of local dependence
C. Monotonicity
1. Graph item mean scores conditional on total score minus item score
2. Examine initial probability functions from nonparametric IRT models

I've underlined the part that references looking at the residual correlation matrix from the factor analysis.  Are other people not using this method?

Thanks all for the edification and discussion,

From: rasch-bounces at acer.edu.au [rasch-bounces at acer.edu.au] on behalf of Mike Linacre [mike at winsteps.com]
Sent: Thursday, September 05, 2013 10:55 AM
To: rasch at acer.edu.au
Subject: Re: [Rasch] local independence

Thank you for the questions, Callie.

EFA residuals are not the same as Rasch residuals. EFA residuals are
"observed correlations - expected correlations"

Rasch residuals are "observed data values - expected data values". They
are correlated by pairs of items (variables) across persons (cases) in
Winsteps Table 23.99.

If there are large EFA residuals, then some possibilities are (1) more
factors need to be extracted, or (2) the data need to be transformed, or
(3) the data need to be pruned.

I cannot see a direct connection between EFA residuals and local
independence, perhaps someone else can ....

Mike L.

On 9/5/2013 7:24 AM, Tyner, Callie wrote:
> Thanks Scott,
> I am looking at this here:
> http://www.winsteps.com/winman/index.htm?table23_99.htm
> Do you know what "TAP" means in the example table? I'm trying to
> understand how to interpret this table.
> I've been running my EFA and residual correlations in R, where the
> output is more of a traditional correlation matrix.
> Thanks for your help!
> -Callie

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