[Rasch] local item independence

Svend Kreiner S.Kreiner at biostat.ku.dk
Fri Feb 22 02:24:23 EST 2008

It is true that residuals are independent if items fit a Rasch model, 
for which reason correlation of residuals are calculated by both 
WINSTEPS and RUMM2020. The problem with these correlation coefficients 
are, unfortunately, that we do not know how these coefficients are 
distributed under the Rasch model. For that reason we cannot evaluate 
the significance of the evidence against the model.

There is, however, a very simple approach.

If the items are A, B, C, D, E , F and if we suspect that items A and B 
are locally dependent, then we can:

    1) Subtract A form the score and treat it as a person covariate 
instead of as an item,
    2) Test whether B functions differentially relative to the reponse on A

If A and B are locally independent then (B,C,D,E,F) will fit a Rasch 
model with no evidence of DIF. If there, on the other hand, is evidence 
of DIF relative to A then A and B must be locally dependent.

The procedure is very simple. You can use whatever procedure for DIF 
testing that you usually apply: the Mantel-Haenzel test, the ANOVA 
analysis of DIF in RUMM2020, comparisons of ICC curves etc.etc. It is 
simply a question of organizing your analyses in such a way that it 
doesn't require too much work.  (It will even work for the 2- and 
3-parameter models if you have proper tests of DIF for these models).

What to do when you find local dependence is another problem. Should 
both or just one item be eliminated? I would like to hear what the rest 
of you are doing.

Best regards

Purya Baghaei skrev:
> Scott,
> Correlation of residuals is an indication of local item dependence.
> It's implemented in WINSTEPS, table 23.
> Regards
> Purya
> On 2/18/08, *SR Millis* <srmillis at yahoo.com 
> <mailto:srmillis at yahoo.com>> wrote:
>     Are there any diagnostic tests available to determine
>     whether there has been a substantial violation of
>     local item independence?
>     Thanks,
>     Scott Millis
>     Scott R Millis, PhD, MEd, ABPP (CN,CL,RP), CStat
>     Professor & Director of Research
>     Dept of Physical Medicine & Rehabilitation
>     Wayne State University School of Medicine
>     261 Mack Blvd
>     Detroit, MI 48201
>     Email:  smillis at med.wayne.edu <mailto:smillis at med.wayne.edu>
>     Tel: 313-993-8085
>     Fax: 313-966-7682
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Svend Kreiner
Associate professor
Department of Biostatistics  
University of Copenhagen 

Øster farimagsgade 5, entr. B
P.O. Box 2099
DK-1014 Copenhagen K, Denmark

Email: S.Kreiner at biostat.ku.dk
Phone: (+45) 35 32 75 97     

Fax: (+45) 35 32 79 07

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