[Rasch] Use of Rasch to a two-item scale

Stuart Luppescu slu at ccsr.uchicago.edu
Wed Mar 12 08:40:10 EST 2014

On Tue, 2014-03-11 at 19:11 +0000, Kenji Yamazaki wrote:
> Dear Rasch practitioners, 
> I have a question about applying the Rasch model to a two-item scale
> in the following scenario.  I am working on a project where I examine
> psychometric properties of a measurement.  I am investigating on one
> scale called professionalism that consists of only two items.  Both
> two items have 10 rating categories ranging from performance levels 0
> through 5.  Each category has different behavioral descriptors in the
> order of difficulty in perform.  The sample size is N=1846.  This is
> actually the total number of the population because the compliance
> rate was 100%.  
> Here is how I did the analysis.  First, I applied the principal
> complement analysis to this data.  The result produced one factor.  

Is this even possible? PCA on two items?

> Then, I applied the Rasch model using person and item as facets with
> partial credit model.  The results show that person reliability
> was .88 and its separation was 2.67.    Also, item reliability was .99
> and the separation was 11.76.  In addition, no inversion of the
> category thresholds were not observed for the two items.
> Given this situation, I was wondering if the way I did the analysis
> was legitimate.  Also, I wonder if these results are sufficient to
> state that this two-item scale has so good psychometric properties
> that there is no need to  modify the scale for improvement.  My
> concerns is the number of items (although the sample size is large and
> the sample is actually the population.)  Thank you very much in
> advance.

I have made 2-item measures before. One measure was composed of 2
4-category survey items. It didn't work so great at the individual level
(reliability around 0.5) but it worked great aggregated to the school
level, which was the level of analysis we were using it at. If you're
getting a reliability of 0.88 with two items consider yourself very
fortunate and go for it.

Stuart Luppescu -=-=- slu <AT> ccsr <DOT> uchicago <DOT> edu
CCSR at U of C ,.;-*^*-;.,  ccsr.uchicago.edu
     (^_^)/    才文と智奈美の父
[Crash programs] fail because they are based on the theory that, 
with nine women pregnant, you can get a baby a month.
                -- Wernher von Braun

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