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

William Fisher william at livingcapitalmetrics.com
Wed Mar 12 09:49:19 EST 2014

It is not clear what you mean when you say each of the two items has ten
rating categories ranging from 0 to 5. Are there ten categories in total
(five for each item)? Or does each item have ten categories? If there are
five categories, how are they scored 0 to 5, which gives six categories? If
there are ten categories, how do you get them from the 0 to 5 levels?

No matter what the answers to these questions are, saying there are two
items does not really represent the situation. As Linacre (1993) shows, the
number of distinctions made by the combination of items and rating
categories determines the model error. If you have ten categories in each of
two items, then there are 18 total distinctions, not just the two that would
be expected from two dichotomous items. The modeled error expected from 18
distinctions is about 0.6, as shown in Linacre's (1993) nomograph. You
apparently are in a multifaceted context, which then brings the replications
of multiple raters and possibly across tasks, etc. to bear as well, reducing
the error yet more.

Then, as Linacre (1993) shows, the next consideration is the variation that
is being observed relative to that error. If all of those categories are
actually being used and are being used consistently to separate distinct
score groups, and if the sample measured varies quite a lot relative to the
error, then you will expect quite a high reliability. Your standard
deviation is over ten times larger than your error, so, depending on what
decision process you need to support, your overall measurement system would
seem to be functioning.

For another approach to setting up very short but meaningful scales, see
DeSalvo, Fisher, Tran, Bloser, Merrill, and Peabody (2006).

DeSalvo, K., Fisher, W. P. J., Tran, K., Bloser, N., Merrill, W., & Peabody,
J. W. (2006, March). Assessing measurement properties of two single-item
general health measures. Quality of Life Research, 15(2), 191-201.

Linacre, J. M. (1993). Rasch-based generalizability theory. Rasch
Measurement Transactions, 7(1), 283-284;


Wm Fisher

From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
Of Kenji Yamazaki
Sent: Tuesday, March 11, 2014 12:12 PM
To: rasch at acer.edu.au
Subject: [Rasch] Use of Rasch to a two-item scale


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.  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.


Kenji Yamazaki


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