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

Kenji Yamazaki kyamazaki at acgme.org
Wed Mar 12 06:19:52 EST 2014


The fit indexes ranges from .94 to 1.01, which I believe is a good indication.

Table 7.4.1  Itm Measurement Report  (arranged by 4MN).
+---------------------------------------------------------------------------------------------------------+
|  Total   Total   Obsvd  Fair-M|        Model | Infit      Outfit   |Estim.| Corr. |                     |
|  Score   Count  Average Avrage|Measure  S.E. | MnSq ZStd  MnSq ZStd|Discrm| PtBis | N Itm               |
|-------------------------------+--------------+---------------------+------+-------+---------------------|
|  7099    1846       3.9   3.89|   -.53   .05 | 1.01   .1   .99  -.3|  .99 |   .62 | 1 comp5_PR_Q1       |
|  6351    1846       3.5   3.39|    .53   .04 |  .95 -1.3   .94 -1.7| 1.02 |   .62 | 2 comp5_PR_Q2       |
|-------------------------------+--------------+---------------------+------+-------+---------------------|
|  6725.0  1846.0     3.7   3.64|    .00   .04 |  .98  -.6   .96 -1.1|      |   .62 | Mean (Count: 2)     |
|   374.0      .0      .2    .25|    .53   .00 |  .03   .7   .02   .7|      |   .00 | S.D. (Population)   |
|   528.9      .0      .3    .36|    .74   .00 |  .04  1.0   .04  1.0|      |   .00 | S.D. (Sample)       |
+---------------------------------------------------------------------------------------------------------+
Model, Populn: RMSE .04  Adj (True) S.D. .52  Separation 11.76  Strata 16.02  Reliability .99
Model, Sample: RMSE .04  Adj (True) S.D. .74  Separation 16.66  Strata 22.55  Reliability 1.00
Model, Fixed (all same) chi-square: 278.7  d.f.: 1  significance (probability): .00
-----------------------------------------------------------------------------------------------------------
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Kenji Yamazaki
Sent: Tuesday, March 11, 2014 2:12 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.
Sincerely,
Kenji Yamazaki
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