# [Rasch] Interpretation of Item Plot

Stephanou, Andrew Stephanou at acer.edu.au
Tue Mar 27 14:45:17 EST 2007

```Greg,

For the sake of clarity, could you please explain what you mean by transitional and modal categories?  Does the Rasch model make such a distinction?

I believe average measure refers to the mean ability for the people in each category.  Mean ability is expected to increase with category and it is a necessary condition for fit but not sufficient.

Cheers,
Andrew

Andrew Stephanou
ACER

________________________________

From: rasch-bounces at acer.edu.au on behalf of Petroski, Greg
Sent: Mon 3/26/2007 4:25 PM
To: Mike Linacre (RMT); rasch
Subject: RE: [Rasch] Interpretation of Item Plot

First off thank you Tevor, Mike, Stephen and others who have responded.  Clearly the plot doesn't tell enough of the story.

1) The item measures disability with 0 = "none" and 4 = "maximal".  So the categories are transitional and not intended to be modal.

2) Model fit: Do the observations in each category fit in those categories?

+-------------------------------------------------------------------+
|ENTRY   DATA  SCORE |     DATA   | AVERAGE  S.E.  OUTF PTMEA|      |
|NUMBER  CODE  VALUE |  COUNT   % | MEASURE  MEAN  MNSQ CORR.| item |
|--------------------+------------+--------------------------+------|
|    3 d 0         0 |    946  19 |   -3.04   .06   .7  -.62 |      | 0
|        1         1 |    495  10 |   -1.25   .03   .3  -.20 |      | 1
|        2         2 |   1133  23 |    -.17   .02   .6  -.10 |      | 2
|        3         3 |    627  13 |    1.09   .04  1.0   .11 |      | 3
|        4         4 |   1799  36 |    2.61   .05  1.4   .64 |      | 4
+-------------------------------------------------------------------+

Fit statistic standardization:  Local = N

+--------------------------------------------------------------------------------------+
|ENTRY    RAW                   MODEL|   INFIT  |  OUTFIT  |PTMEA|EXACT MATCH|         |
|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD|CORR.| OBS%  EXP%| item    |
|------------------------------------+----------+----------+-----+-----------+---------|
|     3  10950   4724    -.40     .02| .84  -7.4| .84  -3.5|d .79| 61.7  54.0|         |
+--------------------------------------------------------------------------------------+

Fit statistic standardization:  Local = Y
+--------------------------------------------------------------------------------------+
|ENTRY    RAW                   MODEL|   INFIT  |  OUTFIT  |PTMEA|EXACT MATCH|         |
|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZEMP|MNSQ  ZEMP|CORR.| OBS%  EXP%| item    |
|------------------------------------+----------+----------+-----+-----------+---------|
|     3  10950   4724    -.40     .02| .84   -.5| .84   -.4|d .79| 61.7  54.0|         |
+--------------------------------------------------------------------------------------+

3) Category inference: Do the average measures (corresponding to the
observations in each category) advance with the categories?

I am not sure I understand this question.  Isn't increasing measure measure inevitable with the partial credit model, regardless of fit?

4) The sample size is 5k so I think we can assume that it is representative of the population.

-----Original Message-----
From: rasch-bounces at acer.edu.au on behalf of Mike Linacre (RMT)
Sent: Sat 3/24/2007 3:43 AM
To: rasch at acer.edu.au
Subject: Re: [Rasch] Interpretation of Item Plot

Greg,

further thought ....

In your five-category scale, categories 2 and 4 are a little below modal.
This means that the category intervals on the latent variable (considered
from a Rasch-Thurstone perspective) are slightly narrower than the .6
logits (or so) necessary for ordered Rasch-Andrich thresholds. But is the
rating scale defective? This depends on several considerations. Here are four:
1) Category meaning: Are the categories intended to be modal, or are
categories 2 and 4 intended to be transitional (lower probability) states?
2) Model fit: Do the observations in each category fit in those categories?
3) Category inference: Do the average measures (corresponding to the
observations in each category) advance with the categories?
4) Sampling variation: Is the non-modality of those two categories (this
time) merely an accident of the data, rarely to be repeated?

The plot does not tell us enough to know whether a 3-category rating scale
would function better (though it might), nor does it tell us which
collapsing of the categories would be optimal.

Mike Linacre
rmt at rasch.org

At 3/23/2007, Petroski, Greg wrote:
>http://i24.photobucket.com/albums/c1/Alpha_Mutt/ItemCategoryPlot.jpg
>The item is ordinal with responses 0 to 4 with larger values indicating
>greater ability.  Note that two of the five catagories do not ever have
>the highest probability of being endorsed.  Am I correct in interpreting
>this as suggesting a defective item -- one that might work as well with
>only three categories?

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  20:4 Spring 2007

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