# [Rasch] Interpretation of Item Plot

Petroski, Greg PetroskiG at health.missouri.edu
Tue Mar 27 14:25:34 EST 2007

```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

```