[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.
To address Mike's questions.
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,
Thank you for asking us about your plot. Its shape certainly prompts
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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