# [Rasch] Categories too wide

Stuart Luppescu slu at ccsr.uchicago.edu
Tue Jun 11 08:37:38 EST 2013

```Hello Raschies, I remember Mike Linacre once saying something about the
situation when the step difficulties spread out much more than the item
difficulties. I have such a situation in the extreme. Between about -9
and 2 logits, the most probable response is 3. Here's the step table:

SUMMARY OF MEASURED STEPS
+----------------------------------------------+
|CATEGORY OBSERVED|AVGE  INFIT OUTFIT|  STEP   |
| LABEL    COUNT  |MEASURE MNSQ  MNSQ| MEASURE |
|-----------------+------------------+---------|
|   1         279 | -6.47  0.92  0.91|  NONE   |
|   2        1828 | -3.20  0.97  0.60|   -6.67 |
|   3        4808 |  2.85  0.96  0.98|   -1.75 |
|   4         645 |  8.63  0.98  0.36|    8.41 |
+----------------------------------------------+
+--------------------------------------------------------+
|CATEGORY  STEP     STEP |  SCORE-TO-MEASURE   |THURSTONE|
| LABEL   MEASURE  ERROR | AT CAT  --INTERVAL--|THRESHOLD|
|------------------------+---------------------+---------|
|   1      NONE          |( -7.77) -INF   -6.69|         |
|   2       -6.67   0.08 |  -4.21  -6.69  -1.72|   -6.67 |
|   3       -1.75   0.04 |   3.33  -1.72   8.41|   -1.74 |
|   4        8.41   0.06 |(  9.51)  8.41  +INF |    8.41 |
+--------------------------------------------------------+

Here are the category probability curves:

TABLE 21.1 Teacher Evaluation Eval                  teva2.out Mon Jun 10
17:00:
2000 PERSONS    5 ITEMS   ANALYZED:  1520 PERSONS    5 ITEMS     4
CATEGS v2.76
--------------------------------------------------------------------------------

CATEGORY PROBABILITIES: MODES - Step measures at intersections
P      ++------+------+------+------+------+------+------+------++
R  1.0 +11                             333333                 444+
O      |  111                       333      333            44   |
B      |     1                     3            3         44     |
A      |      1        222        3              3       4       |
B  0.8 +       1      2   2      3                3     4        +
I      |       1     2     2    3                  3    4        |
L      |        1   2      2   3                   3   4         |
I      |        1  2        2  3                    3  4         |
T  0.6 +         1 2        2 3                     3 4          +
Y      |         12          23                      34          |
0.5 +          *          *                       *           +
O      |         21          32                      43          |
F  0.4 +         2 1        3 2                     4 3          +
|        2  1        3  2                    4  3         |
R      |        2   1      3   2                   4   3         |
E      |       2    1      3    2                  4    3        |
S  0.2 +       2     1    3      2                4     3        +
P      |      2       1   3       2              4       3       |
O      |     2         133         2            4         33     |
N      |  222         33111         222      444            33   |
S  0.0 + *************44444**************************************+
E      ++------+------+------+------+------+------+------+------++
-11     -8     -5     -2      1      4      7     10     13
PERSON [MINUS]  ITEM  MEASURE

The items only vary in difficulty between -0.6 and 0.6. Is this a
pathological condition or what?

--
Stuart Luppescu <slu at ccsr.uchicago.edu>
University of Chicago
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