# [Rasch] Disordered steps?

Trudy Mallinson trudy.mallinson at usc.edu
Thu Oct 14 05:22:05 EST 2010

```Hi All,

We have an odd problem - we have items scored with two rating scales - we want to combine these two scales into a single one. So we developed an algorithm to convert the two scales into a single 6-point rating scale and re-scored all the items.  We obviously had to make some clinical judgements about the algorithm.  If we make a score of 1 from old scale 1 and score of 1 from old scale 2 equal to a score of 4 on the new rating scale we get the best overall item and scale pscyhometrics but step 5 appears disordered.  This is odd, because when you look at the distractor table, only walking on the unit (m2_locosnf) shows any step disordering.  Can someone please explain what is happening?

PS: We tried the algorithm so that a score of 1 from old scale 1 and score of 1 from old scale 2 is equal to a score of 5 to see if redistributing the scores made a difference but the overall psychometrics from that run are much worse and we think, make less clinical sense.

Kind regards,
Trudy

ACTVTY CATEGORY/OPTION/DISTRACTOR FREQUENCIES:  MISFIT ORDER
---------------------------------------------------------------------------
|ENTRY   DATA  SCORE |     DATA   | AVERAGE  S.E.  OUTF PTMEA|            |
|NUMBER  CODE  VALUE |  COUNT   % | ABILITY  MEAN  MNSQ CORR.| ACTVTY     |
|--------------------+------------+--------------------------+------------|
|   23 A 1         1 |      1   0 |   -6.20         .0  -.19 |m2_eat      | 1 Total assistance
|        2         2 |      2   0 |   -3.07   .81   .3  -.15 |            | 2 Maximal assistance
|        3         3 |      8   2 |   -1.18   .39  3.7  -.17 |            | 3 Moderate assistance
|        4         4 |     50  12 |    -.77   .19  7.3  -.35 |            | 4 Minimal contact assistance
|        5         5 |     39   9 |     .01   .17  1.2  -.17 |            | 5 Supervision or setup
|        6         6 |    314  76 |    1.43   .09  1.4   .48 |            | 6 Independence
|        MISSING *** |      1   0#|                      .00 |            |
|                    |            |                          |            |
|   33 B 0       *** |     96  23#|    1.16   .15        .07 |m2_locosnf  |
|        1         1 |     94  30 |    -.34   .18  2.7  -.42 |            | 1 Total assistance
|        2         2 |     52  17 |    -.41*  .13   .9  -.30 |            | 2 Maximal assistance
|        3         3 |     33  11 |     .14   .14  1.0  -.13 |            | 3 Moderate assistance
|        4         4 |     33  11 |    1.28   .16  1.5   .08 |            | 4 Minimal contact assistance
|        5         5 |     17   5 |    2.04   .23  2.4   .15 |            | 5 Supervision or setup
|        6         6 |     84  27 |    2.86   .14  2.6   .64 |            | 6 Independence
|        MISSING *** |      6   1#|    1.74  1.02        .06 |            |
|                    |            |                          |            |
|   25 C 0       *** |     43  10#|    -.50   .21       -.28 |m2_bath     |
|        1         1 |     29   8 |    -.79   .32  1.5  -.32 |            | 1 Total assistance
|        2         2 |    150  41 |     .13   .10  1.6  -.47 |            | 2 Maximal assistance
|        3         3 |     38  10 |     .69   .15  1.0  -.08 |            | 3 Moderate assistance
|        4         4 |     60  17 |    1.86   .10   .9   .19 |            | 4 Minimal contact assistance
|        5         5 |     25   7 |    2.37   .23  2.8   .19 |            | 5 Supervision or setup
|        6         6 |     61  17 |    3.50   .13  1.1   .60 |            | 6 Independence
|        MISSING *** |      9   2#|     .61   .63       -.04 |            |
|                    |            |                          |            |
|   24 D 1         1 |      2   0 |   -4.53  1.67   .5  -.21 |m2_groom    | 1 Total assistance
|        2         2 |     17   4 |   -1.91   .22   .5  -.33 |            | 2 Maximal assistance
|        3         3 |     55  13 |    -.84   .12   .9  -.39 |            | 3 Moderate assistance
|        4         4 |     94  23 |    -.04   .08   .9  -.30 |            | 4 Minimal contact assistance
|        5         5 |     37   9 |     .51   .18  1.0  -.08 |            | 5 Supervision or setup
|        6         6 |    206  50 |    2.24   .09   .9   .72 |            | 6 Independence
|        MISSING *** |      4   1#|     .27  1.34       -.03 |            |
|                    |            |                          |            |
|   26 E 1         1 |     26   6 |   -1.95   .24   .6  -.42 |m2_dress    | 1 Total assistance
|        2         2 |    124  30 |    -.39   .09  1.2  -.48 |            | 2 Maximal assistance
|        3         3 |    107  26 |     .75   .09   .9  -.06 |            | 3 Moderate assistance
|        4         4 |     42  10 |    1.61   .12   .9   .13 |            | 4 Minimal contact assistance
|        5         5 |     15   4 |    2.28   .18   .8   .14 |            | 5 Supervision or setup
|        6         6 |     98  24 |    3.11   .10  1.0   .67 |            | 6 Independence
|        MISSING *** |      3   1#|     .64   .67       -.01 |            |
|                    |            |                          |            |
|   29 F 0       *** |      1   0#|    1.85              .02 |m2_bedmob   |
|        1         1 |     27   7 |   -2.03   .22   .8  -.44 |            | 1 Total assistance
|        2         2 |     50  12 |    -.99   .11   .9  -.40 |            | 2 Maximal assistance
|        3         3 |    103  25 |    -.02   .07   .9  -.31 |            | 3 Moderate assistance
|        4         4 |     35   8 |     .76   .15  1.2  -.03 |            | 4 Minimal contact assistance
|        5         5 |     23   6 |    1.49   .19  1.1   .08 |            | 5 Supervision or setup
|        6         6 |    174  42 |    2.48   .09  1.2   .73 |            | 6 Independence
|        MISSING *** |      2   0#|    2.21              .03 |            |
|                    |            |                          |            |
|   32 e 0       *** |     29   7#|     .05   .26       -.14 |m2_locounit |
|        1         1 |     52  14 |   -1.40   .16  1.2  -.53 |            | 1 Total assistance
|        2         2 |     46  12 |    -.75   .10   .7  -.36 |            | 2 Maximal assistance
|        3         3 |     59  15 |    -.01   .08   .3  -.24 |            | 3 Moderate assistance
|        4         4 |     46  12 |     .78   .09   .3  -.05 |            | 4 Minimal contact assistance
|        5         5 |     23   6 |    1.66   .15   .6   .09 |            | 5 Supervision or setup
|        6         6 |    158  41 |    2.67   .08   .9   .76 |            | 6 Independence
|        MISSING *** |      2   0#|    -.19             -.03 |            |
|                    |            |                          |            |
|   27 d 0       *** |      1   0#|   -3.87             -.13 |m2_toilet   |
|        1         1 |     39   9 |   -1.79   .16   .8  -.50 |            | 1 Total assistance
|        2         2 |     52  13 |    -.75   .09   .7  -.36 |            | 2 Maximal assistance
|        3         3 |     93  23 |     .08   .07   .8  -.27 |            | 3 Moderate assistance
|        4         4 |     42  10 |     .76   .09   .3  -.04 |            | 4 Minimal contact assistance
|        5         5 |     22   5 |    1.14   .15   .7   .02 |            | 5 Supervision or setup
|        6         6 |    163  40 |    2.70   .08   .6   .79 |            | 6 Independence
|        MISSING *** |      3   1#|    -.77  2.08       -.07 |            |
|                    |            |                          |            |
|   30 c 0       *** |     53  13#|   -1.21   .19       -.46 |m2_wlkroom  |
|        1         1 |      9   3 |   -1.69   .24   .7  -.29 |            | 1 Total assistance
|        2         2 |     32   9 |    -.78   .12   .9  -.39 |            | 2 Maximal assistance
|        3         3 |     75  21 |    -.14   .07   .8  -.44 |            | 3 Moderate assistance
|        4         4 |     63  18 |     .69   .08   .6  -.16 |            | 4 Minimal contact assistance
|        5         5 |     19   5 |    1.24   .14   .4   .00 |            | 5 Supervision or setup
|        6         6 |    160  45 |    2.71   .08   .5   .80 |            | 6 Independence
|        MISSING *** |      4   1#|    1.09  1.13       -.01 |            |
|                    |            |                          |            |
|   28 b 0       *** |      1   0#|   -1.38             -.06 |m2_trnsfr   |
|        1         1 |     29   7 |   -2.09   .20   .6  -.46 |            | 1 Total assistance
|        2         2 |     69  17 |    -.74   .09   .7  -.42 |            | 2 Maximal assistance
|        3         3 |     95  23 |    -.01   .06   .4  -.29 |            | 3 Moderate assistance
|        4         4 |     54  13 |    1.07   .08   .4   .03 |            | 4 Minimal contact assistance
|        5         5 |     17   4 |    1.66   .16   .5   .08 |            | 5 Supervision or setup
|        6         6 |    149  36 |    2.80   .08   .6   .77 |            | 6 Independence
|        MISSING *** |      1   0#|                      .00 |            |
|                    |            |                          |            |
|   31 a 0       *** |     86  21#|    -.94   .13       -.54 |m2_wlkcorr  |
|        1         1 |      6   2 |   -1.77   .32   .6  -.28 |            | 1 Total assistance
|        2         2 |     24   7 |    -.67   .16  1.0  -.38 |            | 2 Maximal assistance
|        3         3 |     59  18 |    -.08   .07   .3  -.45 |            | 3 Moderate assistance
|        4         4 |     60  18 |     .74   .08   .5  -.21 |            | 4 Minimal contact assistance
|        5         5 |     25   8 |    1.59   .13   .5   .03 |            | 5 Supervision or setup
|        6         6 |    152  47 |    2.76   .08   .5   .77 |            | 6 Independence
|        MISSING *** |      3   1#|    -.53  1.01       -.10 |            |
---------------------------------------------------------------------------
* Average ability does not ascend with category score
# Missing % includes all categories. Scored % only of scored categories

On Oct 12, 2010, at 9:02 AM, Hsiang-Yi Tseng wrote:

> Hi Trudy,
>    I agree with your comment -1+1=4 has better results. However, it still leads to the disordering average step measure.
> What can we do with the this problem?
>
>
> MDS measure with
> 1+1=5 (old algorithm)
> MDS measure with
> 1+1=4 (new algorithm)
>
>
> CATEGORY
> Rasch-Andrich threshold MEASURE
> Rasch-Andrich threshold MEASURE
>
>
> 1
> 0
> 0
>
>
> 2
> -1.99
> -2.12
>
>
> 3
> -0.57
> -0.67
>
>
> 4
> 1.97
> 0.56
>
>
> 5
> -0.73
> 1.93
>
>
> 6
> 1.33
> 0.31
>
>
>

Trudy Mallinson, PhD, OTR/L, NZROT
Assistant Professor
University of Southern California
Division of Occupational Science and Occupational Therapy
1540 Alcazar Street, CHP 133, Room 101F
Los Angeles, CA 90089-9003
PH: (323) 442-2950
trudy.mallinson at usc.edu

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