Factor Analysis of FIM Residuals

by John M. Linacre
MESA Research Note 5, October 1997

BIGSTEPS provides a principal components factor analysis of Rasch standardized residuals. This is produced as part of Table 10 when PRCOMP=Y is specified.

Analysis of FIMSM residuals shows the same findings as the published "Admit-Discharge" analysis revealed:
1. The Residual structure contrasts the 5 cognitive items against the 13 motor items.
2. The Bowel and Bladder items contain a secondary dimension along with their motor dimension.

TABLE 10.1 measures from alldao.sel at admit - extremes t.out Oct 29 21:05 1997
INPUT: 6144 PERSONS, 18 ITEMS  ANALYZED: 6144 PERSONS, 18 ITEMS, 7 CATS    v2.77
--------------------------------------------------------------------------------

         ITEMS STATISTICS:  OUTFIT ORDER
+---------------------------------------------------------------------------------------+
|ENTRY   RAW                        |   INFIT  |  OUTFIT  |PTBIS|                       |
|NUMBR  SCORE  COUNT  MEASURE  ERROR|MNSQ  ZSTD|MNSQ  ZSTD|CORR.| ITEMS                 |
|-----------------------------------+----------+----------+-----+-----------------------|
|   14  32803  6144     -.84     .01|1.57   9.9|1.80   9.9|  .55| N. COMPREHENSION      |
|   15  32475  6144     -.79     .01|1.60   9.9|1.85   9.9|  .56| O. EXPRESSION         |

|    7  27425  6144     -.18     .01|1.48   9.9|1.35   9.9|  .73| G. BLADDER            |
|   13  14293  6144     1.41     .01|1.39   9.9|1.30   9.9|  .65| M. STAIRS             |
|   18  28179  6144     -.27     .01|1.34   9.9|1.40   9.9|  .65| R. MEMORY             |
|   16  31080  6144     -.61     .01|1.27   9.9|1.27   9.9|  .67| P. SOCIAL INTERACTION |
|   17  26530  6144     -.08     .01|1.23   9.9|1.24   9.9|  .68| Q. PROBLEM SOLVING    |
|    8  28553  6144     -.31     .01|1.27   9.9|1.18   8.2|  .73| H. BOWEL              |
|    1  31421  6144     -.66     .01|1.06   2.9|1.07   3.2|  .71| A. FEEDING            |
|   11  18663  6144      .82     .01|1.00   -.3| .97  -1.2|  .73| K. TUB, SHOWER        |
|   12  21968  6144      .43     .01| .85  -8.9| .94  -2.9|  .76| L. WALK/WHEELCHAIR    |
|    2  29117  6144     -.38     .01| .74  -9.9| .73  -9.9|  .81| B. GROOMING           |
|    4  25659  6144      .02     .01| .65  -9.9| .65  -9.9|  .84| D. UPPER BODY DRESSING|
|    5  22528  6144      .36     .01| .56  -9.9| .55  -9.9|  .85| E. LOWER BODY DRESSING|
|    6  23425  6144      .26     .01| .68  -9.9| .65  -9.9|  .84| F. TOILETING          |
|    3  22830  6144      .33     .01| .54  -9.9| .55  -9.9|  .84| C. BATHING            |
|    9  24184  6144      .18     .01| .50  -9.9| .58  -9.9|  .84| I. BED TRANSFER       |
|   10  23018  6144      .31     .01| .55  -9.9| .59  -9.9|  .83| J. TOILET TRANSFER    |
|-----------------------------------+----------+----------+-----+-----------------------|
| MEAN  25786. 6144.     .00     .01|1.01    .2|1.04    .4|     |                       |
| S.D.   4796.    0.     .57     .00| .38   9.3| .41   9.0|     |                       |
+---------------------------------------------------------------------------------------+

         ITEMS FIT GRAPH:  OUTFIT ORDER
+-----------------------------------------------------------------------------------+
|ENTRY| MEASURE |  INFIT MEAN-SQUARE  | OUTFIT MEAN-SQUARE  |                       |
|NUMBR| -     + |0     0.7 1 1.3     2|0     0.7 1 1.3     2| ITEMS                 |
|-----+---------+---------------------+---------------------+-----------------------|
|   14|*        |       :  .  : *     |A      :  .  :   *   | N. COMPREHENSION      |
|   15|*        |       :  .  : *     |B      :  .  :    *  | O. EXPRESSION         |

|    7|  *      |       :  .  :*      |C      :  .  *       | G. BLADDER            |
|   13|        *|       :  .  *       |D      :  .  *       | M. STAIRS             |
|   18|  *      |       :  .  *       |E      :  .  *       | R. MEMORY             |
|   16| *       |       :  . *:       |F      :  . *:       | P. SOCIAL INTERACTION |
|   17|   *     |       :  . *:       |G      :  . *:       | Q. PROBLEM SOLVING    |
|    8|  *      |       :  . *:       |H      :  .* :       | H. BOWEL              |
|    1| *       |       :  *  :       |I      :  *  :       | A. FEEDING            |
|   11|      *  |       : *.  :       |i      : *.  :       | K. TUB, SHOWER        |
|   12|    *    |       :* .  :       |h      : *.  :       | L. WALK/WHEELCHAIR    |
|    2|  *      |       *  .  :       |g      *  .  :       | B. GROOMING           |
|    4|   *     |      *:  .  :       |f     *:  .  :       | D. UPPER BODY DRESSING|
|    5|    *    |     * :  .  :       |e    * :  .  :       | E. LOWER BODY DRESSING|
|    6|    *    |      *:  .  :       |d     *:  .  :       | F. TOILETING          |
|    3|    *    |     * :  .  :       |c    * :  .  :       | C. BATHING            |
|    9|    *    |     * :  .  :       |b    * :  .  :       | I. BED TRANSFER       |
|   10|    *    |     * :  .  :       |a    * :  .  :       | J. TOILET TRANSFER    |
+-----------------------------------------------------------------------------------+


       PRINCIPAL COMPONENTS (STANDARDIZED RESIDUAL) FACTOR PLOT
      -1                     0                     1                     2
      ++---------------------+---------------------+---------------------++
      |                R     |                                            |
      |                      |                                            |
      |                    Q |                                            |
   .7 +    N                 |                                            +
      |     O                |                                            |
      |         P            |                                            |
   .6 +                      |                                            +
      |                      |                                            |
      |                      |                                            |
   .5 +                      |                                            +
F     |                      |                                            |
A     |                      |                                            |
C  .4 +                      |                                            +
T     |                      |                                            |
O  .3 +                      |                                            +
R     |                      |                                            |
   .2 +                      |                                            +
1     |                      |                                            |
   .1 +                      |                                            +
L     |                      |                                            |
O  .0 +---------------H--G---|--------------------------------------------+
A     |                      |                                            |
D -.1 +        A             |                                            +
I     |                      |                                            |
N -.2 +                      |                                            +
G     |              B       |                                            |
  -.3 +                      |                                            +
      |                      |                                            |
  -.4 +                      |        L                                   +
      |                      |      C          K            M             |
      |                      D     F                                      |
  -.5 +                      |                                            +
      |                      |       E                                    |
      |                      |   I                                        |
  -.6 +                      |                                            +
      |                      |      J                                     |
      ++---------------------+---------------------+---------------------++
      -1                     0                     1                     2
                             ITEM  MEASURE

 FACTOR 1 FROM PRINCIPAL COMPONENT ANALYSIS OF
  STANDARDIZED RESIDUAL CORRELATIONS FOR ITEMS (SORTED BY LOADING)
+-----------------------------------------------------------------+
|      |       |       INFIT OUTFIT| ENTRY                        |
|FACTOR|LOADING|MEASURE  MNSQ MNSQ |NUMBER  ITEM                  |
|------+-------+-------------------+------------------------------|
|  1   |   .76 |    -.27 1.34 1.40 |    18 R. MEMORY              |
|  1   |   .73 |    -.08 1.23 1.24 |    17 Q. PROBLEM SOLVING     |
|  1   |   .68 |    -.84 1.57 1.80 |    14 N. COMPREHENSION       |
|  1   |   .67 |    -.79 1.60 1.85 |    15 O. EXPRESSION          |
|  1   |   .62 |    -.61 1.27 1.27 |    16 P. SOCIAL INTERACTION  |
|      |-------+-------------------+------------------------------|
|  1   |  -.62 |     .31  .55  .59 |    10 J. TOILET TRANSFER     |
|  1   |  -.56 |     .18  .50  .58 |     9 I. BED TRANSFER        |
|  1   |  -.55 |     .36  .56  .55 |     5 E. LOWER BODY DRESSING |
|  1   |  -.47 |     .26  .68  .65 |     6 F. TOILETING           |
|  1   |  -.46 |     .02  .65  .65 |     4 D. UPPER BODY DRESSING |
|  1   |  -.44 |     .82 1.00  .97 |    11 K. TUB, SHOWER         |
|  1   |  -.42 |    1.41 1.39 1.30 |    13 M. STAIRS              |
|  1   |  -.41 |     .33  .54  .55 |     3 C. BATHING             |
|  1   |  -.39 |     .43  .85  .94 |    12 L. WALK/WHEELCHAIR     |
|  1   |  -.24 |    -.38  .74  .73 |     2 B. GROOMING            |
|  1   |  -.12 |    -.66 1.06 1.07 |     1 A. FEEDING             |
|  1   |  -.02 |    -.18 1.48 1.35 |     7 G. BLADDER             |
|  1   |  -.01 |    -.31 1.27 1.18 |     8 H. BOWEL               |
+-----------------------------------------------------------------+
FACTOR 1 EXPLAINS    4.61 OF    18


       PRINCIPAL COMPONENTS (STANDARDIZED RESIDUAL) FACTOR PLOT
      -1                     0                     1                     2
      ++---------------------+---------------------+---------------------++
      |                      |                                            |
   .7 +               H  G   |                                            +
      |                      |                                            |
      |                      |                                            |
   .6 +                      |                                            +
      |                      |                                            |
      |                      |                                            |
F  .5 +                      |                                            +
A     |                      |                                            |
C     |                      |                                            |
T  .4 +                      |                                            +
O     |                      |                                            |
R  .3 +                      |                                            +
      |                      |                                            |
2  .2 +                      |                              M             +
      |                      |   I FJ L                                   |
L  .1 +                      |                                            +
O     |                      |                 K                          |
A  .0 +----------------------|--------------------------------------------+
D     |                      |                                            |
I -.1 +    NO   P      R     |                                            +
N     |                    Q |                                            |
G -.2 +                      |                                            +
      |                      |                                            |
  -.3 +                      |                                            +
      |        A             |                                            |
  -.4 +                      |      CE                                    +
      |                      |                                            |
      |                      |                                            |
  -.5 +              B       D                                            +
      |                      |                                            |
      ++---------------------+---------------------+---------------------++
      -1                     0                     1                     2
                             ITEM  MEASURE

 FACTOR 2 FROM PRINCIPAL COMPONENT ANALYSIS OF
  STANDARDIZED RESIDUAL CORRELATIONS FOR ITEMS (SORTED BY LOADING)
+-----------------------------------------------------------------+
|      |       |       INFIT OUTFIT| ENTRY                        |
|FACTOR|LOADING|MEASURE  MNSQ MNSQ |NUMBER  ITEM                  |
|------+-------+-------------------+------------------------------|
|  2   |   .70 |    -.31 1.27 1.18 |     8 H. BOWEL               |
|  2   |   .70 |    -.18 1.48 1.35 |     7 G. BLADDER             |

|  2   |   .18 |    1.41 1.39 1.30 |    13 M. STAIRS              |
|  2   |   .16 |     .18  .50  .58 |     9 I. BED TRANSFER        |
|  2   |   .16 |     .26  .68  .65 |     6 F. TOILETING           |
|  2   |   .14 |     .43  .85  .94 |    12 L. WALK/WHEELCHAIR     |
|  2   |   .14 |     .31  .55  .59 |    10 J. TOILET TRANSFER     |
|  2   |   .06 |     .82 1.00  .97 |    11 K. TUB, SHOWER         |
|      |-------+-------------------+------------------------------|
|  2   |  -.51 |    -.38  .74  .73 |     2 B. GROOMING            |
|  2   |  -.51 |     .02  .65  .65 |     4 D. UPPER BODY DRESSING |
|  2   |  -.40 |     .33  .54  .55 |     3 C. BATHING             |
|  2   |  -.39 |     .36  .56  .55 |     5 E. LOWER BODY DRESSING |
|  2   |  -.34 |    -.66 1.06 1.07 |     1 A. FEEDING             |
|  2   |  -.14 |    -.08 1.23 1.24 |    17 Q. PROBLEM SOLVING     |
|  2   |  -.12 |    -.27 1.34 1.40 |    18 R. MEMORY              |
|  2   |  -.09 |    -.84 1.57 1.80 |    14 N. COMPREHENSION       |
|  2   |  -.08 |    -.79 1.60 1.85 |    15 O. EXPRESSION          |
|  2   |  -.08 |    -.61 1.27 1.27 |    16 P. SOCIAL INTERACTION  |
+-----------------------------------------------------------------+
FACTOR 2 EXPLAINS    2.10 OF    18

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