MESA Note 5: Factor Structure of FIM Residuals

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 FIM^SM 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

Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
Rasch Books and Publications: Winsteps and Facets
Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

Rasch-Related Resources: Rasch Measurement YouTube Channel

Rasch Measurement Transactions & Rasch Measurement research papers - free

An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse

Rasch Measurement Theory Analysis in R, Wind, Hua

Applying the Rasch Model in Social Sciences Using R, Lamprianou

El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.

Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar

Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch

Rasch Models for Measurement, David Andrich

Constructing Measures, Mark Wilson

Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters

Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias

Diseño de Mejores Pruebas - free, Spanish Best Test Design

A Course in Rasch Measurement Theory, Andrich, Marais

Rasch Models in Health, Christensen, Kreiner, Mesba

Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

Rasch Books and Publications: Winsteps and Facets

Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene

Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver

Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone

Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale

Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland

Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes

Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang

Statistical Analyses for Language Testers (Facets), Rita Green

Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind

Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M

Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind

Rasch Measurement: Applications, Khine

Winsteps Tutorials - free
Facets Tutorials - free

Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre

Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

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