Example 16: Disordered categories - thresholds and person anchoring

This example illustrates two types of disordering in rating scale structures: category disordering and Rasch-Andrich threshold disordering. For further discussion, see disordering. It also illustrates anchor values in the person labels and category labeling.

 

The control file and data are in exam16.txt.

 

; This control file is EXAM16.TXT

title = "Attitude Survey illustrating two types of disordering"

ni    = 3  ; three items

item1 = 1  ; item responses start in column 1

xwide = 2  ; data codes are two columns wide

codes = "1 2 3 " ; valid two character codes

name1 = 9  ; person label starts in column 9

namelength = 3 ; length of person labels

 

; pafile = $s1w3 ; person anchor values in columns 1-3 of person labels

@panchors = 1-3 ; person anchor field is in columns 1 to 3 of person labels

pafile = @panchors ; person anchors in field @panchors

 

ISGROUPS = 0  ; allow each item to have its own rating scale (the partial credit model)

clfile = *  ; category labels: item+category

1+1 Never  ; item 1 category 1 is "Never"

1+2 Sometimes  ; well-behaved rating scale

1+3 0ften

2+1 Car  ; categories as ordered in frequency in 1930

2+2 Ship  ; now these categories are disordered

2+3 Plane  ; ship travel now rarer than planes

3+1 No

3+2 Neutral  ; very few in this narrow intermediate category

3+3 Yes

*

&END  ; item labels follow

Smooth advance everywhere - probability curves a "range of hills"

Disordered categories - disordered empirical average measures for categories

Low middle frequency - high discrimination - disordered Rasch-Andrich thresholds

END LABELS ; end of item labels, data follow ...

1 1 1   0.0 ; person anchor logits in person labels

1 1 1   0.1 ; advancing anchored person measures

2 3 1   0.2 ; but not advancing categories for item 2

2 3 1   0.3

2 2 2   0.4 ; only one observation of category 2 for item 3, but in the correct place = high discrimination

2 2 3   0.5

2 2 3   0.6

3 2 3   0.7

3 2 3   0.8 ; last data record

 


On the Diagnosis Menu: Empirical Item-Category Measures:

 

TABLE 2.5 Attitude Survey

OBSERVED AVERAGE MEASURES FOR PERSONS (BY OBSERVED CATEGORY)

0     1     2     3     4     5

+-----+-----+-----+-----+-----|  NUM   ITEM

|     1     2     3           |    1  Smooth advance everywhere

|     1     3 2               |    2  Disordered categories

|        1  2  3              |    3  Low middle frequency - high discrimination

+-----+-----+-----+-----+-----|  NUM   ITEM

 

On the Diagnosis Menu: Category Function:

 

TABLE 3.2 Attitude Survey

FOR GROUPING "0" ITEM NUMBER: 1  Smooth advance everywhere - probability curves a "range of hills"

 

ITEM DIFFICULTY MEASURE OF 2.00 ADDED TO MEASURES

+------------------------------------------------------------------

|CATEGORY   OBSERVED|OBSVD SAMPLE|INFIT OUTFIT|| ANDRICH |CATEGORY|

|LABEL SCORE COUNT %|AVRGE EXPECT|  MNSQ  MNSQ||THRESHOLD| MEASURE|

|-------------------+------------+------------++---------+--------+

|  1   1       2  22|  1.00  1.62|   .49   .52||  NONE   |(  -.29)| 1 1 Never

|  2   2       5  56|  2.00  2.00|   .00   .00||   -1.11 |   2.00 | 2 2 Sometimes <- Ordered Rasch-Andrich thresholds

|  3   3       2  22|  3.00  2.38|   .49   .52||    1.11 |(  4.29)| 3 3 0ften <- Ordered categories

+------------------------------------------------------------------

 

 


 

TABLE 3.3 Attitude Survey

FOR GROUPING "0" ITEM NUMBER: 2  Disordered categories - disordered empirical average measures for categories

 

ITEM DIFFICULTY MEASURE OF 2.00 ADDED TO MEASURES

+------------------------------------------------------------------

|CATEGORY   OBSERVED|OBSVD SAMPLE|INFIT OUTFIT|| ANDRICH |CATEGORY|

|LABEL SCORE COUNT %|AVRGE EXPECT|  MNSQ  MNSQ||THRESHOLD| MEASURE|

|-------------------+------------+------------++---------+--------+

|  1   1       2  22|  1.00  1.62|   .49   .52||  NONE   |(  -.29)| 1 1 Car

|  2   2       5  56|  2.40  2.00|  1.01  1.01||   -1.11 |   2.00 | 2 2 Ship <- Ordered Rasch-Andrich thresholds

|  3   3       2  22|  2.00* 2.38|  1.28  1.23||    1.11 |(  4.29)| 3 3 Plane <- Disordered categories

+------------------------------------------------------------------

 


 

TABLE 3.4 Attitude Survey

FOR GROUPING "0" ITEM NUMBER: 3  Low middle frequency - high discrimination - disordered Rasch-Andrich thresholds

 

ITEM DIFFICULTY MEASURE OF 2.00 ADDED TO MEASURES

+------------------------------------------------------------------

|CATEGORY   OBSERVED|OBSVD SAMPLE|INFIT OUTFIT|| ANDRICH |CATEGORY|

|LABEL SCORE COUNT %|AVRGE EXPECT|  MNSQ  MNSQ||THRESHOLD| MEASURE|

|-------------------+------------+------------++---------+--------+

|  1   1       4  44|  1.50  1.65|   .74   .64||  NONE   |(   .86)| 1 1 No

|  2   2       1  11|  2.00  2.00|   .00   .00||    1.21 |   2.00 | 2 2 Neutral <- Disordered Rasch-Andrich thresholds

|  3   3       4  44|  2.50  2.35|   .74   .64||   -1.21 |(  3.14)| 3 3 Yes  <- Ordered categories

+------------------------------------------------------------------

 


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