The Rating (or partial credit) scale= statement provides a simple way to provide further information about the scoring model beyond that in the Model= specification. You can name each category of a scale, provide logit step difficulty calibrations for anchoring or starting values, and recode observations.

 

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Components of Rating (or partial credit) scale=

 

Rating scale = user name, structure, scope, numeration

user name of scale or response model

any set of alphanumeric characters, e.g., "Likert". To be used, it must match exactly a user name specified in a Model= statement.

 

structure

any valid scale code, except a user name (see Model= definition)

 

scope

Specific (or # in a Model= specification) means that each occurrence of this scale name in a different Model= specification refers to a separate copy of the scale, with its own calibrations, though each has the same number of categories, category names, etc.

General means that every reference to this scale in any Model= specification refers to the same, single manifestation of the scale.

 

numeration

Ordinal means that the category labels are arranged ordinally, representing ascending, but adjacent, qualitative levels of performance regardless of their values.

Keep means that the category labels are cardinal numbers, such that all intermediate numbers represent levels of performance, regardless as to whether they are observed in any particular data set.

 

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Components of category description lines

 

Rating scale = ......

category number, category name, measure value, anchor flag, recoded values, reordered values

.....

*

category number

quantitative count of ordered qualitative steps, e.g., 2. -1 is treated as missing.

 

category name

label for category, e.g., "agree"

 

measure value

These provide starting or pre-set fixed values. For rating scales (or partial credits items): numeric measure step calibrations. For binomial trials and Poisson counts: scale discrimination, but only when entered for category 0, and with value greater than 0.

 

anchor flag

For rating scales (or partial credit items), ",A" means Anchor this category at its pre-set step calibration value. If omitted, or any other letter, the logit value is only a starting value. Anchoring a category with a pre-set logit step calibration forces it to remain in the estimation even when there are no matching responses. Anchor ",A" the lowest category with pre-set calibration "0" to force it to remain in the estimation. For binomial trials and Poisson counts: ",A" entered for category 0 means anchor (fix) the scale discrimination at the assigned value.

 

recoded values

Data values to be recoded, separated by "+" signs (optional). Example: 5+6+Bad Values in the data file of precisely "5", "6" or "Bad" are recoded.

 

reordered values

Used in Facets-generated anchor files to identify automatically recounted category numbers

 

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Example 1: Anchor a rating scale (or partial credit) at pre-set step calibrations.

 

Model=?,?,faces,1 ; the "Liking for Science" faces

*

Rating (or partial credit) scale=faces,R3

1=dislike,0,A ; always anchor bottom category at "0"

2=don't know,-0.85,A ; anchor first step at -0.85 step calibration

3=like,0.85,A ; anchor second step at +0.85 step calibration

* ; as usual, step calibrations sum to zero.

 

Example 2: Center a rating scale (or partial credit) at the point where categories 3 and 4 are equally probable. Note: usually a scale is centered where the first and last categories are equally probable. More detailed scale rating scale anchoring example.

 

Model=?,?,friendliness,1 ; the scale

*

Rating (or partial credit) scale=friendliness,R4

1=obnoxious

2=irksome

3=passable

4=friendly,0,A ; Forces categories 3 and 4 to be equally probable at a relative logit of 0.

 

Example 3: Define a Likert scale of "quality" for persons and items, with item 1 specified to have its own scale calibrations. Recoding is required.

 

Model=

?,1,quality,1 ; a scale named "quality" for item 1

?,?,quality,1 ; a scale named "quality" for all other items

*

 

Rating (or partial credit) scale=quality,R3,Specific ; the scale is called "quality"

0=dreadful

1=bad

2=moderate

3=good,,,5+6+Good ; "5","6","Good" recoded to 3.

; ",,," means logit value and anchor status omitted

-1=unwanted,,,4  ; "4" was used for "no opinion", recoded to -1 so ignored

* ; "0","1","2","3" in the data are not recoded, so retain their values.

 

Example 4: Define a Likert scale of "intensity" for items 1 to 5, and "frequency" for items 66 to 10. The "frequency" items are each to have their own scale structure.

 

Model=

?,1-5,intensity ; "intensity" scale for items 1-5

?,6-19#,frequency ; "frequency" scale for items 6-10 with "partial credit" format

*

 

Rating (or partial credit) scale=intensity,R4 ; the scale is called "intensity"

1=none

2=slightly

3=generally

4=completely

*

Rating (or partial credit) scale=frequency,R4 ; the scale is called "frequency"

1=never

2=sometimes

3=often

4=always

*

 

The components of the Rating (or partial credit) scale= specification:

Rating (or partial credit) scale=quality,R3,Specific ; the scale is called "quality"

 

"quality" (or any other name you choose)
is the name of your scale. It must match the scale named in a Model= statement.

 

R3 an Andrich rating scale (or partial credit) with valid categories in the range 0 through 3.

 

Specific each model statement referencing quality generates a scale with the same structure and category names, but different step calibrations.

 

Example 5: Items 1 and 2 are rated on the same scale with the same calibrations. Items 3 and 4 are rated on scales with the same categories, but different calibrations:

 

Model=

?,1,Samescale

?,2,Samescale

?,3,Namesonly

?,4,Namesonly

*

Rating (or partial credit) scale=Samescale,R5,General ; only one set of calibrations is estimated

; category 0 is not used ; this is a potentially 6 category (0-5) rating scale (or partial credit)

1,Deficient

2,Satisfactory

3,Good

4,Excellent

5,Prize winning

*

Rating (or partial credit) scale=Namesonly,R3,Specific ; one set of calibrations per model statement

0=Strongly disagree ; this is a 4 category (0-3) rating scale (or partial credit)

1=Disagree

2=Agree

3=Strongly Agree

*

 

Example 6: Scale "flavor" has been analyzed, and we use the earlier values as starting values.

 

Rating (or partial credit) scale=Flavor,R

0=weak ; bottom categories always have a step calibration of 0.

1=medium,-3 ; the step calibration from 0 to 1 is -3 logits

2=strong,3 ; the step value from 1 to 2 is 3 logits

* ; The sum of the anchor step calibration is the conventional zero.

 

Example 7: Collapsing a four category scale (0-3) into three categories (0-2):

 

Rating (or partial credit) scale=Accuracy,R2

0=wrong ; no recoding. "0" remains "0"

1=partial,,,2 ; "2" in data recoded to "1" for analysis.

; "1" in data remains "1" for analysis, ",,," means no pre-set logit value and no anchoring.

2=correct,,,3 ; "3" in data recoded to "2" for analysis.

; "2" in data already made "1" for analysis.

*

data=

1,2,0 ; 0 remains category 0

4,3,1 ; 1 remains category 1

5,4,2 ; 2 recoded to category 1

6,23,3 ; 3 recoded to category 2

13,7,4 ; since 4 is not recoded and is too big for R2, Facets terminates with the message:
Data is: 13,7,4
Error 26 in line 53: Invalid datum value: non-numeric or too big for model
Execution halted

 

Example 8: Recoding non-numeric values.

Categories do not have to be valid numbers, but must match the data file exactly, so that, for a data file which contains "R" for right answers, and "W" or "X" for wrong answers, and "M" for missing:

 

Rating (or partial credit) scale=Keyed,D ; a dichotomous scale called "Keyed"

0=wrong,,,W+X ; both "W" and "X" recoded to "0", "+" is a separator

1=right,,,R ; "R" recoded to "1"

-1=missing,,,M ; "M" recoded to "-1" - ignored as missing data

*

data=

1,2,R ; R recoded 1

2,3,W ; W recoded 0

15,23,X ; X recoded 0

7,104,M ; M recoded to -1, treated as missing data

 

Example 9: Maintaining the rating scale (or partial credit) structure with unobserved intermediate categories. Unobserved intermediate categories can be kept in the analysis.

 

Model=?,?,Multilevel

Rating (or partial credit) scale=Multilevel,R2,G,K ; means that 0, 1, 2 are valid
; if  0 and 2 are observed, 1 is forced to exist.

Dichotomies can be forced to 3 categories, to match 3 level partial credit items, by scoring the dichotomies 0=wrong, 2=right, and modeling them R2,G,K.

Example 9: An observation is recorded as "per cents". These are to be modelled with the same discrimination as in a previous analysis, 0.72.

 

Model=?,?,Percent

Rating (or partial credit) scale=Percent,B100,G ; model % at 0-100 binomial trials

0=0,0.72,A ; Anchor the scale discrimination at 0.72

 

Example 10: Forcing structure (step) anchoring with dichotomous items. Dichotomous items have only one step, so usually the structure calibration is at zero logits relative to the item difficulty. To force a different value:

 

Facets = 2

Model = ?,?,MyDichotomy

Rating scale = MyDichotomy, R2

0 = 0, 0, A ; anchor bottom category at 0 - this is merely a place-holder

1 = 1, 2, A ; anchor the second category at 2 logits

2 = 2 ; this forces Facets to run a rating scale model, but it drops from the analysis because the data are 0, 1.

*

If the items are centered, this will move all person abilities by 2 logits. If the persons are centered, the item difficulties move by 2 logits.

 

Example 11. The item-person alignment is to be set at 80% success on dichotomous items, instead of the standard 50% success.

Model = ?,?,?, Dichotomous

Rating scale = Dichotomous, R1  ; define this as a rating scale with categories 0,1 rather than a standard dichotomy (D)

0 = 0, 0, A ; Place-keeper for bottom category

1 = 1, -1.39, A ; Anchor Rasch - Andrich threshold for 0-1 threshold at -1.39 logits

*

 

Table 6 Standard 50% Offset - kct.txt

----------------------------

|Measr|+Children|-Tapping i|

----------------------------

+   1 + **.     +          +

|     |         | 11       |

|     |         |          |

|     |         |          |

*   0 *         *          *

|     | ******  |          |  ---

|     |         |          |   |

|     |         |          |   80% probability of succes

+  -1 +         +          +   |

|     | *.      |          |   |

|     |         | 10       |  ---

|     |         |          |

+  -2 +         +          +

----------------------------

|Measr| * = 2   |-Tapping i|

----------------------------

 

Table 6 80% offset -1.39 logits

----------------------------

|Measr|+Children|-Tapping i|

----------------------------

+   1 +         +          +

|     |         | 11       |

|     | **      |          |

|     |         |          |

*   0 *         *          *

|     |         |          |

|     | **.     |          |

|     |         |          |

+  -1 +         +          +

|     |         |          |

|     | ******  | 10       | <- Item with 80% probability of success targeted

|     |         |          |

+  -2 +         +          +

----------------------------

|Measr| * = 2   |-Tapping i|

----------------------------

 

Example 12. Data has the range 0-1000, but Facets only accepts 0-254. Convert the data with the Rating Scale= specification:

models = ?,?,...,spscale

rating scale=spscale,R250,Keep ; keep unobserved intermediate categories in the rating scale structure

0,0-1,,,0+1 "0-1" is the category label.

1,2-5,,,2+3+4+5

2,6-9,,,6+7+8+9

3,10-13,,,10+11+12+13

....

248,990-993,,,990+991+992+993

249,994-997,,,994+995+996+997

250,998-1000,,,998+999+1000

*