﻿ Model - matching data with measurement models

# Model - matching data with measurement models

If your models don't seem to match correctly, use Query=Y.Facets allows more than one model statement to be specified for an analysis after a Model= specification. The sequence of the model statements is important. Facets attempts to match each line of data to each model statement in turn, beginning with the first statement. Each datum is analyzed only once in accordance with first model it actually matches. The first "match" selects that datum into the analysis according to that model and that model only.

If a datum does not match any model, then it is ignored.

Example 1: Multiple models used in one analysis. Here, each item has a different model, and only items 1,2,3,4,5,6 and 23 are explicitly listed. Other items will be ignored.

Model=

?,23,?,M ; All responses on Item 23 in Facet 2 are specified to be "missing"

?,1,?,D,2 ; Item 1 is a dichotomy, to be weighted 2

?,2,?,R ; Item 2 has a rating scale (or partial credit)

?,3,#,R ; Each judge on Item 3 has his own rating scale, i.e., a partial credit scale

?,4, ,B2 ; Item 4 is two binomial trials, with no judge

?B,5,?B,R15 ; Item 5 has, at most, a 0-15, 16 category, rating scale (or partial credit)

; a Person-Judge Bias analysis is requested for all data

?,6B,?B,D ; Item 6 is a dichotomy

; an Item-Judge Bias analysis is requested for all data

*

Here is a sample line from the data file:

2,4,1,0 ; Person 2 rated on item 4 by judge 1 with 0.

Which model does it match?

Model=

?,23,?,M ; no match:

the matching process compares

model elements = ?,23, ?

data elements = 2, 4, 1

Facets 1 and 3 of the model are "?" (=every element), and so match the corresponding data elements,

but Facet 2 of the model is element 23, which does not match element 4 in the data, so there is no match.

?,1,?,D,2 ;no match: facet 2, "1" in model, "4" in data

?,2,?,R ;no match: facet 2, "2" in model, "4" in data

?,3,#,R ;no match: facet 2, "3" in model, "4" in data

?,4, ,B2 ;matches, because

facet 1, "?" (any person) in model, "2" in data

facet 2, "4" in model, "4" in data

facet 2, " " (ignore judge) in model, "1" in data. "1" is checked against the Labels= list.

so this datum is modeled as two binomial trials ("B2")

?B,5,?B,R15 ; datum has already matched and been used. No further matching is done.

?,6B,?B,D

*

Example 2: The next data line, with the same model statements as Example 1:

1,23,1,4 ; person 1 rated on item 23 by judge 1 with 4.

Which model does it match?

Model=

?,23,?,M ;matches, so this data is treated as "M", missing.

?,1,?,D,2 ; datum already matched and used. No further matching is done

*

Example 3: The next data line:

102,3,6,2 ; person 102 rated on item 3 by judge 6 with 2

Which model does it match?

Model=

?,23,?,M ;no match: facet 2

?,1,?,D,2 ;no match: facet 2

?,2,?,R ;no match: facet 2

?,3,#,R ;matches

facet 1, "?" (any person) in model, "102" in data

facet 2, "3" in model, "3" in data

facet 2, "#" (any judge) in model, "6" in data

so this datum is modeled on a rating scale (or partial credit) ("R") as used by the particular judge ("#"), which in this case is judge 6, "6" in the data. This rating sale will have Rasch-Andrich thresholds (step calibrations) based solely on judge 6's ratings.

?,4, ,B2 ; not used

?B,5,?B,R15

?,6B,?B,D

*

Example 4: The next data line:

79,3,3,1 ; person 79 rated on item 3 by judge 3 with 1

Which model does it match?

Model=

?,23,?,M ;no match: facet 2

?,1,?,D,2 ;no match: facet 2

?,2,?,R ;no match: facet 2

?,3,#,R ;matches

facet 1, "?" (any person) in model, "79" in data

facet 2, "3" in model, "3" in data

facet 2, "#" (any judge) in model, "3" in data

so this datum is modeled on a rating scale (or partial credit) ("R") as used by the particular judge ("#"), which in this case is judge 3, "3" in the data. This rating scale (or partial credit) will be similar to that for judge 6 in Example 3 above, but will be calibrated on judge 3's ratings alone.

?,4, ,B2 ; not used

?B,5,?B,R15

?,6B,?B,D

*

Example 5: The next data line:

7,5,6,1 ; Person 7 is rated on item 5 by judge 6 with 1

Which model does it match?

Model=

?,23,?,M ;no match: facet 2

?,1,?,D,2 ;no match: facet 2

?,2,?,R ;no match: facet 2

?,3,#,R ;no match: facet 2

?,4, ,B2 ;no match: facet 2

?B,5,?B,R15 ;matches

facet 1, "?B" (any person) in model, "7" in data

facet 2, "5" in model, "5" in data

facet 2, "?B" (any judge) in model, "6" in data

so this datum is modeled on a rating scale (or partial credit) ("R") with a valid range of 0 to 15.

The "B" characters in the model are ignored for matching purposes.

?,6B,?B,D ;ignored

*

Example 6: The next data line:

67,8,32,5 ; Person 67 rated on item 8 by judge 32 with 5

Which model does it match?

Model=

?,23,?,M ;no match: facet 2

?,1,?,D,2 ;no match: facet 2

?,2,?,R ;no match: facet 2

?,3,#,R ;no match: facet 2

?,4, ,B2 ;no match: facet 2

?B,5,?B,R15 ;no match: facet 2

?,6B,?B,D ;no match: facet 2

*

There is no match, so this datum is ignored for this analysis.

Example 7: The next data line:

8,5,4,12 ; Person 8 is rated on item 5 by judge 4 with 12

Which model does it match?

Model=

?,23,?,M ;no match: facet 2

?,1,?,D,2 ;no match: facet 2

?,2,?,R ;no match: facet 2

?,3,#,R ;no match: facet 2

?,4, ,B2 ;no match: facet 2

?B,5,?B,R15 ;matches

facet 1, "?B" (any person) in model, "8" in data

facet 2, "5" in model, "5" in data

facet 3, "?B" (any judge) in model, "5" in data

The "B" characters in the model are ignored for matching purposes.

?,6B,?B,D ;ignored

*

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Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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