Table 23.99 Largest residual correlations for items

These Tables show items (Table 23.99) that may be locally dependent. Specify PRCOMP=R (for score residuals, Yen Q3) or PRCOMP=S or Y (for standardized residuals) or PRCOMP=L (for logit residuals) to obtain this Table. Residuals are those parts of the data not explained by the Rasch model. High correlation of residuals for two items (or persons) indicates that they may not be locally independent, either because they duplicate some feature of each other or because they both incorporate some other shared dimension.

 

Table 23.0 Variance components scree plot for items

Table 23.1, 23.11 Principal components plots of item loadings

Table 23.2, 23.12 Item Principal components analysis/contrast of residuals

Table 23.3, 23.13 Item contrast by persons

Table 23.4, 23.14 Item contrast loadings sorted by measure

Table 23.5, 23.15 Item contrast loadings sorted by entry number

Table 23.6, 23.16 Person measures for item clusters in contrast. Cluster Measure Plot for Table 23.6.

Table 23.99 Largest residual correlations for items

Youtube video explaining Table 23

 

Missing data are deleted pairwise if both of a pair are missing or PRCOMP=O (for observations), otherwise missing data are replaced by their Rasch expected residuals of 0.

 

     LARGEST STANDARDIZED RESIDUAL CORRELATIONS

     USED TO IDENTIFY DEPENDENT TAP

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

|CORREL-| ENTRY             | ENTRY             |

|  ATION|NUMBER TAP         |NUMBER TAP         |

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

|  1.00 |    16 1-4-2-3-1-4 |    17 1-4-3-1-2-4 |

|   .52 |     6 3-4-1       |     7 1-4-3-2     |

|   .45 |     7 1-4-3-2     |     8 1-4-2-3     |

|   .28 |     8 1-4-2-3     |     9 1-3-2-4     |

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

|  -.67 |     8 1-4-2-3     |    14 1-4-2-3-4-1 |

|  -.58 |     7 1-4-3-2     |    14 1-4-2-3-4-1 |

|  -.49 |     6 3-4-1       |    12 1-3-2-4-3   |

|  -.48 |     7 1-4-3-2     |    11 1-3-1-2-4   |

|  -.43 |    15 1-3-2-4-1-3 |    16 1-4-2-3-1-4 |

|  -.43 |    15 1-3-2-4-1-3 |    17 1-4-3-1-2-4 |

|  -.38 |     7 1-4-3-2     |    12 1-3-2-4-3   |

|  -.37 |    12 1-3-2-4-3   |    16 1-4-2-3-1-4 |

|  -.37 |    12 1-3-2-4-3   |    17 1-4-3-1-2-4 |

|  -.32 |     5 2-1-4       |    10 2-4-3-1     |

|  -.31 |     6 3-4-1       |    10 2-4-3-1     |

|  -.29 |    12 1-3-2-4-3   |    13 1-4-3-2-4   |

|  -.29 |    11 1-3-1-2-4   |    13 1-4-3-2-4   |

|  -.28 |     6 3-4-1       |    11 1-3-1-2-4   |

|  -.28 |     4 1-3-4       |     8 1-4-2-3     |

|  -.26 |     4 1-3-4       |     5 2-1-4       |

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

 

Note: Redundant correlations of 1.0 are not printed. If A has a correlation of 1.0 with B, and also with C, assume that B and C also have a correlation of 1.0. After eliminating redundant correlations, the largest correlations are shown in the Table. To see all correlations, output ICORFILE= or PCORFILE=

 

In this Table, high positive residual correlations may indicate local item dependency (LID) between pairs of items or persons. When raw score residual correlations are computed, PRCOMP=R, it corresponds to Wendy Yen's Q3 statistic. It is used to detect dependency between pairs of items or persons. Wendy Yen suggests a small positive adjustment to the correlation of size 1/(L-1) where L is the test length.

Yen, W. M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8, 125-145.

Yen, W. M. (1993). Scaling performance assessments: Strategies for managing local item dependence. Journal of Educational Measurement, 30, 187-213.

See also Cristensen K.B., et al. Critical values of Q3 - https://eprints.whiterose.ac.uk/106017/

 

Local dependence would be a large positive correlation. Highly locally dependent items (Corr. > +.7), such as items "Q." and "R." share more than half their "random" variance, suggesting that only one of the two items is needed for measurement. But, in classical test theory terms, these items may have the highest point-biserial correlations and so be the "best" items.

 

A large negative correlation indicates the opposite of local dependence, as usually conceptualized. If you look at the item fit tables, item "J." or "R." is likely to have large misfit.

 

Remember that "common variance = correlation^2", so items 10 and 11 only share .40*.40 = 16% of the variance in their residuals in common. 84% of each of their residual variances differ. In this Table we are usually only interested in correlations that approach 1.0 or -1.0, because that may indicate that the pairs of items are duplicative or are dominated by a shared factor.

 

Suggestion: simulate Rasch-fitting data like yours using the Winsteps SIFILE= option. Analyze these data with Winsteps. Compare your correlation range with that of the simulated data.

 

An influential paper says "[Readers] expect to see that this issue has been dealt with, if only to report that no response dependency was found." However, even simulated Rasch-fitting data will report some accidental response dependency, so this statement is too extreme.  Let's amend it. to say "if only to report that no consequential response dependency was found.".

Tennant A, Conaghan PG. The Rasch measurement model in rheumatology: what is it and why use it? When should it be applied, and what should one look for in a Rasch paper? Arthritis Rheum. 2007 Dec 15;57(8):1358-62.

 


 

Locally-Dependent Items

 

In practical terms, a correlation of r=0.40 is low dependency. The two items only have 0.4*0.4=0.16 of their variance in common. Correlations need to be around 0.7 before we are really concerned about dependency.

 

If you want to create one super-item out of two dependent items, then use Excel (or similar) to add the scored responses on the two item together. Include the super-item in the data file instead of the dependent items. Change CODES= and use ISGROUPS= to model the additional super-item. You will notice a very small reduction in the variances of the measures.

 

Procedure:

1. Winsteps analyze the original data

2. Output the scored responses: "Output file", "RFILE=", responses.xls

3. In Excel, open responses.xls

4. Sum the scored responses of dependent items into a new item

5. Delete the original dependent items

6. Save responses.xls

7. In Winsteps, "Excel/RSSST" menu, "Excel", Import responses.xls

8. Create Winsteps file of the new set of items (you may need edit ISGROUPS=)

9. Analyze the new Winsteps control file

 


 

Item Calibration without Local Item Dependency (LID)

 

If you need item difficulties from your dataset, but without the effect of LID, here is a procedure:

 

1. Analyze all the dataset with Winsteps with PRCOMP=R to produce the raw residuals.

Output IFILE=iforig.txt as a reference for the original data.

2. Output ICORFILE= for the raw residuals to Excel  in list format

3. Sort the list by correlation

4. Look at the top and bottom of the list. How many inter-item residual correlations are >.02 (or your correlation cut-off value)? (In my empirical dataset about .1%)

Save these item pairings to avoid administering these pairs of item together in CAT or test forms.

5. Make an IDFILE=LID.txt list of one item from each item pair with inter-item residual correlation >.02  (or your correlation cut-off value)

 

6. Reanalyze all the data with Winsteps and IDFILE=LID.txt

7. Output PFILE=pf.txt  - these are the person measures matching only the LID-free items

 

8. Reanalyze all the data with Winsteps without IDFILE=.  Include PAFILE=pf.txt

This forces all the item difficulties and rating-scale structures to conform with the LID-free person measures.

Anchoring the person measures prevents LID from impacting the item difficulties.

9. Output IFILE=if.txt, SFILE=sf.txt - these are the item difficulty and rating-scale threshold values for the item bank or whatever.

 

10. Scatterplot if.txt against iforig.txt. How much is the impact of LID on iforig.txt? Was all this work worth it?

 


 

Q1, Q3: Yen, Wendy (1984) Effects of Local Item Dependence on the Fit and Equating Performance of the Three-Parameter Logistic Model. Applied Psychological Measurement. 8:2, 125-145. https://conservancy.umn.edu/bitstream/handle/11299/107543/v08n2p125.pdf


Help for Winsteps Rasch Measurement and Rasch Analysis Software: www.winsteps.com. Author: John Michael Linacre

Facets Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation Minifac download
Winsteps Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation Ministep download

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn, 2024 George Engelhard, Jr. & Jue Wang 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
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes 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 Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
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
Other 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
As an Amazon Associate I earn from qualifying purchases. This does not change what you pay.

facebook Forum: Rasch Measurement Forum to discuss any Rasch-related topic

To receive News Emails about Winsteps and Facets by subscribing to the Winsteps.com email list,
enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Winsteps.com
The Winsteps.com email list is only used to email information about Winsteps, Facets and associated Rasch Measurement activities. Your email address is not shared with third-parties. Every email sent from the list includes the option to unsubscribe.

Questions, Suggestions? Want to update Winsteps or Facets? Please email Mike Linacre, author of Winsteps mike@winsteps.com


State-of-the-art : single-user and site licenses : free student/evaluation versions : download immediately : instructional PDFs : user forum : assistance by email : bugs fixed fast : free update eligibility : backwards compatible : money back if not satisfied
 
Rasch, Winsteps, Facets online Tutorials


 

 

 

Our current URL is www.winsteps.com

Winsteps® is a registered trademark