These Tables show items (Table 23.99, formerly Table 23.1) and persons (Table 24.99, formerly 24.1) that may be locally dependent. Specify PRCOMP=R (for score residuals) 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.

 

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  ITEMS

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

|RESIDUL| ENTRY                        | ENTRY                        |

|CORRELN|NUMBER  ITEM                  |NUMBER  ITEM                  |

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

|   .71 |    17 Q. PROBLEM SOLVING     |    18 R. MEMORY              |

|   .69 |    14 N. COMPREHENSION       |    15 O. EXPRESSION          |

|   .61 |     9 I. BED TRANSFER        |    10 J. TOILET TRANSFER     |

|   .61 |     7 G. BLADDER             |     8 H. BOWEL               |

|   .54 |     4 D. UPPER BODY DRESSING |     5 E. LOWER BODY DRESSING |

|   .46 |    16 P. SOCIAL INTERACTION  |    17 Q. PROBLEM SOLVING     |

|   .45 |    16 P. SOCIAL INTERACTION  |    18 R. MEMORY              |

|   .40 |    10 J. TOILET TRANSFER     |    11 K. TUB, SHOWER         |

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

|  -.37 |    10 J. TOILET TRANSFER     |    18 R. MEMORY              |

|  -.36 |    10 J. TOILET TRANSFER     |    17 Q. PROBLEM SOLVING     |

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

 

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 10 largest correlations are shown in the Table. To see all correlations, output ICORFILE= or PCORFILE=

 

This Table is used to detect 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. is used to detect dependency between pairs of items or persons. 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.

 

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.