Local Dependence

In some data designs, data are collected from the same persons more than once, or observations are collected on equivalent items. Consequently there is reason to suspect that local dependence exists in the data. What is its impact on the Rasch measures?

 

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.

 

Local dependence usually squeezes or stretches the logit measures, but does not usually change cut-points much when they are expressed in raw-score terms.

 

Procedure A. If a subset of items may have strong local dependence, then rescore the subset as one partial-credit item.

1) Analyze all the data with subset of items as separate items. Output the person measures to Excel. PFILE=

2) Combine the scores on the subset of items into one partial credit item. All the other items remain unchanged. Analyze all the data. Output the person measures to Excel. PFILE=

3) In Excel, cross-plot the person measures from (1) and (2). The curvature of the plot shows the influence of the local dependence on linearity.

4) Is the curvature big enough to be important to your audience? If yes, use the person measures from (3). If no, use the person measures from (2). My guess is usually "No".

 

Procedure B. To avoid local dependence in measuring change from pre-test to post-test:

1.Create a random, "stacked" dataset, in which each patient only appears once, either at pre-test or post-test.  For instance, see FORMAT= example 7.

2.Run an initial Winsteps analysis and create item and step anchor files: IFILE=if.txt, SFILE=sf.txt

3.Run Winsteps on the full pre-test data set using the IAFILE=if.txt and SAFILE=sf.txt from step #2

4.Run Winsteps on the full post-test data set using the IAFILE-if.txt and SAFILE=sf.txt from step #2

5. You can determine the effect of local dependence by cross-plotting the person measures from 3) and 4) against the measures from an unanchored stacked analysis of all the data.

Marais I. Response dependence and the measurement of change. J Appl Meas. 2009;10(1):17-29

 

Procedure C. Here is an experiment to determine whether local dependence is a problem. Assuming that data from the same persons may be a problem, select from your cases one of each different response string. This will make the data as heterogeneous as possible. Perform an analysis of this data set and see if that changes your conclusions markedly. If it does, then local dependence may be a concern. If it doesn't then local dependence is having no substantive impact.

 

Using Excel, a method of obtaining only one of each different response string:

0. Import the data into excel as a "character" column

1. from the Excel data pull down menu choose -> filter -> advanced filter

2. under "action" choose "copy to another location"

3. click "list range" and highlight the range of element numbers - if you want the whole column click on the letter at the top of the column

4. click "copy to" and choose an empty column, e.g., column J.

5. click "unique records only"

6. click "OK"

7. look at column J. The data are unique.