Plausible values

Plausible values are estimates intended to represent the distribution of measures that could produce the observed scores. They were developed for large-scale educational assessments from which group-level measures are to be obtained, but with data too thin to support individual-level measurement.

 

Winsteps is designed for individual measurement. When this is possible, then group-level reporting can be done, e.g., with PSUBTOT=. The Winsteps estimate approximates the mean of the plausible-value distribution.

 

Plausible values are values from the error distribution of the estimate. Winsteps reports each person's estimate (measure) and its standard error. Plausible values are values selected at random from a normal distribution with its mean at the estimated measure and with standard deviation equal to the standard error. You can generate these with Excel or other statistical software.

 

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Varma Kay asked:

1) Is it possible to apply sample weights in rasch analysis using Winsteps?

 

2) Is it possible to generate plausible values including information from both the test data as well as data from background questionnaires?

 

Your 1) Sample weights in Winsteps - yes, use PWEIGHT=

 

Your 2a) Plausible values.

Following www.rasch.org/rmt/rmt182c.htm - we can see that plausible values are used to obtain unbiased theta estimates. The problem is that MLE estimates are inflated and EAP values are deflated, so usually a complex estimation procedure is employed. Here is a simple alternative:

0. the true values from the original data: we discover these values at step 5.

1. estimate theta and delta from the original data using any analysis method

2. simulate a dataset using the step 1 theta and delta values

3. estimate theta and delta from the data simulated in step 2.

4. the change in theta mean and S.D. from step 1 to step 2 will tell us how much the estimates inflate or deflate from the original "true" values in step 0 to step 1.

5. compute the "true" values by rolling back the values from step 1 to plausible values from step 0.

[Interestingly, this technique is being used with photography software to defuzz photographs!]

 

Data from background questionnaires?

yes, this is incorporated in the analysis as weighted polytomous items

1. take a background variable, e.g., age or grade level.

2. formulate it as a polytomy

3. add it to the dataset as an extra item: give it zero weight: IWEIGHT=

4. analyze the data with the extra item using ISGROUPS=

5. look at Table 14.3 for the polytomous item. Adjust the polytomous categories and their scoring until the average measures advance with category.

6. repeat 1.-5. for all the other background variables.

7. all the background are now correlating with the known latent variable

8. adjust IWEIGHT= for each background variable depending on the influence you want it to have on the plausible values.