Extreme scores: what happens

Estimation:

Extreme scores are the lowest and highest possible scores for persons on items, or for items by persons. They include zero and perfect scores. They are shown in the Tables as MINIMUM ESTIMATE MEASURE and MAXIMUM ESTIMATE MEASURE.

 

Mathematically, they correspond to infinite or indefinite measures on the latent variable and so are not directly estimable. Accordingly persons or items with extreme scores are dropped for the duration of the measurement estimation process. The extreme persons are dropped casewise. The extreme items are dropped listwise.

 

Sometimes the effect of dropping extreme items and persons is to make other items and persons extreme. If so, these are also dropped. If the data have a Guttman pattern, ultimately all items and persons are dropped and the measures for that data set are reported as inestimable.

 

After the measures of all non-extreme items and persons have been estimated, then the extreme scores are reinstated. Reasonable extreme measures are imputed for them (using a Bayesian approach), so that all persons and items have measures. This is done by making small score adjustments using EXTREMESCORE=.

 

With TARGET=, CUTLO=, CUTHI= or ISGROUPS=, it may not be possible to estimate a measure for an extreme score. There are reported as INESTIMABLE.

 

Fit computation:

Item Infit and Outfit: In the IFILE=, these are reported for each item and summarize fit across all scored responses excluding responses in extreme person scores.

In the DISFILE=, these are reported for each scored response and summarize fit excluding responses in extreme person scores.

 

Let's set PDROPEXTREME=YES, so that extreme scores for persons are not counted. Then, here is an example:

IFILE:   Infit and Outfit mean-squares for 16237 responses scored 1 or 0 = 1.0873 and 1.1317

DISFILE: Infit and Outfit mean-squares for 10537 responses scored 1      = 1.0733 and 1.0916

        Infit and Outfit mean-squares for  5700 responses scored 0 have different values for each incorrect response code.

 

Responses in extreme person scores always have perfect fit (infit and outfit mean-squares = 0), so they are excluded from fit computations everywhere.

 

Extreme person scores do have estimated measures, so they are included in the item and item-option response counts, average measures, and correlations.

 

Example 1: We want statistics that exclude responses in all person and item extreme scores.

PDROPEXTREME= Yes

IDROPEXTREME= Yes