Center facet =

One facet must be non-centered in most analyses. Center= specifies which facets are to be centered, so that the mean of the element measures is zero (or Umean=). Other facets are non-centered, unless they are anchored or group-anchored. If both Center= and Noncenter= and Center= are specified, only the first encountered in the specification file is actioned. When any element within a facet is anchored, or group-anchored, then the origin of the scale for that facet is set by the anchoring. Both Center= and Noncenter= are ignored for that facet.

 

a)Center= facet number, facet number, ...
a mean element measure of zero (or Umean=) for element measures with non-extreme scores
Example: Center= 2, 3, 4
 

b)Center= facet number Z, facet number Z, ...
a mean element measure of zero (or Umean=) for all element measures, including extreme scores
Example: Center= 2Z, 3Z, 4Z
 

c)Center= facet number, facet number Z, ...
a combination of (a) and (b)
Example: Center= 2, 3Z, 4
 

Extreme measures (corresponding to minimum and maximum possible scores) are included in the Means in Table 7, so that these may not be 0  (or Umean=) for centered facets unless: Center= facet number Z

 

In most analyses, if all facets are centered or anchored, then the estimates are over-constrained and displacements are reported. If more than one facet is non-centered, the frame of reference is not sufficiently constrained and the element measures are ambiguous (non-identified). The usual convention is to center the frame of reference on the agents of measurement: items, tasks, judges. This establishes the origin. Then the objects of measurement, persons, are positioned with respect to this origin. Technically, centering is an identifiability constraint, so that the estimates are uniquely defined.

 

Example 1: facets 2 (items) and 3 (raters) are to be centered; facet 1 is non-centered.

•Center= 2, 3 ; non-extreme element measures are centered in facets 2 and 3.

•Center= 2Z, 3Z ; all element measures are centered in facets 2 and 3

•Center= 2, 3Z ; non-extreme element measures are centered for facet 2; all element measures are centered for facet 3

 

Example 2: No facets are to be centered. This is an unusual situation such as when there is only one active facet so that the item difficulties are defined relative to an implicit origin as in the "Three Mile Island" example.

Center=0