Improving Communication:

The standard unit of measurement is the logit (log-odds unit). These measurement units are inconvenient for reporting results to examinees, parents, administrators etc. They can be linearly rescaled to make the reported results more useful to the user. The standard origin (mean) is the mean of the item difficulties, the standard scaling is 1, i.e., 1 reported unit per logit. These values may be changed by

Umean = user origin value, user units per logit, decimal places to report

 

Example 1:

A useful transformation is to take the high and low measures on the vertical rulers in Table 6.0 or Table 7 and assign that range to 0-100. Then linearly transform all other measures.

Suppose the highest measure is +8.0 logits and the lowest measure is -7.0 logits on Table 6.0 of an analysis. This gives a range of 15 logits, i.e., 100/15 = 6.67 points per logit.

For reporting purposes, transform all measures by Measure* 6.67 + 46.7 and report with 1 decimal place.
Umean = 7, 6.67, 1
A measure of +2.0 logits becomes 2+*6.67 + 46.7 = 60.0 user-scaled points
Standard errors becomee (Standard error logits) * 6.67.
A standard error of .03 logits becomes (.03)*6.67 = .2 user-scaled points

 

Example 2: Set the origin of the measurement scale at 50 units, with 10 units per logit, and report 0 decimal places. This usually gives a measure range somewhat like 0-100.

Umean = 50, 10, 0

 

Example 3: From an earlier run, the lowest person measure is -6.23 logits, and highest 7.45 logits. Rescale so that the person measure range is 0 - 100.

The new scale is 100 units. The old range was 6.23 + 7.45 = 13.68 logits, so scaling factor = 100 / 13.68 = 7.31 units per logit.

The new origin is offset 6.23 logits = 6.23*7.31 units = 45.54 units

Umean = 45.54, 7.31 ; the standard number of decimal places, 2, is reported.

 

Example 4: You wish to treat an element as a dummy. It is used for selection, fit analysis and bias detection only.

If Umean = 0 (the standard)
Labels=
4=dummy facet,A
1=dummy element,0 ; anchor this at the umean= value
....
*

 

If Umean = 50 (user setting)
Labels=
4=dummy facet,A
1=dummy element,50 ; anchor this at the umean= value
...
*

 

Example 5:  -5 to +3 is to be reported as 0 to 25.

Usually the "previous Umean=" is zero.

The computation generally is:

Existing range of measures =  -5 to +3  (or whatever is in your Facets report)

Desired range = 0 to 25

Then:

Scaling = (25 - 0) / (3 - -5)  = 25/8 = 3.125

Umean= is given by equivalent values: 25 matches 3

New value = old value * scaling + Umean

25 = 3.125 * 3 + Umean

Umean = 15.625

So that the Facets specification is:

Umean = 15.625,  3.125

Checking this for the 0 point:

0 = -5*3.125 + 15.625