Polytomous mean-square fit statistics

For a general introduction, see Diagnosing Misfit, also Dichotomous mean-square fit statistics.

 

from Smith R.M. (1996) Rasch Measurement Transactions 10:3 p. 516

 

The z-score standardized statistics report, as unit normal deviates, how likely it is to observe the reported mean-square values, when the data fit the model. The term z-score is used of a t-test result when either the t-test value has effectively infinite degrees of freedom (i.e., approximates a unit normal value) or the Student's t-statistic value has been adjusted to a unit normal value.

 

* "folded data" can often be rescued by imposing a theory of "not reached" and "already passed" on to the observations. For instance, in archaeological analysis, the absence of bronze implements can mean a "stone age" or an "iron age" society. A useful recoding would be "1" = "stone age", "2" = "early bronze", "3" = "bronze", "2=>4" = "late bronze", "1=>5" = "iron age". This can be done iteratively to obtain the most self-consistent set of 4's and 5's. (Folding is discussed in Clive Coombes' "A Theory of Data".)

 

Example: Identify persons who respond in the same category to every item:

Anchoring all the items at the same difficulty and using the Rating Scale Model. Then the distribution of the mean-square fit statistics will indicate the extent to which all items are rated the same. We expect strings like 333333333333333333 to have zero mean-square fit statistics. Set NAME1= and NAMLEN= so that the response strings are also the person labels.

 

If the responses start in column 1 and there are 9 items:

NAME1 = 1

NAMLEN = 9

ISGROUPS=

IAFILE=*

1-9 0

*

FITP=0  ; show everyone in Table 6.

 

Output PFILE= to Excel, then you can draw a histogram of the mean-square fit statistics.

For instance: www.ablebits.com/office-addins-blog/2016/05/11/make-histogram-excel/