CATEGORY FREQUENCIES AND THRESHOLD ORDER  

            Question:

Is threshold order dependent on category frequency in a Rasch analysis?

            Explanation:

When you have an item format in which the categories are intended to reflect order, then the structure demands that ordered thresholds are relevant and central. When assessing threshold order, it is important to consider the standard errors as it is possible that the threshold estimates are unstable and so reversed because of this. They in fact should be ordered and significantly different from each other.

For such an item, it is important to realize a distinction between the distribution of frequencies from the sample and the probabilities in a particular item. It is possible to have few frequencies in a particular category and yet have the thresholds properly ordered. Reversals in an item are not simply a function of small empirical frequencies, but of the relationship between the frequencies. 

The issue is not that there are few people in a category, but given all the evidence that has been put together in the estimation process, the issue is that persons who by their location estimates should be responding in a category, are not responding in it at the required rate. Thus it does not matter that a whole lot of people from a sample are not responding in the category, it is only a problem that the people who should be responding in the category are not responding in it.