Category boundaries and thresholds 
Conceptualizing rating scales and partialcredit response structures for communication can be challenging. Rasch measurement provides several approaches. Choose the one that is most meaningful for you.
Look at this edited excerpt of Table 3.2:
Here are three ways of conceptualizing and communicating the transition, threshold, boundary between category 1 and category 2:
(1) Raschhalfpoint thresholds (Zone). Someone at the boundary between "1" and "2" would have an expected rating of 1.5, or 1000 persons at the boundary between "1" and "2" would have an average rating of 1.5. This boundary is the "zone" = "Expected Measure at 1+0.5 or 2 0.5" which is .03 logits, the Raschhalfpoint threshold. To illustrate this, use the model item characteristic curve. The expected score ogive / model ICC (Table 21.2  second on list in Graphs menu). The CAT+.25, CAT0.5, AT CAT, and CAT.25 columns in the ISFILE= plot points on this ogive. The expected score ogive relates most directly to the estimation of the Rasch parameters. Since it is only one line, it is also convenient for summarizing performance at any point on the latent variable by one number. Crucial points are the points on the variable corresponding to the lower category value + 0.5, i..e, more than the higher adjacent category value  0.5. These Raschhalfpoint thresholds are "average score thresholds" or "RaschICC thresholds".
(2) RaschThurstone thresholds (50% Cumulative Probability). Someone at the boundary between "1" and "2" would have a 50% chance of being rated 1 or below, and a 50% chance of being rated 2 or above. This is the RaschThurstone threshold of .07 logits. To illustrate this, use the cumulative probability curves. The cumulative probability curves (Table 21.3  and third on list in Graphs menu). The 50%PRB columns in the ISFILE= are the crucial points on these curves. and are the RaschThurstone thresholds, useful for identifying whether a person is most likely to respond below, at or above a certain category.
(3) RaschAndrich thresholds. Someone at the boundary between "1" and "2" would have an equal chance of being rated 1 or 2. This is the RaschAndrich Threshold of .15 logits. To illustrate this, use the category probability curves. The probability curves (Table 21.1  and top of list in Graphs menu). The Andrich Threshold in the ISFILE= gives the point of equal probability between adjacent categories. The points of highest probability of intermediate categories are given by the AT CAT values. These probability curves relate most directly to the Rasch parameter values, also called RaschAndrich thresholds. They are at the intersection of adjacent probability curves, and indicate when the probability of being observed in the higher category starts to exceed that of being observed in the adjacent lower one. This considers the categories two at a time, but can lead to misinference if there is RaschAndrich threshold disordering.
d) Empirical average measures. For any particular sample, there is the average ability of the people who scored in any particular category of any particular item. This is the "Average Measure" reported in Table 3.2. This is entirely sampledependent. It is not reported in ISFILE=. In the Table, the empirical average measure of the persons responding in category 1 is .47 logits, and in category 2 is 1.07 logits. Halfway between is .77 logits.
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