Applied in a given empirical context, the model can be considered a mathematical hypothesis that the probability of a given outcome is a probabilistic function of these person and item parameters. The graph showing the relation between the probability of a given category as a function of person location is referred to as a "Category Probability Curve" (CPC). An example of the CPCs for an item with five categories, scored from 0 to 4, is shown in Figure 1. A given threshold formula_18 partitions the continuum into regions above and below its location. The threshold corresponds with the location on a latent continuum at which it is equally likely a person will be classified into adjacent categories, and therefore to obtain one of two successive scores. The first threshold of item "i", formula_19, is the location on the continuum at which a person is equally likely to obtain a score of 0 or 1, the second threshold is the location at which a person is equally likely to obtain a score of 1 and 2, and so on. In the example shown in Figure 1, the threshold locations are −1.5, −0.5, 0.5, and 1.5 respectively. Respondents may obtain scores in many different ways. For example, where Likert response formats are employed, "Strongly Disagree" may be assigned 0, "Disagree" a 1, "Agree" a 2, and "Strongly Agree" a 3. In the context of assessment in educational psychology, successively higher integer scores may be awarded according to explicit criteria or descriptions which characterise increasing levels of attainment in a specific domain, such as reading comprehension. The common and central feature is that some process must result in classification of each individual into one of a set of ordered categories that collectively comprise an assessment item. In elaborating on features of the model, Andrich (2005) clarifies that its structure entails a "simultaneous classification process", which results in a single "manifest" response, and involves a series of dichotomous latent responses. In addition, the latent dichotomous responses operate within a Guttman structure and associated response space, as is characterised to follow. Let  be a set of independent dichotomous random variables. Andrich (1978, 2005) shows that the polytomous Rasch model requires that these dichotomous responses conform with a latent Guttman response subspace:  in which "x" ones are followed by "m-x" zeros. For example, in the case of two thresholds, the permissible patterns in this response subspace are:  where the integer score "x" implied by each pattern (and vice versa) is as shown.