The item parameter a _ i represents the discrimination of the item : that is, the degree to which the item discriminates between persons in different regions on the latent continuum.
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Consider a person A, whose location on the latent continuum is at the threshold between regions on the continuum at which a pass and credit are most likely to be awarded.
3.
Persons are ordered by the estimates of their locations on the latent continuum and classified into Class Intervals on this basis in order to graphically inspect the accordance of observations with the model.
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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.
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The grey line maps a person with a location of approximately 0.2 on the latent continuum, to the probability of the discrete outcome X _ { ni } = 1 for items with different locations on the latent continuum.
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The grey line maps a person with a location of approximately 0.2 on the latent continuum, to the probability of the discrete outcome X _ { ni } = 1 for items with different locations on the latent continuum.
7.
It should be noted, however, that this does not mean that a measurement process entails making such counts in a literal sense; rather, threshold locations on a latent continuum are usually " inferred " from a matrix of response data through an estimation process such as Conditional Maximum likelihood estimation.
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