Person changes can be of three kinds: developmental trends, swells, and tremors. Person unreliability in the tremor sense (momentary fluctuations) can be estimated from person characteristic curves. Average person reliability for groups can be compared from item characteristic curves.

All test items are perfectly reliable. The unreliability of tost moms results solely from person fluctuations. The theory implies that: (1) test length effects are a sampling phenomenon; (2) person roliabilities can be compared from perRon characteristic curves; (3) all ICC for a unidimensional test have the s m e slope; (4) ICC are not necessarily invariant from one group to another; and (6) reliabilities of groups can be compared from ICC.A reliability coefficient of the theory is defined as the proportion of variance in obtained scores attributable to variance in average attribute level for subjects. Lower bounds for the classical reliability coefficient are also lower bounds for the new coefficient. Statistics calculated from this coefficient have no useful application.

A test model based on the Thurstone judgmental model is described. By restricting various parameters of the model, 3 Rasch models, 2 pseudoRasch models, 3 two-parameter ICC models, and a Weber's Law model are derived.The thematic model for latent trait approaches to test scaling was developed by Thurstone (1927) from his law of comparative judgment. The model was variously termed the method of successive intervals (Saffir, 1937), the method of graded dichotomies (Attneave, 1949), and the law of categorical judgment (Torgerson, 1958). In the model, stimuli were conceived as having a discriminal dispersion around a central location on an attribute continuum and judgmental categories (or category boundaries) as having a similar distribution on the same continuum. A variant of this model, which will be called Thurstone Model A, is produced by substituting items for stimuli and persons for judgmental categories, as illustrated in Figure 1.Thurstone Model A locates items and persons on the same attribute continuum. Each item and each person has a normal distribution of values on the attribute resulting from moment to moment fluctuation. The standard deviations of APPLIED the distributions may differ from item to item or from person to person. Item and person param_eters are assumed to be independent of each other (ri, = 0). The correlation between location and dispersion parameters is unspecified for either items or persons. A person answers an item correctly if, at the moment of attempting it, his/her momentary attribute value is higher than the momentary attribute value of the item; otherwise he/she answers it incorrectly. Torgerson (1958) suggested certain simplifications of the thematic model in order to overcome the formidable estimation problems. He set the standard deviations for categories (subjects) equal and called the result Condition B; he set standard deviations for stimuli (items) equal and called the result Condition C; finally, he set both the standard deviations of categories and the standard deviations of stimuli equal and called the result Condition D. It is the purpose of this paper to examine more systematically a wider range of simplifying possibilities and to relate these to ancient and modern approaches to test scaling. Restrictions on Both Item and Person Dispersions Torgerson did not consider the cases where item and person dispersions are set to zero. It

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