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A Thurstonian model is a stochastic transitivity model with latent variables for describing the mapping of some continuous scale onto discrete, possibly ordered categories of response. In the model, each of these categories of response corresponds to a latent variable whose value is drawn from a normal distribution , independently of the other ...
The scale is then obtained as a left-adjusted column marginal average of this standard score matrix (Thurstone, 1927b). The underlying rationale for the method and basis for the measurement of the "psychological scale separation between any two stimuli" derives from Thurstone's Law of comparative judgment (Thurstone, 1928).
Guttman scale has been generalized to the theory and procedures of "multiple scaling" which identifies the minimum number of scales needed for satisfactory reproducibility. As a procedure that ties substantive contents with logical aspects of data, Guttman scale heralded the advent of facet theory developed by Louis Guttman and his associates.
The Guttman scale is related to Rasch measurement; specifically, Rasch models bring the Guttman approach within a probabilistic framework. Constant sum scale – a respondent is given a constant sum of money, script, credits, or points and asked to allocate these to various items (example : If one had 100 Yen to spend on food products, how much ...
That is, the scale represents how heavy people perceive the objects to be based on the comparisons. Although Thurstone referred to it as a law, as stated above, in terms of modern psychometric theory the 'law' of comparative judgment is more aptly described as a measurement model. It represents a general theoretical model which, applied in a ...
The initial development of common factor analysis with multiple factors was given by Louis Thurstone in two papers in the early 1930s, [42] [43] summarized in his 1935 book, The Vector of Mind. [44] Thurstone introduced several important factor analysis concepts, including communality, uniqueness, and rotation. [ 45 ]
This is the defining feature of the class of models, as is elaborated upon in the following section. The Rasch model for dichotomous data has a close conceptual relationship to the law of comparative judgment (LCJ), a model formulated and used extensively by L. L. Thurstone, [12] [13] and therefore also to the Thurstone scale. [14]
The BTL model is identical to Thurstone's model if the simple logistic function is used. Thurstone used the normal distribution in applications of the model. The simple logistic function varies by less than 0.01 from the cumulative normal ogive across the range, given an arbitrary scale factor.