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A Thurstonian model is a latent variable model 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 response variables and with constant variance. Thurstonian models have been used as an alternative to generalized linear models in analysis of sensory discrimination tasks. They have also been used to model long-term memory in ranking tasks of ordered alternatives, such as the order of the amendments to the US Constitution. Their main advantage over other models ranking tasks is that they account for non-independence of alternatives. ==Definition== Consider a set of ''m'' options to be ranked by ''n'' independent judges. Such a ranking can be represented by the ordering vector rn = (rn1, rn2,...,rnm). Rankings are assumed to be derived from real-valued latent variables ''zij'', representing the evaluation of option ''j'' by judge ''i''. Rankings ri are derived deterministically from zi such that ''z''i(ri1)'' < ''zi(ri2)'' < ... < ''zi(rim)''. The zij are assumed to be derived from an underlying ground truth value ''μ'' for each option. In the most general case, they are multivariate-normally distributed: : where ''εj'' is multivariate-normally distributed around 0 with covariance matrix Σ. In a simpler case, there is a single standard deviation parameter ''σi'' for each judge: : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Thurstonian model」の詳細全文を読む スポンサード リンク
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