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This paper gives a numerical procedure for estimating the parameters of the law of comparative judgement under a variety of conditions. A broad class of goodnessof-fit functions is treated, including weighted least-squares and maximumlikelihood criteria. Any response function that has the necessary derivatives can be employed. Various kinds of constraints may be imposed on the parameters of the model. Special attention is given to linear constraints; and to equality constraints, where any of the parameters may be assumed to be known in advance and any subset of the parameters may be assumed to take on either a specified or an unspecified common value. In the maximum-likelihood case, for large samples, approximate standard errors and confidence intervals for the estimated parameters may be obtained, and goodness of fit may be tested by the likelihoodratio technique. Numerical examples are provided. the symbol, vs,, the law of comparative judgement states that Letting n,, = P(X, < X,).pc=B(X,) ( l < i < n ) , ada = uq2 rsj = raq ( l < j d i < n ) ,the random variable, Xi -X,, has an expected value of prpi and a variance of d,a = uia + u,a -2ri, ui 0 , . Consequently,Z d 5 = (4 -4 -Pi + P,)/dd$ 1973,26, 240-2601

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factor analysis, principal components, rotation, factor transformation,