For purposes of evaluating INDSCAL’s goodness-of-fit index (R₁), random data were generated for various
combinations of N (the number of individuals),
ranging from 3 to 30, and n (the number of stimuli),
ranging from 10 to 40. Results from INDSCAL analyses
of random data were then used to provide an
easy-to-use equation for estimating the expected value
of R₁ as a function N, n, and r (the number of dimensions).
The equation was highly successful in predicting
expected values of R₁ for random data, as indicated
by a multiple correlation of .9965.