DOVE, A RATIONAL ANALYSIS OF SPARSE DATA

Dove is an unconventional statistical procedure which can be useful, even when many or most data are missing, for (1) generalized least-squares fitting to evaluate a self-consistent set of all parameters in an expression for predicting data, and (2) transforming the set of parameters obtained in phase 1, without changing the predicted data, so that each final parameter has a simple, pure, realistic, physical meaning. Since predicted data are expressed as aixj+biyj+. ct with n product terms, phase 2 requires incorporation of n2+n independent subsidiary conditions, of which In are arbitrary, i. e., merely fix zero reference points and scale unit sizes, but n2-n are critical, i. e., must be relationships between particular parameters supported by other information. Both phases are illustrated by an example with n=2, 1 ≤ ≤ 7, 1 ≤ j ≤ 10, which therefore needs 41 parameters to fit 70 data plus the 6 subsidiary conditions. Valid parameters are obtained even if 30 of the 70 possible data are missing. DOVE provides a general method for evaluating all the parameters in linear free-energy relationships with two or more product terms. © 1979, American Chemical Society. All rights reserved.