DOVE, a Rational Analysis of Sparse Data

Realistic parameters are attainable in spite of missing data. DOVE can be useful, even when many or most data are missing, for generalized least squares fitting to evaluate a self-consistent set of all parameters in an expression for predicting all missing data, and without changing the predicted data, to transform the set of parameters obtained in phase 1 so that each final parameter has a simple, pure, realistic, physical meaning. Since predicted data are expressed as a(i)x(j)+b(i)y(j)+...+c(i) with n product terms, phase 2 requires incorporation of n squared + n independent subsidiary conditions, of which 2n are arbitrary, i.e., merely fix zero reference points and scale unit sizes, but n squared - n are critical, i.e., must be relationships between particular parameters supported by other information. Both phases are illustrated by a two-mode application with 7 i, 10 j, hence 41 parameters, to fit the data plus the 6 subsidiary conditions. Valid parameters are obtained although 30 of the 70 possible data are missing.