검사가중치 방법에 대한 제고찰

다국어 초록 (Multilingual Abstract)

When measures are to be combined to form a composite score or to predict a criterion, the question of weighting of the measures arises. We commonly seek a weighted linear combination of the measures, choosing weights that are best weights. The literature on the weighting problem suggests many procedures: multiple regression analysis, canonical correlation analysis, principal component analysis, maximum reliability, equal contribution, and some other procedures.
Given n-1 independent variables and a single dependent variable, we choose weights to maximize the squares of the correlation between the linear combination of n-1 variables and the dependent variable. Also, with two subsets of variables, a weighted linear combination of each subset such that these two combinations have maximum correlation is chosen. Another solution, namely, minimizing intra-individual differences and maximizing inter-individual differences is chosen to find the weights. The weights are chosen so as to maximize the reliability of the composite measure. When external criterion is not available, weights may be derived by the method of least squares to equalize the correlation of each variable with the resulting composite score. To ensure equal effective weights, the variables in a composite have equal contributions to total variance. A linear function of the variables is sought such that the generalized variance of individuals having that value is minimized. However, since each of these methods is not perfect, it is not easy to choose the best weight in some sense.
This paper outlines different types of weights and methods of deriving weights and discusses their merits and demerits. But, when these methods are applied to actual data, supplementary research about choosing best weights should be followed.