It has been found that there are some relationships between the projection matrix of unbalanced model and that of corresponding balanced model(Sunwoo, 1990). The corresponding balanced model is defined to be the model containing exactly one observation in each cell whether some cells are empty or not. By this method much of the computational storage can be reduced because these results can be accomplished by handling matrices having small order.
Unfortunately the results of the balanced model cannot be used directly if there are some missing cells. For this reason the projection matrix of the balanced model must be computed by another method. By some procedure we can obtain the projection matrix of the unbalanced model having missing cells and find in the case of connected model it is much easier to compute the projection matrix.
선형모형의 분석에서 사영행렬은 매우 중요한 역할을 한다.
결측치를 갖는 불균형 모형의 사영행렬은 대응되는 균형모형과 그것의 Moore-Penrose 역행렬에 관계된다.
그러나 Moore-Penrose 역행렬은, 유일하게 그리고 항상 존재하지만, 계산은 매우 어렵고 복잡하다.
본 논문에서는 Model 이 connected일 경우 Moore-Penrose 역행렬이 역행렬로 대치될 수 있다는 것을 보였다.