Categorical Constraints Guided Imputation For Nonresponse In Surveys

Abstract

For studying quadratic response surfaces, a prevailing strategy in the literature is the response surface methodology, proposed by Box and Wilson (1951). In their seminal paper, it was shown that the designs are inappropriate for studying quadratic response surface because of their uneconomical run size. We take a different approach and propose, for the designs, a two-stage data analysis strategy, i.e., first screening and then fitting quadratic response surfaces on the projected design of the factors identified as important in screening. Under the strategy, the run size of the designs can be utilized efficiently for two objectives, factor screening and surface fitting, without adding more runs. Based on this analysis strategy, we study projection properties of the designs. The projected designs are classified into different types in terms of combinatorial isomorphism (traditional) and model isomorphism (new). The latter is based on the coding under the linear-quadratic system while the former is based on the orthogonal component system. It is shown by examples that model isomorphism can characterize the geometric structure of designs better than combinatorial isomorphism. The performance of these projected designs is then compared with that of some second-order designs, such as the central composite designs, in terms of D-, G- and efficiencies. In addition to the designs, we also study the projection properties of some nonregular three-level designs, such as the OA (18, ) and the OA (36, ). These three-level designs are evaluated according to an eligible projection criterion, which is based on the total of projected designs that can be used to fit quadratic response surfaces. A new method to construct designs that can significantly improve the eligible projection property of the designs is also presented.