When applied to contingency tables, dual scaling and correspondence are mathematically equivalent methods. For the analysis of rating data, however, the methods differ. To a large extent this is due to differences in preprocessing of the data. In particular, in dual scaling, ratings are either transformed to rank order, or to successive category data before applying a customised dual scaling approach. In correspondence analysis, on the other hand, a so-called doubling of the original ratings is applied before applying the usual correspondence analysis formulas. In this paper, we consider these differences in detail. We propose a dual scaling variant that can be applied directly to the ratings and we compare theoretical as well as practical properties of the different approaches.

翻译：当应用于列联表时，双尺度分析与对应分析在数学上是等价的方法。然而，在分析评价数据时，这两种方法有所不同。这很大程度上源于数据预处理阶段的差异。具体而言，在双尺度分析中，评价数据要么被转换为等级顺序，要么被转换为连续类别数据，随后再应用定制化的双尺度分析方法。相比之下，对应分析则是在应用常规对应分析公式之前，对原始评价数据进行所谓的"加倍"处理。本文详细考察了这些差异。我们提出了一种可直接应用于评价数据的双尺度分析变体，并从理论与实际应用层面比较了不同方法的特点。