Scaling Methods: A Taxonomy

Scaling methods germinated in the pioneering work of Karl Pearson and Charles Spearman, who in the first decade of the 20th century developed methods to describe relationships between variables. Pearson created the correlation coefficient for metric data, while Spearman introduced the rank order correlation and an algorithm designed to document the existence of a general factor in intelligence research. Since then, these ideas have been extended to permit an (in theory) unlimited number of factors obtained from data ranging from crude categorical to refined metric and permitting the imposition of a variety of constraints on the variables. What all scaling methods have in common, however, is that they can be used to transform a set of observed variables to a smaller number of latent variables or factors (dimensions).

Scaling methods differ with respect to the type of input data for which they are most appropriate. Principal component analysis (PCA) and factor analysis (FA) make the assumption that the data are metrically scaled. If the data are ordered categories, such as Likert-type responses, categorical (or nonlinear) principal component analysis (CATPCA) is probably the best choice. Multiple correspondence analysis (MCA) is particularly suited for the analysis of unordered categorical (or nominal) data. For paired-comparison data, the proper choice would be multidimensional scaling. Rasch scaling or the unfolding model are proper choices when the response options are dichotomous (Yes/No) with an implicit item difficulty order, which usually means that they have a one-dimensional solution. The following documents the similarities and differences of the most popular scaling methods in the political and social sciences, namely, PCA, CATPCA, and MCA.

To demonstrate these methods, we chose seven variables on national pride from the U.S. portion of the International Social Survey Program (ISSP) 2003. To avoid a lengthy discussion on missing data, possible imputation techniques, and their impact on the solution, we use listwise deletion, which reduces the sample from 1,216 cases to 1,148 cases. The seven variables (identified with the abbreviations that will be used in subsequent figures) are as follows:

• A.
  I would rather be a citizen of [Country] than of any other country in the world.
• B.
  There are some things about [Country] today that make me feel ashamed of [Country].
• C.
  The world would be a better place if people from other countries were more like the [Country Nationality].
• D.
  Generally speaking, [Country] is a better country than most other countries.
• E.
  People should support their country even if the country is wrong.
• F.
  When my country does well in international sports, it makes me proud to be [Country Nationality].
• G.
  I am often less proud of [Country] than I would like to be.

Five response options ranging from agree strongly (1), to neither agree nor disagree (3), to disagree strongly (5) were made available for all items. Five of the seven variables have a positive formulation, such that agree strongly implies a favorable attitude toward the country. The remaining two items (2 and 7) have a negative formulation, requiring respondents to (strongly) disagree to express a favorable attitude.