AN OVERVIEW OF MULTIVARIATE METHODS

Multivariate methods can be classified along different features:

• Confirmatory vs. exploratory. This feature refers to the general aim of a method, as some are aimed at confirming a theory or a hypothesis, and others are aimed at analyzing data and discovering hidden patterns.
• Metric vs. nonmetric. This feature refers to the kind of variables that the method is able to deal with, i.e., quantitative or qualitative. We recall that sometimes numerical codes are associated with qualitative variables, which have no real content. In such a case, we speak of nominal scales.⁴ When variables are quantitative, we distinguish the following types of scale:
  • Ordinal scales, where variables have numerical values that can sensibly ordered, but their differences have no meaning. As an example, imagine a set of customers ranking different brands by assigning a numerical evaluation.
  • Interval scales, where differences between numerical values have a meaning, but there is no “natural” origin of the scale. For instance, consider temperatures, which can be measured with different scales.
  • Ratio scales, where there is an objective reference point acting as the origin of the scale.
• Interdependence vs. dependence. When we are focusing on dependence, there is a clear separation between the set of independent variables (e.g., factors) and the set of dependent variables (e.g., effects). One such case is simple linear regression. In interdependence analysis there is no such clear-cut distinction.

In the following sections we outline some multivariate methods, suggesting a classification along the above dimensions. We do not aim at being comprehensive; the idea is getting to appreciate the richness of this field of statistics, as well as the classification above in concrete terms.