Multivariate Approaches and Variables
What we did in Part III (Relationships between Two Variables) is often labeled bivariate analysis. The chapters that form this last part of the book extend the investigation of relationships between two variables into the multivariate arena. There are many different approaches to multivariate analysis. Those discussed here represent only a very small selection, one that emphasizes techniques particularly suitable for exploration that seeks patterns in multivariate datasets (as contrasted to evaluating the strength and significance of particular patterns that are hypothesized in advance). The perspective of this final section of the book, then, strongly recalls the exploration of batches in Part I. The exploration here, though, is not of single batches of numbers, or variables. It goes on beyond relationships between two variables to approach directly the more complicated situation in which we have a larger number of variables for each case. We could, of course, approach a large number of variables piecemeal by looking at their relationships by pairs, taking them two at a time, and evaluating the strength and significance of the relationships between them with the tools discussed in Part III. This would soon get out of hand without some way to truly combine the results of all those pairwise evaluations of relationships. In Chapter 15 we actually discussed one way to accomplish just this, using the residuals from one regression analysis as the dependent variable in another regression analysis. This is, in fact, the avenue toward one form of multivariate analysis. Multiple regression does just this in an integrated way as a single analysis, and most statpacks will perform multiple regression. Since its basic principles are precisely those described in Chapter 15 for integrating several bivariate regression analyses into a single set of results, multiple regression will not be further discussed here. Multiple regression has, however, been used in archaeology, especially in situations where the aim is to use a number of variables together to predict the value of a single important dependent variable. Models for predicting site locations, for example, have often made heavy use of multiple regression. Multiple regression differs from the multivariate techniques we will discuss in another way as well. Like bivariate regression, multiple regression evaluates the strength and significance of a particular kind of relationship between variables – a relationship expressed in an equation for predicting the value of a dependent variable, based on the values of a series of independent variables. It is thus less an exploration for patterning than an evaluation of how well a particular hypothetical way of expressing relationships works on a given dataset.