An Ipsative Clustering Model for Analyzing Attitudinal Data

Abstract

Patterns of behavior depend in part on patterns of attitudes and beliefs (Burt, 1937; Fishbein & Ajzen, 1975). Individuals in a given social aggregate are expected to report consistent patterns of behavior and attitudes, while the response sets for people in different social aggregates may vary substantially (Ditton, Goodale, & Johnsen, 1975; Driver & Knopf, 1977; Jackson, 1989). When inhomogeneous populations are not recognized and accounted for, the use of certain analysis techniques (e.g., factor analysis) is questionable, can render research conclusions invalid, and can lead to erroneous management actions (Beaman, 1975; Beaman & Lindsay, 1975; Cunningham, Cunningham, & Green, 1977; Guilford, 1952; Greenleaf, 1992; Bucklin & Gupta, 1992). If the appropriate model of reality identifies different social aggregates with different wants and needs, an analysis strategy is needed to correctly identify members of the groups and their associated attributes. Only when such groups are validly recognized and analyzed properly can management policies correctly address the demands of competing groups.This paper is concerned with finding aggregates of people who have similar attitude profiles, and are thus postulated to display similar behaviors. We define a model for the structure of attitude data for people who are in different groups or clusters which allows for (1) individual, ipsative effects (a respondent having a personal average or modal score across a number of variables), and for (2) ipsative amplitude effects of narrow to wide response patterns (standard deviation around a mean or modal deviation). Based on the model, it is argued that the Pearson Correlation (r sub p ) between objects (e.g., people) provides the foundation for a valid measure of resemblance between individuals based on their attributes. Three transformations of r sub p are examined as distance measures for cluster analysis to derive groups of similar people. Of the three, the arccos (r sub p ) or arccos (r sub p ) sup 2 is recommended.An Overview of Cluster AnalysisCluster analysis is a general set of methodological tools for estimating groups of similar objects. Similarity is usually based on resemblance coefficients derived from an object's attributes (Romesburg, 1979, 1990). Applications of cluster analysis to recreation have evaluated people (objects) on attributes such as participation rates (Romsa, 1973; Ditton et al., 1975), or motivations for engaging in an activity (Hautaloma & Brown, 1978; Manfredo & Larson, 1993). In other recreation studies (Dawson, Hinz, & Gordon, 1974; Romesburg, 1979), the objects were elements of the physical environment (e.g., sites along a hiking trail or river), while the attributes were characteristics of these physical objects (e.g., the presence or absence of different plant species, the extent of human impact).Regardless of the choice of object and attributes, cluster analysis typically includes five steps (Romesburg, 1990). Step 1 involves constructing a data matrix. In common computer programs (e.g., SAS, SPSS), the rows in the matrix represent objects (e.g., individuals), while the columns are attributes (e.g., participation rates or responses on attitude variables). By convention, cluster analyses exploring resemblance among objects are called Q-techniques; procedures examining relationships among attributes are called R-techniques (Aldenderfer & Blashfield, 1984; Sneath & Sokal, 1973). This paper focuses on techniques. Step 2 involves transforming the data (e.g., by receding the attributes' units of measurement into dimensionless units). Although this step is optional, different standardization procedures can have dramatic consequences. In step 3, a coefficient measuring the resemblance as a similarity, or dissimilarity, distance between each pair of objects is calculated, resulting in a resemblance matrix. A variety of resemblance coefficients are available; for example, Euclidean distance or the Pearson product moment correlation, r sub p , (Romesburg, 1990, Chapters 8 and 10). …