Lattice Analysis: an Approach For Studying the Dual Containment Structures of Consumption Phenomena

Stephen Brownstein, Arizona State University
James Ward, Arizona State University
Peter Reingen, Arizona State University
Ajay Sirsi, York University
ABSTRACT - Consumer researchers have had a long fascination with the complex interrelations of the forces producing consumption behavior, but have struggled with a limited set of graph analytic tools for visualizing the interrelations of different types of phenomena (e.g., social relations, beliefs, consumption preferences). The purpose of this paper is to introduce lattice analysis as a method for revealing and visualizing the dual containment structures of unlike and complexly ordered phenomena.
[ to cite ]:
Stephen Brownstein, James Ward, Peter Reingen, and Ajay Sirsi (2001) ,"Lattice Analysis: an Approach For Studying the Dual Containment Structures of Consumption Phenomena", in NA - Advances in Consumer Research Volume 28, eds. Mary C. Gilly and Joan Meyers-Levy, Valdosta, GA : Association for Consumer Research, Pages: 391.

Advances in Consumer Research Volume 28, 2001     Page 391

LATTICE ANALYSIS: AN APPROACH FOR STUDYING THE DUAL CONTAINMENT STRUCTURES OF CONSUMPTION PHENOMENA

Stephen Brownstein, Arizona State University

James Ward, Arizona State University

Peter Reingen, Arizona State University

Ajay Sirsi, York University

ABSTRACT -

Consumer researchers have had a long fascination with the complex interrelations of the forces producing consumption behavior, but have struggled with a limited set of graph analytic tools for visualizing the interrelations of different types of phenomena (e.g., social relations, beliefs, consumption preferences). The purpose of this paper is to introduce lattice analysis as a method for revealing and visualizing the dual containment structures of unlike and complexly ordered phenomena.

Consider a set of individuals who are members of a group involved in a subcultural belief system that motivates them to consume (or avoid consuming) a set of products. At least three setsBthe sets of people, beliefs, and productsBinteract in creating behavior. For example, expertise in the belief system is likely to vary. Cultural participants who are more deeply embedded in the belief system are likely to behave differently and have different cultural roles than those less embedded. Furthermore, the belief system is likely to vary in its relevance to products. The intersection of beliefs and chains of beliefs with products is likely to influence their categorization, meaning, and consumption. Thus, the structures of people, beliefs, and products are embedded intricately in one another. Understanding how the orders of people, beliefs, and products relate to one another in a way that at once captures the intimate idiographic detail of single linkages between a particular person, belief, and/or product, and at the same time reveals the overall gestalt of linkages across sets seems crucial for a deeper understanding of consumption behavior.

In this paper we employ lattice analysis as a method for revealing and visualizing such linkages. Lattice analysis applies rigorously developed mathematical theorems to construct graphs that reveal the dual ordering of two-mode binary data. Dual mode binary data are repreented in a table where the rows and columns represent different phenomena (e.g., actors in the rows and beliefs in the column) rather than the same phenomena (e.g., actors by actors in social network analysis or beliefs by beliefs in cognitive network analysis). Lattices summarize complex dual orderings in a single easily grasped picture that is capable of revealing overall patterns in a data set that might otherwise not be discerned.

The ability of lattice analysis to reveal the dual ordering of different types of phenomena and the relevance of these dual orders for understanding consumer motivation is illustrated using data from a study of animal rights activists. Beginning with data on the participants’ food avoidances, their beliefs about these food avoidances, and their social relations we examine three types of lattices: participants-by-beliefs lattices, beliefs-by-foods avoidance lattices, and participants-by-cliques membership lattices.

These three types of lattices each summarized the complex relations between two different orders of phenomena into a single diagram that revealed interrelations that might have otherwise been difficult to discern. The lattice diagrams of beliefs by participants for honey and beef provided, at a single glance, pictures of the distribution of motivating beliefs across participants, their implicational structure, and the cognitive containment structure relating the individuals. These diagrams produced immediate insight into which beliefs were more structurally central in the subculture for motivating product avoidance, and which individuals were likely to supply the cognitive motives for avoidance to others through their deep embedding in the belief system. The participants-by-cliques lattice provided additional insight into how these expert participants bound together the many cliques within the group through their embeddedness in the social structure, and, thus, how they were in positions of both cognitive and social dominance. Finally, the food avoidances-by-beliefs lattices provided insight into the degree to which foods were central to or perhaps good exemplars of the belief system, prompting speculation about the role of ideologies in categorization processes.

The paper concludes by noting that lattice analysis may be productive of insight in any circumstance where the consumer researcher is interested in the patterning of the interrelations of two phenomena.

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