# Methods For Analyzing Consumer Information Processing Models

##### Citation:

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James R. Bettman (1971) ,"Methods For Analyzing Consumer Information Processing Models", in SV - Proceedings of the Second Annual Conference of the Association for Consumer Research, eds. David M. Gardner, College Park, MD : Association for Consumer Research, Pages: 197-207.
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Several researchers have recently proposed information processing models of individual consumers' decision processes (Alexis et. al., 1968; Bettman, 1970; Haines, 1969; King, 1969; Russ, 1971). However, it has been difficult to interpret and analyze these models, since they have been presented as complex discrimination nets. It is readily apparent that the lack of attempts at internal analysis of the properties of these models stems from the almost complete lack of work on analysis techniques for information processing models.

Several types of analyses might be fruitful. First, information processing models of different individuals seem to be quite dissimilar and idiosyncratic. However, particular information processing models should serve as data points from which a general information processing model structure could be induced. Methods for comparing particular information processing models would be useful for this purpose.

Secondly, examining how complex process models can be collapsed into conditional simpler process models can yield insights into the dynamics of change in information processing models. Formal mathematical representations that allow for manipulation of the models are helpful here.

Third, by analyzing the fine grain details of structure in an information processing model, it may be possible to develop experimental situations to attempt to verify particular aspects of information processing models. To do this, measures of fine structures must be developed. Finally, parsimony in model building often requires testing simple models to see if they fit data. With complex information processing models, there are many possible corresponding simple models. To have a strong test of parsimony, it is desirable to have a 'rational' simple model; i.e., one that fits the data better than other simple models. Otherwise one can conclude, if a simple model fits poorly, that he just chose a bad simple model, rather than conclude that a more complex model is needed to describe the data.

This is a brief overview of some analyses of information processing models that would be useful. In previous work (Bettman, 1971), it has been shown how graph theory is useful in performing the second type of analysis outlined above, collapsing complex models into simpler models. The present study will consider further analytical tools based on graph theory that attack the other problems mentioned. The main thrust of the paper, however, deals with the first problem considered, comparing information processing models of different individuals. Accordingly, after presenting a brief review of the necessary graph theory concepts, a method for comparing information processing models will be developed. This method is then applied to artificial cases and to actual information processing models of consumer decisions. These results are interpreted. Finally, other graph theory applications are briefly considered, and the problems and prospects for this type of research are outlined.

GRAPH THEORY TERMINOLOGY

A graph consists of a set of nodes, or points, with arcs (lines) connecting pairs of nodes. In the graphs to be considered in the present study, the arcs have direction - that is, arcs are specifically directed from one node to another node. Consumer information processing models can be represented as graphs in the following manner. Each node represents a test of a particular condition (e.g., is price high?), and the arcs directed out of such a node depict the processing sequence taken, depending upon the outcome of the test. For example, in Figure 2, the first node in the model of raincoat purchasing for Subject C tests whether color of the coat is orange. If it is, an arc leads to rejection of the raincoat. Otherwise, the next node tests if the color is blue or peacock, the next node tests for brand, and so forth.

Several concepts from graph theory are useful in analyzing such information processing models. A path from some node i to some other node j is a sequence of arcs which lead from node i to node j, taking the direction of the arcs into account. In Figure 2 there is a path from node 2B to node 8B in Subject C's model, but no path from node 8B to node 7B, because the arc directions are not correct. If there is a path from node i to node j, node j is said to be reachable from node i. The distance between nodes i and j in a graph is the number of arcs in the shortest path joining nodes i and j. For Subject C of Figure 2, the distance between nodes 2B and 8B is 4.

Finally, the following matrices for any graph, based on the above concepts, will be necessary:

a) The n

^{th}reachability matrix R_{n}r

^{n}_{ij}= 1 if there is a path from node i to node j of length n or lessr

^{n}_{ij}= 0 otherwiseb) The reachability matrix R

r

_{ij}= 1 if there is a path from node i to node j regardless of lengthr

_{ij}= 0 otherwise.

The following result will also be needed:

Theorem: If y is the minimum value of n such that R

_{n}=R_{n+1}, then R_{y}= R (Harary et.al., 1965, p. 122).

AN INFORMATION PROCESSING MODEL SIMILARITY COEFFICIENT

Given the graph theoretic concepts outlined above, it is now possible to develop a method for comparing information processing models. The overall goal in developing such a tool is to allow a researcher to develop process-based typologies from models of several individuals. From such typologies, more general models might ensue. The rationale used in developing the method will now be Presented.

Following Haines (Haines, 1969), decision process models can be thought of as attitude structures. The essence of an attitude structure is the particular rules implied for processing information. Therefore, one should compare attitude structures in terms of the order in which information is processed and the interrelationships of various types of information as implied by the attitude structure. That is, if attitude structures can be represented as graphs, the order and sequence of particular nodes should be examined. Since the nodes in a decision net represent cues, two models are similar in the way they process information if corresponding nodes are processed in roughly the same sequence and have similar interrelations in the two models.

Thus, one way of defining similarity is by examining path and reachability structure. If for some given node i there is a path to node j of length n or less in one model, then if such a path also exists in the second model, this should add to a measure of similarity between the two graphs. Note that it is therefore necessary to label all of the nodes and retain these labels, since the identity of cues is important in making comparisons. Both models will not necessarily use the same sets of cues, so this must also be taken into account.

Suppose we have two graphs representing decision processes which we wish to compare, G_{1} and G_{2}. Let N_{1} and N_{2} be the sets of nodes for G_{1} and G_{2} respectively. Consider the binary variables, p^{n}_{ij1} and p^{n}_{ij2}, based on reachability structure, for the graphs G_{1} and G_{2} respectively:

p

^{n}_{ijk }= r^{n}_{ij}(G_{k}) if both i, j in N_{k}p

^{n}_{ijk }= 0 if i or j are not in N_{k}

for i,j = 1,2,...,t and k = 1,2. The total number of different cues used by both graphs is t. Thus, p^{n}_{ijk} just describes reachability for nodes in the same process, but is zero if node i or node j is not used in process k.

If Q_{1} is the value of X in the Theorem above for G_{1}, and l_{2} the value for G_{2}, define l = max (l_{1},l_{2}) Then a path structure similarity coefficient, S_{p}(G_{1},G_{2}), which we will use as a basis for comparing information processing models, is given by

This coefficient mirrors the following ideas as discussed above: if both graphs have a path from node i to node j of length n or less, this increases both the numerator and denominator, and hence similarity. If there is only a path in one graph, only the denominator increases. Also, nodes not used by both graphs can only increase the denominator, not the numerator, because of the way p^{n}_{ijk} is defined. Thus, the greater the set of cues used by both of the two decision processes, the greater similarity can be. Finally, note that if a node i is in N_{k}, p^{n}_{iik} for all n.

This coefficient is certainly somewhat arbitrary. Many other possible definitions could be proposed. However, this alternative does deal with path structure and in that sense has a firm underlying rationale. A somewhat similar measure was developed independently in numerical taxonomy by Jackson (Jackson, 1969). Efficient methods for computing the coefficient using the distances between nodes can be developed.

APPLICATION OF THE SIMILARITY COEFFICIENT

Artificial Cases

Now the method will be applied to a series of examples. First a small set of artificial cases is examined to gain some initial insights into the behavior of the coefficient. The artificial cases to be considered are shown in Figure l. Applying the coefficient to selected pairs of these graphs yields the following results:

S

_{p}(A,B) = .453 S_{p}(A,C) = .149 S_{p}(A,D) = .635

Note that these graphs in Figure 1 all represent conjunctive satisficing processes. An accept decision is made only if all cues are satisfactory. Also, given acceptable levels for each cue, all conjunctive processes having the same set of cues have the same output, regardless of cue order. However, the basic idea underlying information processing models is an interest in process structure as well as output. Thus, the coefficients comparing the above model pairs should differ based on the order of cues for each graph, even though the outputs are the same. That is in fact what happens. Also, it can be seen that the coefficient varies directly with the similarity of the cue orderings for these simple cases. Of course, for more complex process graphs the results would be less obvious.

The Alexis, Haines, and Simon Models

Alexis, Haines, and Simon have developed models of two consumers' decision processes for raincoats (Haines, 1969) and of two consumers' decision processes for women's clothing (Alexis et. al., 1968). The graphs depicting these models are shown in Figures 2 and 3 respectively. Two analyses were run for each set of data. First, the similarity coefficient was applied to the entire processes, with all nodes included. Second, an analysis was performed where the similarity coefficient was computed using only those cues used by both subjects modeled. Cues idiosyncratic to each individual were ignored. For example, for the raincoat decision both subjects used cues 2B, 3, 4, 5, 8B, 8D, 9A, and 9B, and the analysis was carried out with respect to these cues. The results of the analyses were:

Raincoats Models Women's Clothing Models

Entire Process .150 .060

Common Nodes Analysis .554 .537

RAINCOAT SHOPPING DECISION MODELS: ALEXIS, HAINES, AND SIMON

DRESS SHOPPING DECISION MODELS: ALEXIS, HAINES, AND SIMON

Note that the entire process similarities are quite low, but that for the commonly used cues the similarities are fairly high. This suggests that the common cues used by both processes have similar information processing interrelations within the context of the larger decision processes including the idiosyncratic cues. It is the idiosyncratic cues which detract from overall process similarity rather than different use of the same cues. This suggests that general models may be possible where the emphasis is on the interrelations and processing rules for a set of generally used cues. Finally, note that the raincoat models are more similar overall than the women's clothing models. However, the more complex women's clothing models still have a fairly high coefficient for the common cues, so complexity per se may not detract from the goal of building general models. The above kind of micro analysis of information processing structure is made possible by the similarity coefficient developed. One point of the present study is that this kind of analysis must be done to fully understand the implications of decision process models. The real value is in setting up a formal analysis approach rather than using casual inspection.

Process-Oriented Typologies

The path similarity coefficient can be used to develop process-oriented typologies. A matrix of interindividual path similarity coefficients could be developed if one had models of several individuals. This matrix could be used as a basis for cluster analysis to form groups. One problem with this type of approach is that obtaining large data sets of models is very time consuming, although work is being done on formal analysis of protocols (Newell, 1966).

Other methods for defining typologies might be possible. One could try to define content and structure measures for the graphs representing the processes (the specific nodes used and the structure of the graph) and develop a content vs. structure cross-classification scheme. Finally, other types of similarity coefficients could be defined. The one in this study defines similarity in terms of path structure. Other possible bases for similarity are isomorphisms or pure structural measures; distances between nodes; and clusterings of nodes. (For development of these notions, see (Bettman, 1969, pp. 169-223).)

FURTHER ANALYTICAL TOOLS

As discussed in the introduction, other types of analyses might be fruitful for information processing models. Analyzing fine grain structure can be approached by measuring properties of the decision process graphs and using these measures to suggest corroborating experiments. For example, using the graph theory notion of gradability (Harary et.al., 1965, pp. 265-280), which formalizes the notion of the depth of a node in a graph, one can design an experiment to test the preferred order of cue reception in a decision making task. The results of the experiment can then be compared with the gradability measures as one means of verifying model microstructure.

The development of 'rational' simple models for a given set of data, as briefly outlined in the introduction, can also be approached from the graph theory point of view. The problem can eventually be formulated as a complex integer programming problem. The computational problems here have not been solved, however.

PROBLEMS AND PROSPECTS

There are definite problems with attempting to develop analytical tools for information processing models. The tools proposed here share several problems. Path coefficients computed for graphs with differing numbers of nodes are not strictly comparable. Some form of adjustment needs to be investigated. The methods proposed are all reasonably arbitrary, of necessity. Many other measures could be defined. Examination of alternatives must be undertaken. Finally, for large and complex models, the computations become burdensome.

However, even with all these problems and potential pitfalls, the contention of this study is that it is essential to analyze information processing models to advance the state of the art for these models. This study has attempted to outline some of the possibilities and discuss one particular method. The results show that the prospects are good for developing a solid analytical framework.

REFERENCES

Alexis, M., Haines, G., and L. Simon, "Consumer Information Processing: The Case of Women's Clothing," American Marketing Association Proceedings, Marketing and the New Science of Planning, Series 28. 1968. 197-205

Bettman, J., "Behavioral Simulation Models in Marketing Systems," Unpublished doctoral dissertation, Yale University, 1969.

Bettman, J., "Information Processing Models of Consumer Behavior," Journal of Marketing Research, August 1970, 370-376.

Bettman, J., "The Structure of Consumer Choice Processes," Journal of Marketing Research, November 1971, forthcoming.

Haines, G., "Information and Consumer Behavior," Working Paper, University of Rochester, College of Business Administration, July 1969.

Harary, F., Norman, R., and D. Cartwright, Structural Models: An Introduction to the Theory of Directed Graphs, New York, Wiley, 1965.

Jackson, D., "Comparison of Classifications," in Cole, A., ed., Numerical Taxonomy, New York: Academic Press, 1969, 91-113.

King, R., "A Study of the Problem of Building a Model to Simulate the Cognitive Processes of a Shopper in a Supermarket," in Haines, G., Consumer Behavior: Learning Models of Purchasing, New York: Free Press, 1969, 22-67.

Newell, A., "On the Analysis of Human Problem Solving Protocols," Working Paper, Carnegie-Mellon University, 1966.

Russ, F., "Consumer Evaluation of Alternative Product Models," Unpublished doctoral dissertation, Carnegie-Mellon University, 1971.

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##### Authors

James R. Bettman, University of California, Los Angeles

##### Volume

SV - Proceedings of the Second Annual Conference of the Association for Consumer Research | 1971

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