Editor’s note: Betsy Charles is an account manager and senior research analyst at The Dieringer Research Group, Inc., Milwaukee, Wis.

Modeling buying behavior by measuring customer satisfaction brings to mind the story about the blind men describing an elephant. Each one made an accurate assumption based on limited knowledge but drew the wrong conclusion.

Based upon limited knowledge, marketing researchers blindly assume that customer satisfaction is necessary for loyalty and that loyalty is necessary for repeat purchase. This hierarchical assumption is inaccurate because factors may directly influence repeat purchase without funneling from customer satisfaction through loyalty to repeat purchase. In fact, repeat purchase is not necessarily contingent upon customer satisfaction and loyalty. For example, do you repeatedly buy lunch at a nearby deli even though you are so dissatisfied with the deli that you refer your colleagues to other restaurants? In this example, convenience directly influences repeat purchase, rather than directly funneling through customer satisfaction and loyalty. Thus the hierarchical assumption can bias results because it ignores direct influences on buyer behavior.

The bias inherent in assumptions is avoided by using unconstrained models — algorithms that make no assumptions and have no requirements about causality. In contrast to unconstrained models, constrained models either assume causality or confirm causality only if the requirements of concomitant variation, a time lag, and the logical elimination of all other possible causal factors are met.

Unconstrained models

Unconstrained models include causal modeling, path analysis, latent structure analysis, structural equation modeling, LISREL, and AMOS. Unconstrained models assume that all factors could be influenced by other factors and thus are endogenous. As a heuristic device, unconstrained models hypothesize nonrecursive (or reciprocal) linkages between all possible factors that could impact the outcome. Figure 1 shows how unconstrained models represent both directions of causality using arrows and feedback loops.

All possible relationships

The arrows in Figure 1 convert to a system of equations in which each factor (Xi) is measurable, each weight (Pij) is the unknown path coefficient of a factor, and each error term (Ri) is the residual for the equation. Each equation in the system is similar to a regression equation, but without the intercept.
Xi = Pij Xi + Pij Xi + . . Ri

Confirmed relationships

The system of equations is solved through an iterative process using multiple regression until a stable solution is obtained. When the number of equations is greater than the number of unknowns, divergent solutions may occur. If this occurs, substituting extra equations into the initial system of equations identifies the best solution. Solving for path coefficients derives the direction of each factor’s impact on the endogenous variable. After standardizing the regression coefficient (beta weight), each factor’s impact can be compared relative to the impact of other factors. If the impact of a factor is zero or negligible, the relevant arrow is deleted from the model to reduce the number of unknowns as shown in Figure 2.

Interpretation

Unconstrained models measure the relative contribution of each factor to desired outcomes such as customer satisfaction, loyalty, and/or purchase. The impact of factors is decomposed into direct and indirect paths. The relative contribution of a factor is calculated by multiplying the beta weights of the indirect paths and aggregating the result with the beta weights of the direct paths as shown in Table 1. In this example, the contribution of Price to purchasing is three times cleanliness, two times convenience, and half again service.

Table 1

Convenience ~.15 = (.40 * .60 * .20) + .10

Cleanliness ~.10 = (.80 * .60 * .20)

Service = .20 = (.50 * .60 * .20) + (.70 * .20)

Price = .30

Process

The process is similar for all types of unconstrained modeling:

  • measure a battery of factors that may impact desired outcomes;
  • hypothesize all possible causal relationships and diagram them;
  • convert the diagram into a system of equations;
  • solve the equations for the impact of each factor on one another;
  • standardize and test the stability of the solution;
  • reject hypothesized relationships with a negligible impact;
  • confirm the direction and impact of remaining relationships with a diagram;
  • calculate the relative impact of each factor on desired outcomes.

Summary

Unconstrained modeling has become a popular technique because it confirms causal relationships without unrealistic assumptions and requirements. Rather than assuming that customer satisfaction funnels through loyalty and repeat purchase, unconstrained modeling allows the data to speak for itself.