Modeling Customer Survey Data

Abstract

In customer value analysis (CVA), a company conducts sample surveys of its customers and of its competitors' customers to determine the relative performance of the company onmany attributes ranging from product quality and technology to pricing and sales support. The data discussed in this paper are from a quarterly survey run at Lucent Technologies. We have built a Bayesian model for the data that is partly hierarchical and has a time series component. By "model" we mean the full specication of information that allows the computation of posterior distributions of the data - sharp specications such as independent errors with normal distributions and diffuse specifications such as probability distributions on parameters arising from sharp specifications. The model includes the following: (1) survey respondent effects are modeled by random location and scale effects, a t-distribution for the location and a Weibull distribution for the scale; (2) company effects for each attribute through time are modeled by integrated sum-difference processes; (3) error effects are modeled by a normal distribution whose variance depends on the attribute; in the model, the errors are multiplied by the respondent scale effects. The model is the first full description of CVA data; it provides both a characterization of the performance of the specic companies in the survey as well as a mechanism for studying some of the basic notions of CVA theory. Building the model and using it to form conclusions about CVA, stimulated work on statistical theory, models, and methods: (1) a Bayesian theory of data exploration that provides an overall guide for methods used to explore data for the purpose of making decisions about model specifications; (2) an approach to modeling random location and scale effects in the presence of explanatory variables; (3) a reformulation of integrated moving-average processes into integrated sum-difference models, which enhances interpretation, model building, and computation of posterior distributions; (4) post-posterior modeling to combine certain specic exogenous information - information from sources outside of the data - with the information in a posterior distribution that does not incorporate the exogenous information; (5) trellis display, a framework for the display of multivariable data.