Donald G. Morrison

Do We Really Need Multiple-Item Measures in Service Research?

Increasingly, marketing academics advocate the use of multiple-item measures. However, use of multiple-item measures is costly, especially for service researchers. This article investigates the incremental information of each additional item in a multiple-item scale. By applying a framework derived from the forecasting literature on correlated experts, the authors show that, even with very modest error term correlations between items, the incremental information from each additional item is extremely small. This study’s “information” (as opposed to “reliability”) approach indicates that even the second or third item contributes little to the information obtained from the first item. Furthermore, the authors present evidence that added items actually aggravate respondent behavior, inflating across-item error term correlation and undermining respondent reliability. Researchers may want to consider the issue of item information in addition to reliability. This article discusses ways in which researchers can construct scales that maximize the amount of information scale items offer without compromising measurement reliability.

Generalizing the NBD Model for Customer Purchases: What Are the Implications and Is It Worth the Effort?

An often-used scenario in marketing is that of individuals purchasing in a Poisson manner with their purchasing rates distributed gamma across the population of customers. Ehrenberg (1959) introduced the marketing community to this story and the resulting negative binomial distribution (NBD), and during the past 30 years the NBD model has been shown to work quite well. But the basic gamma/Poisson assumptions lack some face validity. In many product categories, customers purchase more regularly than the exponential. There are some individuals who will never purchase. The purpose of this article is to review briefly the literature that addresses these and other issues. The tractable results presented arise when the basic gamma/Poisson assumptions are relaxed one issue at a time. Some conjectures will be made about the robustness of the NBD when multiple deviations occur together. The NBD may work, but there are still opportunities for working on variations of the NBD theme.

A Parsimonious Description of the Hendry System

In this paper we will present some basic concepts of the Hendry System and derive the results claimed in the HendroDynamics Chapters [HendroDynamics: Fundamental Laws of Consumer Dynamics, Hendry Corporation, Chapter 1 (1970) and Chapter 2 (1971).] from two simple probabilistic assumptions; namely, zero order consumers and switching proportional to market share. We will develop the notion of partitioning which constitutes a major component of the Hendry System by briefly describing the procedure for identifying the partitioning structure in a given market. With this illustration we will point out various implications which can be drawn from a correctly identified market structure. All of our results are obtained without resorting to the entropy concept that has caused so much confusion in recent debates over the validity or usefulness of the Hendry Model.

Upper Bounds for Correlations Between Binary Outcomes and Probabilistic Predictions

Abstract There are many types of diverse models that yield probabilistic predictions for outcomes that are binary. We show that a correlation between the 0, 1 binary outcomes and the prediction probabilities can yield meaningful results. The upper bound for the resulting R2 turns out to be a surprisingly simple expression for a class of situations which contain a quite general assumption on the distribution of the prediction probabilities. Some implications for subjective probability estimates are also given.

Jobs, strikes, and wars: Probability models for duration☆

Abstract A class of stochastic models with behaviorally meaningful parameters and manpower planning implications is presented. These models are used to reanalyze some previously published data on the durations of wars, strikes, and jobs. Job durations are found to be qualitatively different from strike durations. The concepts developed in this paper also allow researchers to “eyeball” and plot their data better even if a formal statistical analysis is not performed.

The Median Residual Lifetime: A Characterization Theorem and an Application

The concept of the median residual lifetime for a probability distribution is outlined and shown to have several advantages over its more common counterpart, the mean residual lifetime. A characterization theorem shows that a Pareto distribution of the second kind or equivalently, a gamma mixture of exponentials is the unique distribution with a linearly increasing median residual lifetime. An empirical example from the literature on strike durations is presented.

Prediction of Future Random Events with the Condensed Negative Binomial Distribution

Abstract The condensed negative binomial distribution (CNBD) has been proposed as a stochastic model that is more appropriate for consumer purchasing behavior than is the common negative binomial distribution. Since this model was motivated previously and shown to fit single-period purchasing data, the focus here turns to the dynamics of the process, as reflected in the aggregate characteristics of interpurchase times and period-to-period predictions. The theoretical results are useful for comparing the predictive effectiveness of the CNBD with the commonly used negative binomial distribution.

A Modified Beta Binomial Model with Applications to Multiple Choice and Taste Tests.

A modified beta binomial model is presented for use in analyzing ramdom guessing multiple choice tests and certain forms of taste tests. Detection probabilities for each item are distributed beta across the population subjects. Properties for the observable distribution of correct responses are derived. Two concepts of true score estimates are presented. One, analogous to Duncans empirical Bayes posterior mean score, is appropriate for assessing the subjects performance on that particular test. The second is more suitable for predicting outcomes on similar tests.

A Probability Model for Forced Binary Choices

Abstract In this article a natural extension of the beta-binomial distribution is developed. Forced binary choice situations are modeled such that each individual has a probability p of knowing the correct answer. (This probability is distributed f(p) across the population.) Hence each individual will guess at the correct answer with probability 1 – p. The observable random variable R, the total number of correct answers (both by knowing and guessing) out of k trials has a rather complicated distribution. However, when f(p) is distributed beta with parameters m and n, the distribution P(r; k, m, n) can be expressed in terms of the well-known Gaussian hypergeometric function. This distribution has implications for true-false tests, taste tests, and virtually every other forced binary choice situation.

The Effect of Nonhomogeneous Populations on Markov Steady-State Probabilities

Abstract An important aspect of many Markovian analyses is the steady-state solution. This can give insight into the dynamics or momentum existing in a system. However, when we obtain Markov transition matrices by aggregating across non-homogeneous (with respect to transition probabilities) individuals, this matrix may not bear any resemblance to the transition matrices possessed by the individuals. This article investigates the effect of this heterogeneity on the calculated steady-state solution obtained from the aggregate transition matrix. We find that under various conditions this calculated steady-state solution is quite close to the true steady-state solution. These results have important implications for Markovian forecasting methods.