bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Bayesian Cross-Validated Likelihood Method for Comparing Alternative Specifications of Quantitative Models
Authors: Rust Roland T. , Schmittlein David C. 
Published: October 2008

There are many situations in marketing in which several alternative quantitative models may be built to model a particular marketing phenomenon or system. Few methods exist for comparing the fit of such models if the models are not nested, especially if their performance on each of several criteria is important. This paper proposes a Bayesian cross-validated likelihood (BCVL) method for comparing quantitative models. It can be used when the models are either nested or nonnested, and is especially useful for nonnested models. A simulation based upon a typical marketing modeling situation shows the incremental benefit of using the BCVL method rather than existing techniques, and explores the circumstances under which BCVL works best. The applicability of the BCVL method is demonstrated using several typical marketing modeling situations.
The Impact of Competitive Entry in a Developing Market Upon Dynamic Pricing Strategies
Authors: Eliashberg Jehoshua , Jeuland Abel P. 
Published: October 2008

This paper analyzes dynamic pricing strategies for new durable goods in a two-period context. The first period is characterized as a monopoly market structure for a new product having dynamic demand. The second period begins when a new firm enters the market, and thereby changes the market structure to a duopolistic one. We begin by analyzing the pricing strategies of three types of monopolists: nonmyopic, myopic and “surprised.” A nonmyopic monopolist is a first entrant who perfectly predicts the competitive entry. A myopic monopolist totally discounts the duopolistic period, and a “surprised” monopolist is a first entrant who has the longer time horizon of the nonmyopic monopolist, but who does not foresee the competitive entry. Our results indicate that the nature of these pricing strategies may be quite different. It is optimal for the nonmyopic firm to price its product at a higher level than the myopic monopolist. Additional results indicate under what circumstances the “surprised” monopolist will price too high during the monopoly period. The intuition behind these results is the fact that the myopic monopolist overestimates competition while the surprised monopolist underestimates it. We also characterize the nature of the dynamic equilibrium prices that will prevail during the competitive period. For example, we show that products having higher prices (because of cost differences) will exhibit a more rapid rate of price decline. Moreover, a discontinuity in the first entrant's pricing strategy, as a response to a second entry—which is often observed in the market place—is also captured by our model. Because these analyses are limited to situations where the time of second entry is predictable, a scenario that fits our model better would be the health-care equipment industry where a specified period of government observation and/or testing is required. Immediate extensions of our model should include a discount factor and learning effects on both costs and demand.
The Channel Design Decision: A Model and an Application
Authors: Rangan V. Kasturi 
Published: October 2008

This paper proposes a channel design model based on the notion that distribution functions are the basic determinants of channel structure. The purpose of the model is to assist manufacturers in making effective channel decisions. The model evaluates what distribution structure the firm should adopt, how many intermediaries it should use, and what levels of service it should offer its customers. The proposed model-based decision approach is illustrated with an industrial marketing application. First, parameters were established for the model, using a combination of field data and managerial judgment. Next, the model was used to optimize profits over several channel alternatives. The profit-maximizing alternative determined the optimal channel structure, distribution intensity, and channel service. The implications of the model results for the manufacturer are discussed.
Modeling Competitive Marketing Strategies: The Impact of Marketing-Mix Relationships and Industry Structure
Authors: Carpenter Gregory S. 
Published: October 2008

This paper empirically analyzes the formulation of competitive marketing strategies consisting of product quality levels, promotional expenditures and prices. Using a simultaneous-equation model, we examine the use of prices and promotional spending as signals or indications of product quality, the impact of promotional spending on prices, and the impact of industry structure on the formulation of the complete marketing mix. The structural equations are developed using a theoretical model of optimal competitive marketing mix, and are estimated using business-level PIMS data, which consists largely of industrial, durable goods producers. For a cross-section of 1,100 of these businesses, three results of the estimation are especially interesting: • Price-cost margins are high for high quality products, suggesting that high prices indicate or signal high quality. • Promotional intensity is unrelated to product quality, suggesting that promotional effort provides no reliable signals of quality. Intensely promoted products earn low price-cost margins, however, indicating that promotional spending is associated with high price sensitivity. • Quality levels, promotional intensity, and price-cost margins vary significantly with competitive and market conditions such as the concentration of competitors and the stability of market shares, although these relationships are generally weaker than relationships between quality, promotion, and price-cost margins. Quality levels are high and margins low in markets with unstable shares or unconcentrated competitors.
Note—Competitive Price and Positioning Strategies
Authors: Hauser John R. 
Published: October 2008

Brand positioning and brand pricing are important strategic decisions for marketing managers. Such decisions are interrelated and depend upon competitive brand positions and prices. However, any unilateral decisions may encourage repositioning and price adjustment by competitors thus leading to either new market equilibria or a price/positioning “war.” This paper examines such price and positioning decisions in a competitive environment by extending the ‘Defender’ consumer model to more complex equilibria. We assume that the brands are already in the market and that positions are “sticky” in the sense that brands cannot leapfrog one another. Among the insights for such incumbent brands are: • if prices are symmetric and held constant, firms seek to reposition toward the center of the market, • but price advantages by central firms can mediate that central tendency such that an equilibrium exists with positive profits; • if brand positions are held constant, the Nash equilibria for prices exist and are unique, and • category profits, the sum of brand profits, are maximized for maximum brand differentiation; • for two and three brand markets the (subgame perfect Nash) equilibrium, where positioning decisions are made with foresight on the price equilibria, causes firms to unilaterally seek maximum brand differentiation; but • for four or more brands greater foresight and/or cooperation appears necessary to reach the point of maximum brand differentiation. These results apply where the Defender consumer model is an exact description of consumer response and where the competitive reaction assumptions hold. In any empirical situation such forces might be softened resulting in differentiated, but not maximally differentiated, brands.
Invariant Estimators for Market Share Systems and their Finite Sample Behavior
Authors: Gaver Kenneth M. , Horsky Dan , Narasimhan Chakravarthi 
Published: October 2008

The sales-marketing mix relationships for brands of a product class are often modelled as a multiple equation system. Whenever sales are expressed as shares, such systems are sum-constrained and therefore singular. Singular systems can be calibrated by deleting one equation from the model and estimating the remaining equations using the seemingly unrelated regressions (SUR) technique. A two-step procedure is typically adopted whenever the disturbance covariance structure is unknown. This study highlights an issue often overlooked by marketing researchers. Traditional two-step estimators that delete one equation at the initial step usually lack invariance to the equation deleted. Invariant estimates are available using maximum likelihood estimation (MLE) or iterated least squares. However, relative to simple, two-step procedures, these approaches require more computation and are often less accurate in small samples. We describe several ways to obtain invariant, two-step estimators and conduct a sampling experiment to compare the finite sample behavior of these and other estimators to an iterated solution. Our results show that a “balanced” two-step estimator which deletes no equations initially outperforms the iterated solution over a wide range of conditions. Our results also show that a constrained, single-step estimator which deletes no equations from the system frequently outperforms all two-step methods examined. Further, the results of our study also apply to nonlinear specifications of market share models since the invariance issue arises in this context as well.
The Metric Quality of Ordered Categorical Data
Authors: Srinivasan V. , Basu Amiya K. 
Published: October 2008

We quantify the information loss incurred by categorizing an unobserved continuous variable (X) into an ordered categorical scale (Z). The continuous variable is conceptualized as true score (τ) (which varies across individuals) plus random error (ϵ), with both components assumed to be normally distributed. The index of metric quality is operationalized as r2 (Z, τ)/r2(X, τ), where r2, the squared correlation coefficient, is a descriptive measure of the power of X or Z to predict τ. The index is useful in defining limits on explanatory power (population R2) in multiple regression models in which an ordered categorical variable is regressed against a set of predictors. The index can also be used to correct correlations for the effects of ordered categorical measurement. The index of metric quality is extended to the case when several ordered categorical scales are averaged as in the multi-item measurement of a construct. We prove theoretically that as long as the error variance is “large,” the index of metric quality for the average Z̄ of ordered categorical scales goes to 1 as the number of scales becomes “large.” The index for averaged data is useful in answering questions such as whether the measurement of a construct by averaging three 5-point scales is better or worse than the measurement obtained by averaging five 3-point scales. The results indicate that the loss of information by marketing researchers' ad hoc use of Z as opposed to the more refined X is small (<10%) when the Z scale is well designed with at least five categories. The loss would be even smaller when a multi-item based Z̄ is employed.
Perceptual Mapping Using Ordered Logit Analysis
Authors: Katahira Hotaka 
Published: October 2008

This study is to present a new method for constructing a perceptual map based on logit analysis. This is an extension of the explosion logit model of an individual choice to a problem of perceptual mapping giving rise to advantages over existing methods in various aspects. Firstly, input data format is flexible and user-friendly. Unlike traditional methods which typically requires a total dissimilarity ordering on all the pairs of the objects, it allows a partial ordering to any rank depth and a ‘pivot’ ordering which gives a dissimilarity ordering of objects with respect to a specific ‘pivot’ or ‘anchored’ object. Secondly, it introduces the concept of an evoked set into perceptual mapping and allows a respondent to make judgments only within his/her evoked set. This, together with the first point, contributes to the reduction of the respondents' burden and the data noise. Thirdly, Monte Carlo experiments have revealed that our ML estimates give a considerably better fit to data than ALSCAL, one of the most widely used algorithms of MDS. Particularly worth noting is that our method using the data ranked only up to the top two thirds gives as good a fit as ALSCAL using totally ordered data. Although not exploited here, opening up a way for statistical inference in nonmetric MDS would be yet another advantage. An empirical application is made to a Canadian car market for illustration.
A Knowledge-Based System for Advertising Design
Authors: Burke Raymond R. , Rangaswamy Arvind , Wind Jerry , Eliashberg Jehoshua 
Published: October 2008

In recent years, artificial intelligence research has provided new tools and techniques for marketing model builders. These tools, when combined with problem-solving knowledge from a specific domain, can be used to create expert systems. This methodology is most applicable in semistructured problem domains where the key relationships are logical rather than numerical and problem-solving knowledge is incomplete. One such problem in marketing is advertising design. In this paper, we describe the application of expert system techniques to the development of ADCAD, a system designed to assist advertisers of consumer products with the formulation of advertising objectives, copy strategy, and the selection of communication approaches. The paper highlights the assembly of ADCAD's knowledge base of ad design heuristics from multiple sources of published research and practitioner expertise and describes its structure and content. We discuss the procedures and obstacles associated with building, implementing, and validating such an expert system. Our experiences with ADCAD suggest that knowledge-based systems have significant potential for the consolidation and integration of marketing knowledge as interactive input for decision makers. We conclude by noting several avenues for the future development of advertising expert systems.
On Paths Generated by Fixed Point Algorithms
Authors: Saigal R. 
Published: October 2008

This paper considers algorithms that compute fixed points (or more generally solve equations) which are based on complementary pivoting. These algorithms, starting with a map f0 and its fixed point x0, deform ft to f∞ = f as t goes from 0 to ∞, and follow the path xt of fixed points of ft. In this paper we study these paths. In particular, we treat some special applications of these algorithms from a global point of view, and thus look at the behavior and properties of these paths sufficiently far from the solution. Our methods are motivated by methods of global analysis. We show that in many implementations of these algorithms the path can be specified. These include the cases when the mapping is linear and when it is smooth and monotone. The results of the linear analysis are used to study the local behavior of these paths (i.e., properties and behavior sufficiently close to the solution) for smooth mappings. An important implication of this study is that the paths can be modified and thus the work done by these algorithms can be controlled. We also show, for smooth mappings, how our results can be implemented to increase the efficiency of some standard algorithms.
Average Optimal Singular Control and a Related Stopping Problem
Authors: Taksar M. I. 
Published: October 2008

We observe a (μ, σ2) Brownian motion Xt. We can increase or decrease the value of the process paying r times the size of increase and l times the size of decrease. Holding costs are incurred continuously at a rate h(Zt) where Zt is the resulting process. We consider a convex holding cost function h which is either finite everywhere or finite inside a finite interval and equal to infinity outside this interval. The objective is to minimize average (per unit of time) expected cost. It is shown that the optimal behavior is characterized by two constants a and b, a < b, such that the optimal policy is to keep the process inside the interval [a, b] with minimal efforts. It is shown that to find the optimal interval [a, b], one must solve a free boundary problem for the second order differential equation. We give a probabilistic solution of the free boundary problem in terms of the value of a special game. This game is a generalization of the optimal stopping problem. There are two players observing the (μ, σ2) Brownian motion, and two regions where respectively the first and the second players have the right to stop the process. The one who stops the process pays a constant fee. In addition the first player pays to the second a certain accumulated amount of money. The existence of optimal minmax strategies is shown and it is shown that the region where neither the first nor the second player should stop the process corresponds to the optimal interval [a, b] in the original control problem.
Extremal Splittings of Point Processes
Authors: Hajek Bruce 
Published: October 2008

The sequence with nth term defined by [(n + 1)p] − [np] is an extremal zero-one valued sequence of asymptotic mean p in the following sense (for example): if a fraction p of customers from a point process with iid interarrival times is sent to an exponential server queue according to a prespecified splitting sequence, then the long-term average queue size is minimized when the above sequence is used. The proof involves consideration of the lower convex envelope J (which is a function on Rm) of a function J on Zm. An explicit representation is given for J in terms of J, for J in a broad class of functions, which we call “multimodular.” The expected queue size just before an arrival, considered as a function of the zero-one splitting sequence, is shown to belong to this class.
Optimal Sequential Selection of Secretaries
Authors: Mallows C. L. , Nair V. N. , Shepp L. A. , Vardi Y. 
Published: October 2008

The problem is to select as rapidly as possible a pre-specified number of secretaries (sequentially and without recall) from a proffered queue of applicants. Each candidate makes demands in each of several currencies, and we know the joint probability distribution of these demands. We also have a given total budget in each currency. We consider procedures that minimize the expected number of interviews and derive an asymptotically optimal procedure. Derivation of this procedure depends on the following result. Given a probability measure F on the positive orthant Q and a point ρ0 ∈ Q, consider a region A ⊂ Q whose center of gravity lies below ρ0 coordinatewise. Then F(A) is maximal when A is a simplicial section A = {ρ : ρ · θ ≤ r}, where r ≥ 0 and θ is a unit vector in Q. The original motivation for this problem arose in connection with a scheme for selecting optical fibers.
On the Augmented Lagrangian
Authors: Han S.-P. 
Published: October 2008

It is well known that, for a nonlinear program, any Karush–Kuhn–Tucker point that satisfies the second order sufficient condition is also a strict local minimum of the augmented Lagrangian with an underlying penalty parameter sufficiently large. A main theme of the paper is to strengthen the theorem and bring to light an interesting connection among general critical points of a nonlinear program and its augmented Lagrangian. When a penalty parameter is sufficiently large, it will be shown that a Karush–Kuhn–Tucker point of a nonlinear program is also a critical point of its augmented Lagrangian with the same index and the same nullity. The aforementioned theorem is just the special case when the index and the nullity are zeros. This result is established through an extension of a lemma due to Finsler and Debreu, which is interesting in its own right. Consequently, under a constraint qualification, any Karush–Kuhn–Tucker point can also be shown to satisfy a second order necessary condition for a local maximum of the generalized Wolfe dual induced from the augmented Lagrangian. Interestingly, this relation holds without requiring the Karush–Kuhn–Tucker point itself to satisfy any second order optimality condition.
Computational Complexity of Some Problems in Parametric Discrete Programming. I
Authors: Blair C. E. , Jeroslow R. G. 
Published: October 2008

We explore the computational complexity of certain issues regarding parametric linear and integer linear programming. For example, we demonstrate that: (1) The equality of optimal value of two integer programs for all right-hand sides (r.h.s) is NP-complete either when the problem is stated in matrix or in functional form; (2) The equality of optimal value of two linear programs for all r.h.s. in matrix form is polynomial, but it becomes NP-complete when one desires equality for all r.h.s. in a polyhedral cone described by generators; (3) The equality of a general polyhedral function (allowing nested “maxes”) to the value of a linear program in matrix form, or to another polyhedral function, is NP-complete; (4) The shortest expression, for the optimum to the subadditive dual of an integer program in matrix form, can require exponential space.
Double-Exponential Utility Functions
Authors: Bell David E. 
Published: October 2008

Ordinal additivity between two attributes X and Y is a property that permits the utility function u(x, y) to be represented as ϕ(v(x) + w(y)) for some functions ϕ, v and w where ϕ may be thought of as a single attribute utility function over v + w. In applications ϕ is usually taken to be either linear (the additive decomposition) or exponential (the multiplicative decomposition). The utility function can be shown to be exactly one of these forms whenever the two attributes are mutually utility independent. In this paper we introduce a relaxation of utility independence and show that it too implies ordinal additivity. We identify the class of utility functions ϕ that are consistent with the relaxed assumptions. One member of this class, ϕ(z) = −exp(b exp(−cz)), which we call double-exponential, seems particularly appealing, for when b and c are positive it is increasing, risk averse and decreasingly risk averse for all z. The multiattribute decomposition corresponding to it −exp(b exp(−c(v + w))) may be represented as u(x, y) = c exp(cv(x)w(y)) which we call the exponential product.
Layered Augmenting Path Algorithms
Authors: Tardos Éva , Tovey Craig A. , Trick Michael A. 
Published: October 2008

Augmenting path algorithms, first introduced by Ford and Fulkerson (Ford, L. R., D. R. Fulkerson. 1962. Flows in Networks. Princeton University Press, Princeton, N.J.), are widely used in optimization. Examples include Schönsleben's polymatroid intersection algorithm (Schönsleben, P. 1980. Ganzzahlige polymatroid-intersection-algorithmen. Ph.D. thesis, Eidgenössischen Technischen Hochschule, Zürich.), the maximum polymatroidal network flow algorithm of Lawler and Martel (Lawler, E. L., C. U. Martel. 1982. Computing maximal polymatroidal network flows. Math. Oper. Res. 7 334–347.), Frank's algorithm for the Edmonds–Giles polyhedron (Frank, A. 1984. Finding feasible vectors of Edmonds-Giles polyhedra. J. Combin. Theory Ser. B 36 221-239.) and Cunningham's algorithm for testing membership in matroid polyhedra (Cunningham, H. W. 1984. Testing membership in matroid polyhedra. J. Combin. Theory Ser. B 36 161–188.). Here we give an order of magnitude improvement for the above algorithms by using an approach analogous to that of Dinits’ maximum flow algorithm (Dinits, E. A. 1970. Algorithm for solution of a problem of maximum flow in a network with power estimation. Soviet Math. Dokl. 11 1277–1280.).