A mixture likelihood approach for generalized linear models

A mixture model approach is developed that simultaneously estimates the posterior membership probabilities of observations to a number of unobservable groups or latent classes, and the parameters of a generalized linear model which relates the observations, distributed according to some member of the exponential family, to a set of specified covariates within each Class. We demonstrate how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature. As such we generalize the McCullagh and Nelder approach to a latent class framework. The parameters are estimated using maximum likelihood, and an EM algorithm for estimation is provided. A Monte Carlo study of the performance of the algorithm for several distributions is provided, and the model is illustrated in two empirical applications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45934/1/357_2005_Article_BF01202266.pd

—Structural Demand Estimation with Varying Product Availability

This paper develops a model that extends the traditional aggregate discrete-choice-based demand model (e.g. Berry et al. 1995) to account for varying levels of product availability. In cases where not all products are available at every consumer shopping trip, the observed market share is a convolution of two factors: consumer preferences and the availability of the product in stores. Failing to account for the varying degree of availability would produce incorrect estimates of the demand parameters. The proposed model uses information on aggregate availability to simulate the potential assortments that consumers may face in a given shopping trip. The model parameters are estimated by simulating potential product assortment vectors by drawing multivariate Bernoulli vectors consistent with the observed aggregate level of availability. The model is applied to the UK chocolate confectionery market, focusing on the convenience store channel. We compare the parameter estimates to those obtained from not accounting for varying availability and analyze some of the substantive implications.structural modeling, availability, retailing

Manufacturer-Retailer Channel Interactions and Implications for Channel Power: An Empirical Investigation of Pricing in a Local Market

The issue of “power” in the marketing channels for consumer products has received considerable attention in both academic and practitioner journals as well as in the popular press. Our objective in this paper is to provide an empirical method to measure the power of channel members and to understand the reasons (demand factors, cost factors, nature of channel interactions) for this power. We confine our analysis to pricing power in channels. We use methods from the game-theory literature in marketing on channel interactions to obtain the theoretical framework for our empirical model. This literature provides us a definition of power—one that is based on the proportion (or percentage) of channel profits that accrue to each of the channel members. There can be a variety of possible channel interactions between manufacturers and retailers in channels. The theoretical literature has examined some of these games. For example, Choi (1991) examines how channel profits for manufacturers and retailer vary if channel interactions are either vertical Nash, or if they are Stackelberg leaderfollower with either the manufacturer or the retailer being the price leader. Each of these three channel interaction games has different implications for profits made by manufacturers and retailers, and consequently for the relative power of the channel members. In contrast to the previous literature that has focused largely on the above three channel interaction games, our model extends the game-theoretic literature by allowing for a continuum of possible channel interactions between manufacturers and a retailer. Furthermore, for a given product market, we empirically estimate from the data where the channel interactions lie in this continuum. More critically, we obtain measures of how channel profits are divided between manufacturers and the retailer in the product market, where a higher share of channel profit is associated with higher channel power. We then examine how channel power is related to demand conditions facing various brands and cost parameters of various manufacturers. In going from game-theory-based theoretical models of channel interactions to empirical estimation, we use the “new empirical industrial organization” framework (Bresnahan 1988). As part of this structural modeling framework, we build retail-level demand functions for the various brands (manufacturer and private label) in a given product category. Given these demand functions, we obtain optimal pricing rules for manufacturers and the retailer. In determining their optimal prices, manufacturers and the retailer account for how all the players in the channel choose their optimal prices. That is, we account for dependencies in decision making across channel members. These dependencies are characterized by a set of “conduct parameters,” which are estimated from market data. The conduct parameters enable us to identify the nature of channel interactions between manufacturers and the retailer (along the continuum mentioned previously). In addition to the demand and conduct parameters, manufacturers' marginal costs are also estimated in the model. These marginal cost estimates, along with the manufacturer prices and retail prices available in our dataset, enable us to compute the division of channel profits among the channel members. Hence, we are able to obtain insights into who has pricing power in the channel. In the empirical application of the model, we analyze a local market for two product categories: refrigerated juice and tuna. In both categories, there are three major brands. The difference between them is that the private label has an insignificant market share in the tuna category. Our main empirical results show that the usual games examined in the marketing literature do not hold for the given data. We also .nd that the retailer's market power is very significant in both these product categories, and that the estimated demand and cost parameters are consistent with the estimated pattern of conduct between the manufacturers and the retailer. Given the evidence from the trade press of intense manufacturer competition in these categories, as well as the “commodity” nature of these products, the result of retailer power appears intuitive.Channel Power, Private Labels, Competitive Games