MOSHE GIVON and DAN HORSKY* A composite model of brand choice is presented. It allows individuals to differ in the order of the stochastic process they follow as well as in the magnitude of the process parameters. Procedures for estimating the parameters of the composite model and selecting the best submodel are proposed. Examination of several sets of panel data reveals that in some product categories consumers seem to follow the Linear Learning Model, in some the Bernoulli model, and in some divide into Markovian and Bernoulli segments. Application of a Composite Stochastic Model of Brand Choice Kuehn's (1962) modeling of brand choice behavior as a stochastic linear learning process has generated an increasing interest in the application of stochastic processes to the brand choice phenomenon. However, subsequent studies by Frank (1962) and Massy (1966) refuted a basic assumption underlying Kuehn's work, that of homogeneous individuals. In those studies an individual type of analysis conducted on long purchase strings demonstrated that individuals did not have identical transition probabilities and, further, that individuals differed in the order of the stochastic processes they followed. These findings were support- ed by Blattberg and Sen (1976). Heterogeneity also has been recognized in studies analyzing consumers with shorter strings of purchases. In those studies all consumers were assumed to follow the same process, but the vector of probabilities was allowed to vary over individuals in accordance with some distributional forms. Studies based on zero-order models in which the consumer's probability of pur- chasing a specific brand is independent of his previous purchases were performed by Morrison (1966), Herni- ter (1973), and Bass et al. (1976). Morrison (1966) also has allowed for heterogeneity in special versions of the first-order Markov model-the Brand Loyal and the Last-Purchase-Loyal models. The homoge- neous Linear Learning Model proposed by Kuehn *Moshe Givon is Lecturer, Jerusalem School of Business Admin- istration, The Hebrew University. Dan Horsky is Assistant Profes- sor, Graduate School of Management, The University of Rochester. The authors thank Subrata Sen for his helpful comments. 258 (1962) was modified by Massy et al. (1970, p. 157-67) to allow for heterogeneity through the initial response probabilities. Jones (1973) took a major step forward by allowing individuals to differ in the order of the stochastic process they follow as well as in the process parame- ters. In his model individuals are allocated to Bernoulli, Markov, and Linear Learning segments, each segment heterogeneous within itself. Because of its functional complexity and the ensuing estimation problems, the Jones model has not been applied to date. However, its potential for providing a much clearer description of the composition of consumer populations has led the authors to apply it to several panel data bases. In the following section the different stochastic models are specified and the Jones model is detailed. Next, procedures are proposed for estimating the parameters of the composite model and selecting the "best" submodel. Finally, the model is applied to several panel data bases and the empirical findings and their implications are discussed. THE COMPOSITE HETEROGENEOUS MODEL The brand choice behavior of an individual consumer is assumed in this study to be well described by one of three models: (1) the zero-order Bernoulli, (2) the first-order Markov, and (3) the Linear Learning Model (LLM). The more general of the three is the LLM as it nests the other two as constrained versions. The following exposition demonstrates how a model based on the LLM can encompass population heterogeneity in both order and parameters. Journal of Marketing Research Vol. XVI (May 1979), 258-67