Mixed Markov and latent Markov modelling applied to brand choice behaviour

Abstract

Two models, the mixed Markov and the latent Markov model, are presented. Both can be seen as generalizations of Lazarsfeld's latent class model. The mixed Markov model is defined as a finite mixture of (manifest) Markov chains, allowing for individual differences in transition probabilities. It generalizes the latent class model by relaxing the assumption of local independence. The latent Markov model describes a Markov chain operating at the unobservable or latent level, due to, for example, errors in the determination of the relevant states. From a marketing perspective, a partial segmentation approach is taken. This is implemented in well-defined statistical models that can be estimated and tested efficiently. The structural insights and predictions provided by the models are illustrated using a data set from Aaker (1970) on brand switching.