Modeling Temporal Dominance of Sensations with semi-Markov chains

Temporal Dominance of Sensations (TDS) data are usually represented by TDS curves of dominance rates and analyzed by linear models of dominance durations. Such approaches do not properly take into account the fact that the selection of a new dominant attribute likely depends on the current dominant attribute. Thus, modeling TDS data with a stochastic process seems natural, as recently proposed by Franczak et al. (2015) who used discrete time Markov chains. This approach gives the probabilities of transition from one dominant attribute to another. However Markov chains present some limitations when applied to TDS data. As an alternative, this paper considers semi-Markov chains (SMC), a generalization of Markov chains, which allow the duration of the dominant attribute to be distributed arbitrarily. Because probabilities of transition from one attribute to another one can also depend on time, SMC are applied on sequences split into time periods with specific durations, with one model per time period. Graphs built upon this stochastic pattern can be plotted to represent chronological main transitions between attributes. Contrarily to the TDS curves which summarize a mean panel overview, these graphs can be interpreted as individual's most probable paths and contribute to a better understanding of consumer perception.