Abstract 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.

中文翻译：

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用半马尔可夫链模拟感觉的时间优势

摘要 感觉时间优势（TDS）数据通常用优势率的TDS曲线表示，并通过优势持续时间的线性模型进行分析。这种方法没有正确考虑到新的主导属性的选择可能取决于当前的主导属性这一事实。因此，正如 Franczak 等人最近提出的那样，使用随机过程对 TDS 数据建模似乎很自然。(2015) 谁使用了离散时间马尔可夫链。这种方法给出了从一种主导属性到另一种主导属性的转换概率。然而，马尔可夫链在应用于 TDS 数据时存在一些限制。作为替代方案，本文考虑了半马尔可夫链 (SMC)，这是马尔可夫链的推广，它允许任意分布主导属性的持续时间。由于从一种属性转换到另一种属性的概率也可能取决于时间，因此 SMC 应用于分为具有特定持续时间的时间段的序列，每个时间段有一个模型。可以绘制建立在这种随机模式上的图形来表示属性之间按时间顺序排列的主要转变。与总结平均面板概览的 TDS 曲线相反，这些图表可以解释为个人最可能的路径，有助于更好地了解消费者的看法。