MARTER: Markov True and Error model of drifting parameters

This paper describes a theory of the variability of risky choice that describes empirical properties of choice data, including sequential effects and systematic violations of response independence. The Markov True and Error (MARTER) model represents the formation and fluctuation of true preferences produced by stochastic variation of parameters over time, which produces changing true preference patterns. This model includes a probabilistic association between true preferences and overt responses due to random error. Computer programs have been developed to simulate data according to this model, to fit data to the TE model, and to test and analyze violations of iid (independent and identical distributions) that are predicted by the model. Data simulated from MARTER models show properties that are characteristic of real data, including violations of iid similar to those observed in previous empirical research. This paper also illustrates how methods based on analysis of binary response proportions do not and in many cases cannot correctly diagnose what model was used to generate the data. The MARTER model is extremely general and neutral with respect to models of risky decision making. For example, the transitive transfer of attention exchange (TAX) model and intransitive Lexicographic Semiorder (LS) models can both be represented as special cases of MARTER, and they can be tested against each other, even when binary choice proportions cannot discriminate which model was used to simulate the data. Software to simulate data according to this model, and to fit data to this model, to test this model, and to compare special case theories are included or linked to this article.