A.A.J. Marley

Modeling the choices of individual decision-makers by combining efficient choice experiment designs with extra preference information

Abstract We show how to combine statistically efficient ways to design discrete choice experiments based on random utility theory with new ways of collecting additional information that can be used to expand the amount of available choice information for modeling the choices of individual decision makers. Here we limit ourselves to problems involving generic choice options and linear and additive indirect utility functions, but the approach potentially can be extended to include choice problems with non-additive utility functions and non-generic/labeled options/attributes. The paper provides several simulated examples, a small empirical example to demonstrate proof of concept, and a larger empirical example based on many experimental conditions and large samples that demonstrates that the individual models capture virtually all the variance in aggregate first choices traditionally modeled in discrete choice experiments.

An integrated model of choices and response times in absolute identification.

Recent theoretical developments in the field of absolute identification have stressed differences between relative and absolute processes, that is, whether stimulus magnitudes are judged relative to a shorter term context provided by recently presented stimuli or a longer term context provided by the entire set of stimuli. The authors developed a model (SAMBA: selective attention, mapping, and ballistic accumulation) that integrates shorter and longer term memory processes and accounts for both the choices made and the associated response time distributions, including sequential effects in each. The models predictions arise as a consequence of its architecture and require estimation of only a few parameters with values that are consistent across numerous data sets. The authors show that SAMBA provides a quantitative account of benchmark choice phenomena in classical absolute identification experiments and in contemporary data involving both choice and response time.

The “horse race” random utility model for choice probabilities and reaction times, and its competing risks interpretation

Random utility models have traditionally been applied to probabilistic choice data, with little attention to reaction times. We describe the class of “horse race” random utility models that can be applied to both choice probabilities and reaction times. We show that any (well behaved) set of choice probabilities and reaction times on a fixed set can be represented by an independent “horse race” random utility model, and relate this result to work in the theory of competing risks. We use the latter theory to motivate the condition that the option chosen and the time of choice be independent, a condition that is satisfied by a large class of (extreme value) “horse race” random utility models. Combining the latter condition with the assumption of an independent “horse race” random utility model yields a new characterization of Lute’s choice model, and a generalization of these conditions to subset choices (as opposed to choosing a single “best” element) yields the transition probabilities of Tversky’s elimination-by-aspects model.

A model of response time effects in symbolic comparison

A cognitive process model is developed that predicts the 3 major symbolic comparison response time effects (distance, end, and semantic congruity) found in the results of the linear syllogistic reasoning task. The model includes a simple connectionist learning component and dual evidence accumulation decision-making components. It assumes that responses can be based either on information concerning the positional difference between the presented stimulus items or on information concerning the endpoint status of each of these items. The model provides an excellent quantitative account of the mean correct response times obtained from 16 participants who performed paired comparisons of 6 ordered symbolic stimuli (3-letter names).

Rescaling quality of life values from discrete choice experiments for use as QALYs: a cautionary tale

BackgroundResearchers are increasingly investigating the potential for ordinal tasks such as ranking and discrete choice experiments to estimate QALY health state values. However, the assumptions of random utility theory, which underpin the statistical models used to provide these estimates, have received insufficient attention. In particular, the assumptions made about the decisions between living states and the death state are not satisfied, at least for some people. Estimated values are likely to be incorrectly anchored with respect to death (zero) in such circumstances.MethodsData from the Investigating Choice Experiments for the preferences of older people CAPability instrument (ICECAP) valuation exercise were analysed. The values (previously anchored to the worst possible state) were rescaled using an ordinal model proposed previously to estimate QALY-like values. Bootstrapping was conducted to vary artificially the proportion of people who conformed to the conventional random utility model underpinning the analyses.ResultsOnly 26% of respondents conformed unequivocally to the assumptions of conventional random utility theory. At least 14% of respondents unequivocally violated the assumptions. Varying the relative proportions of conforming respondents in sensitivity analyses led to large changes in the estimated QALY values, particularly for lower-valued states. As a result these values could be either positive (considered to be better than death) or negative (considered to be worse than death).ConclusionUse of a statistical model such as conditional (multinomial) regression to anchor quality of life values from ordinal data to death is inappropriate in the presence of respondents who do not conform to the assumptions of conventional random utility theory. This is clearest when estimating values for that group of respondents observed in valuation samples who refuse to consider any living state to be worse than death: in such circumstances the model cannot be estimated. Only a valuation task requiring respondents to make choices in which both length and quality of life vary can produce estimates that properly reflect the preferences of all respondents.

Random utility models with equality: An apparent, but not actual, generalization of random utility models☆

Abstract A probabilistic model for choice, and preference, is introduced that includes (Tverskys) elimination by aspects model, and the random utility model, as special cases. The model is based on a covert sequential elimination process, the element that is finally chosen in a simple choice experiment being the eventual lone survivor of the elimination process. The model leads us to question the usual form of simple choice experiments, in which a subject must (eventually) choose one of the currently available alternatives, and to suggest that a much more realistic experimental design would allow the subject the no-choice option, i.e., he may refuse to accept any of the currently available alternatives.

Some probabilistic models of simple choice and ranking

Abstract A simple choice experiment is one in which a subject is asked to select among several alternatives according to some specified criterion, and a ranking experiment is one in which he is asked to rank order the alternatives, again according to some specified criterion. When decisions are governed by a probabilistic process, various connections are possible between simple choice and ranking behavior. In this paper we consider a set of conditions that assumes that the ranking probabilities can be expressed as a “natural” function of the simple choice probabilities. Under these conditions the binary choice probabilities on a finite set A determine the simple choice and ranking probabilities on every subset of A , and explicit forms are given for the functions relating the simple choice and ranking probabilities to the binary choice probabilities.

Best-worst scaling: theory and methods

Choice modelling is an increasingly important technique for forecasting and valuation, with applications in fields such as transportation, health and environmental economics. For this reason it has attracted attention from leading academics and practitioners and methods have advanced substantially in recent years. This Handbook, composed of contributions from senior figures in the field, summarises the essential analytical techniques and discusses the key current research issues. It will be of interest to academics, students and practitioners in a wide range of areas.

A Connectionist Model of Choice and Reaction Time in Absolute Identification

A connectionist architecture is developed that can be used for modeling choice probabilities and reaction times in identification tasks. The architecture consists of a feedforward network and a decoding module, and learning is by mean-variance back-propagation, an extension of the standard back-propagation learning algorithm. We suggest that the new learning procedure leads to a better model of human learning in simple identification tasks than does standard back-propagation. Choice probabilities are modeled by the input-output relations of the network and reaction times are modeled by the time taken for the network, particularly the decoding module, to achieve a stable state. In this paper, the model is applied to the identification of unidimensional stimuli; applications to the identification of multidimensional stimuli—visual displays and words—is mentioned and presented in more detail in other papers. The strengths and weaknesses of this connectionist approach vis-a-vis other approaches are discussed

Choice and response time processes in the identification and categorization of unidimensional stimuli

Lacouture and Marley (1991, 1995, 2001) have successfully modeled the probabilities of correct responses and the mean correct response times (RTs) in unidimensional absolute identification tasks for various stimulus ranges and stimulus/response set sizes, for individual and group data. These fits include those to a set of phenomena often referred to asend-anchor effects. A revised model, with the independent accumulator decision process replaced by aleaky competing accumulator decision process, fits the probabilities of correct responses and the full distributions of RTs in unidimensional absolute identification. The revised model is also applied successfully to a particular class of unidimensional categorization tasks. We discuss possible extensions for handling sequential effects in unidimensional absolute identification, and other extensions of the given class of categorization tasks that are of potential empirical and theoretical importance as a supplement to the study of multidimensional absolute identification tasks.