Discrete dynamic choice: An extension of the choice models of thurstone and luce

The present paper deals with the extension of two well-known static discrete choice theories to the dynamic situation in which individuals make choices at several points in (continuous) time. A dynamic version of Luce's Axiom, “independence from irrelevant alternatives”, is proposed and some of its implications are derived. In the static case Yellott (J. Math. Psych. 1977, 15, 109–146) and others have demonstrated that an independent random utility model generated from the extreme value distribution exp(?e^?ax?b) becomes equivalent to Luce's Axiom. Yellott also introduced an axiom called “invariance under uniform expansions of the choice set”, and he proved that within the class of random utility models with independent identically distributed utilities (apart from a location shift) this axiom is equivalent to Luce's Axiom. These results are extended to the dynamic situation and it is shown that if the utility processes are expressed by so-called extremal processes the corresponding choice model is Markovian. A nonstationary generalization is proposed which is a substantial interest in applications where the parameters of the choice process are influenced by previous choice experience or by time-varying exogenous variables. In particular, it is demonstrated that the nonstationary model is Markovian if and only if the joint choice probabilities at two points in time have a particular form. Thus, the paper provides a rationale for applying a specific class of Markov models as the point of departure when modelling mobility processes that involve individual discrete decisions over time.     

A maximum likelihood hierarchical disaggregate model for predicting choices of individuals

The absence of operational disaggregate lexicographic decision models and Tversky's observation that choice behavior is often inconsistent, hierarchical, and context dependent motivate the development of a maximum likelihood hierarchical (MLH) choice model. This new disaggregate choice model requires few assumptions and accommodates the three aspects of choice behavior noted by A. Tversky (1972, Journal of Mathematical Psychology, 9, 341–367). The model has its foundation in a prototype model developed by the authors. Unlike the deterministic prototype, however, MLH is a probabilistic model which generates maximum likelihood estimators of the aggregate “cutoff values.” The model is formulated as a concave programming problem whose solutions are therefore globally optimal. Finally, the model is applied to data from three separate studies where it is demonstrated to have superior performance over the prototype model in its predictive performance.     

Divided attention: Evidence for coactivation with redundant signals

Many models of divided attention assume that signals presented on different channels produce separate activations, any one of which can initiate a response. According to these models, detection responses are especially fast when signals are presented on two channels at the same time because the system can detect a signal in either of two ways. Such models predict a testable relation among reaction time distributions for conditions in which a single signal is presented as compared with a condition in which two signals are presented, and this prediction is tested in two tasks. A bimodal detection task required a simple speeded response to either a visual or an auditory signal. A letter search task required a choice response depending on whether or not a two-letter display included the signal letter “A.” Data from both tasks are inconsistent with the prediction. When two signals are presented, responses are faster than separate-activation models can explain. The results favor “coactivation” models, in which signals presented on different channels contribute to a common pool of activation that initiates a response.     

Maximum likelihood estimation for Luce's choice model

A terminology for general choice models based on the choice axiom is given. It applies to all kinds of choice experiments, such as confusion choice experiments, paired comparisons, triadic comparisons, directional rankings, scores on binary test items, and others. Maximum likelihood estimation for such general choice models is considered. Conditions for the uniqueness of maximum likelihood estimates are given, and it is shown that the estimates can be derived by iterative proportional fitting. This offers the opportunity of a general test of the choice axiom for all kinds of choice experiments using the likelihood ratio. The estimation and testing procedure is applied to data from a form recognition experiment, reported by W. A. Wagenaar (Nederlands Tijdschrift voor de Psychologie, 1968, 23, 96–108).     

On the aggregation across subjects in analyzing individual choice behavior

Authors dealing with models of individual choice behavior often point out the pitfalls of using group data to test such models. However, it is possible to derive properties of the choice behavior of the population based on these models of individual choice behavior. The present paper develops a procedure for the aggregation of choice data which takes into account individual differences. The utility of using aggregated choice data and the properties of the present procedure in comparison to other methods which utilized group data in analyzing choice behavior are discussed.     

A model of problem solving with incomplete constraint knowledge

The problem-solving behavior of subjects presented with a series of Tower of Hanoi problems is examined. A production system model which incorporates elements of domain-specific knowledge into a general problem-solving framework is presented. Other models developed for the task are based on understanding of complete solution strategies and are not satisfactory models of nonexpert human performance. The current model discriminates between problem-solving behavior based on constraint knowledge and behavior based on nonspecific general search strategies. A variety of move choice and latency measures are used to compare the performance of the model to human subject performance.     

Testing models for the structure of vocational interests

Several studies aimed at testing the validity of Holland's hexagonal and Roe's circular models of interests showed results on which the null hypothesis of random arrangement can be rejected, and the investigators concluded that the tested models were supported. None of these studies, however, tested each model in its entirety. The present study is based on the assumption that the rejection of the null hypothesis of chance is not rigorous enough. Reanalysis of 13 data sets of published studies, using a more rigorous method, reveals that although the random null hypothesis can in fact be rejected in 11 data sets, the hexagonal-circular model was supported by only 2 data sets and was rejected by 11 data sets. The hierarchical model for the structure of vocational interests (I. Gati, Journal of Vocational Behavior, 1979, 15, 90–106) was submitted to an identical test and was supported by 6 out of 10 data sets, including 4 data sets that rejected the hexagonal-circular model. The predictions of each of the models which tend to be discontinued by empirical data were identified. The implications of the findings for the structure of interests and occupational choice are discussed.     

Effects of choice task on attribute memory

Winnowing process models of multiattribute choice in which alternatives are successively eliminated in stages based on partial information predict differential memory for minor attributes as a function of an alternative's relative desirability. This prediction, which differs from the results of judgment studies finding little or no relationship between evaluation and memory, was tested in two experiments in which the choice task (Choose 1 vs Choose 3) and the density of the option set were varied. Better memory for minor attributes of relatively desirable alternatives was observed for those conditions requiring the more difficult decisions, namely the Choose 1 task with a dense set of good alternatives. A third experiment replicated these results and demonstrated that the minor attributes did influence choice. The results of all three experiments are generally consistent with winnowing models. However, detailed analysis of the memory data revealed that only attributes of the chosen alternative were remembered better; this is not entirely consistent with those models. Implications of these results for models of memory and choice are discussed.     

Perceptions of labor market variables by college students in business,education, and psychology

The perceptions of psychic and economic rewards available in different occupations, the perceptions of psychic and economic costs of preparing for these occupations, and the perceived availability of jobs for college majors in business, education, and psychology is examined. The findings indicate that these different majors have quite similar perceptions of these variables despite major differences in occupational choices. Further analysis examines the relationships of these variables to occupational choice for these three groups of college majors. Although the perceptions of rewards and costs have limited independent relations to measures of occupational choice, benefits-to-costs comparisons are highly related to occupational choice for all three groups of college majors.     

确定、不确定及风险状态下选择反转:“齐当别”选择方式的解释

应用广义“弱优势”（weak dominance）模型检验确定、不确定及风险状态下的选择反转现象。该模型将人们的二择一选择行为描述为一种搜寻一备择方案在主观上优越于另一备择方案的过程。即：在甲方案在某一维度上优越于乙方案,而乙方案在另一维度上优越于甲方案的情况下,为了利用“弱优势”（weak dominance）原则达成决策,人们必须在一维度上将两者间较小的差异人为地“齐同”掉,而在另一维度上将“辨别”两者间较大的差异作为最终选择的依据。因此,在每次选择时,如果不认为最大的差异都是来自同一维度,就会导致选择反转。此项研究设计了一“匹配”任务,并借此检验,在不同的决策状态下,判断两备择方案在各维度上的差异是否能预测人们的重复选择变异。总的测试-再测试结果支持“齐当别”选择方式的解释。其发现表明：重复选择之所以可能是一致的,并不是因为每次都认定被选中的备择方案具有最大值,而是因为每次选择都认定最大的差异来自一固定的维度。     

A conditional logit model of collegiate major selection

The choice of a major by a college student is viewed as depending upon the quantity of various outputs (such as income and status) each major provides and the taste structure of the student for these outputs. Tradeoffs in outputs occur so that high status may overcome low-income potential in the occupation into which the major provides entry. Different taste structures among students mean tradeoffs occur at different rates, so that taste structues are best associated with student major selection in a probability sense. Changes in the probability of selecting a collegiate major are associated with changes in student taste structures via a conditional logit model. The taste structure of a student is hypothesized to depend upon the environment in which the student was raised and the environment in which the student now lives. The relationship between environment and taste is also best stated in a probability sense and a second logit model is used to describe this relationship. Estimation of the two logit models, using survey data, attempts to quantify the hypothesized route from environment to taste structure to major selection for entry into an occupation. An example of this route is the finding that women students place more importance on obtaining high income than do men students and the greater the importance of high income, the lower the probability of selecting an education major, the greater the probability of selecting a humanities or social science major. Other results of estimation are presented and discussed.     

Stochastic transitivity and the unidimensional control of choice

A concurrent-chains paradigm was used to test three models of preference for schedules of reinforcement. Each model assumes choice to be a monotonic function of values on a single dimension (“simple scalability”). For choices involving variable-interval and fixed-interval schedules, this dimension is assumed to be an harmonic average of the interreinforcement intervals; for choices involving fixedinterval and fixed-ratio schedules, the dimension is the time to reinforcement irrespective of response rate; for choices involving different combinations of rate and duration of reinforcement, the dimension is the rate of “reinforcement-time”, or the product of the two parameters. Each model implies a strong form of transitivity (“functional equivalence”), which held for half the subjects (that half exclusively sensitive to the reinforcement variable specified by the model). An alternative unidimensional model which implies a weaker form of transitivity (“weak binary utility model”) was consistent with the preferences of all subjects. This model states that a single factor controls the direction of preferences but not necessarily the exact choice probability, as simple scalability assumes.     

Short-term memory in the pigeon with presentation time precisely controlled

Delayed matching-to-sample was studied in the pigeon using a procedure which precisely controlled the presentation time of the sample stimulus. Experiments 1 and 2 revealed that (a) accuracy of matching increased as a negatively accelerated function of presentation time, (b) accuracy declined when an interstimulus interval was introduced between successive presentations of the sample stimulus, and (c) the rate at which accurate matching was restored after an interstimulus interval was greatest when the initial presentation of the sample was short and the interval was long. It was concluded that a theory of STM based on the growth and decay of trace strength could account adequately for all of these findings. Experiment 3 studied trace interaction by presenting two sample stimuli first in succession and then simultaneously for choice. Predictions from trace competition theory about the specific lengths of presentation of these stimuli at which choice of the second stimulus should be 50% or deviate systematically below 50% were not supported. It appears that a recency mechanism in addition to competition is necessary to explain trace interaction effects.     

Interaction of stimulus dimensions in concept and choice processes

Four major types of interaction of stimulus dimensions based on perceptual research are described: integral, configural, separable, and asymmetric separable. Implications of these interactions for concept and choice processes are discussed. With regard to concept learning, it is argued that integral or configural interactions are desirable within the set of relevant and within the set of irrelevant dimensions used to generate stimuli, but that relevant dimensions should be separable from irrelevant dimensions. With regard to choice processes, integral or configural dimensions produce choices based on ordinary distance relations or equivalent parallel processing of dimensions. With separable dimensions, however, serial processing is at least possible; and such processing can lead to choices in which the subset of stimuli and the order of processing of dimensions affects the choice outcomes.     

Conflict-mediated choice

Research on behavioral decision making has demonstrated that preferences are affected by the set of options under consideration. Formal models offer an account of such choice-set effects on the basis of principles according to which the similarity of the options in the choice set has an effect on choice probabilities. Behavioral formulations are Tversky's (1972) elimination-by-aspects (EBA) model, based on the principle of sequential elimination, and Tversky and Simonson's (1993) componential context (CC) model, based on the principle of pairwise comparisons subject to loss aversion. While these principles are assumed to determine choice behavior, the conflict induced by the set of options under consideration is assumed to be merely a source of indeterminacy in choice behavior. This paper challenges past models by offering a behavioral account of choice-set effects according to which the effect of similarity on choice probabilities is mediated by conflict. A conflict-mediated choice (CMC) model is developed, its testable implications are derived, and its predictions are contrasted with those of the EBA model and the CC model. Specifically, it is described how, according to each of the three models, choice probabilities are affected by the similarity of the options in the choice set and how choice-set effects are moderated by the relative weight of the attributes along which the options are positioned. In two experimental studies, the CMC model offers an accurate account of observed choice-set effects and outperforms the alternative models.     

Signaling and affective functions of conditioned aversive stimuli in an appetitive choice discrimination: US intensity effects

Different groups of rats received Pavlovian aversive conditioning in which US-shock intensity (0.25–1.0 mA) and CS-US correlation (+, 0, ?) were factorially varied. Then, the CS was administered for each group contingent upon the reinforced response in an appetitive choice discrimination. Absolute and ratio measures of speed of running in the presence of the CS showed that, at the start of discrimination training, CS+ suppressed and CS- facilitated performance. However, later in training but prior to any evidence of choice learning, these speed effects reversed, with the magnitude of both the initial and reversed effects being a positive function of US intensity. Consistent with the reversal of speeds, associative (choice) measures showed that CS+ facilitated and CS- retarded discrimination learning relative to CSo and, within limits, these effects were also amplified by stronger USs. The findings suggest that a CS has both affective (motivational) and signaling (associative) functions and that both are influenced by US intensity; however, the CS's affective property is rapidly extinguished in the presence of a hedonicly different reinforcer, while leaving the CS's signaling property largely intact. Hence, the CS functions as a transformed signal for the new (appetitive) reinforcer and facilitates or retards learning by mediating the reinforcer's presence (CS+) or absence (CS-).     

Probabilistic choice (models) as a result of balancing multiple goals

We conceptualize probabilistic choice as the result of the simultaneous pursuit of multiple goals in a vector optimization representation, which is reduced to a scalar optimization that implies goal balancing. The majority of prior theoretical and empirical work on such probabilistic choice is based on random utility models, the most basic of which assume that each choice option has a valuation that has a deterministic (systematic) component plus a random component determined by some specified distribution. An alternate approach to probabilistic choice has considered maximization of one quantity (e.g., utility), subject to constraints on one or more other quantities (e.g., cost). The multiple goal perspective integrates the results regarding the well-studied multinomial logit model of probabilistic choice that has been derived from each of the above approaches; extends the results to other models in the generalized extreme value (GEV) class; and relates them to recent axiomatic work on the utility of gambling.     

Choice Environment, Market Complexity, and Consumer Behavior: A Theoretical and Empirical Approach for Incorporating Decision Complexity into Models of Consumer Choice

Most empirical models of choice in economics and consumer research assume that the decision maker assesses all alternatives and information in a perfect information-processing sense. The complexity of the choice environment, the ability of the individual to make complex decisions, and the effect of choice context on the decision strategy are generally not considered in statistical model development. One of the reasons for this omission is that theoretical literature on choice complexity and imperfect ability to choose that has developed in psychology and behavioral decision theory (BDT) literatures has not been translated into empirical econometric analysis. Second, the data used in economics and consumer research studies tend to be somewhat different from the data structures used in psychology and BDT literatures. In this paper we outline a theoretical model that simultaneously considers task complexity, effort applied by the consumer, ability to choose, and choice. We then construct a measure of task complexity and incorporate this in an analysis of a number of data series based on the random utility framework. We also examine the performance of our measure of task complexity in a composite data set that allows for increased variability in factors affecting decision context. Our approach provides a mechanism to link research in BDT and econometric modeling of consumer choice. Our findings suggest that task complexity does affect inferences about choice model parameters and that context effects, such as complexity, have a systematic impact on the parameters of econometric models of choice. The modeling approach provides a mechanism for inclusion of results from psychology and BDT in traditional economic models of consumer choice.     

Problems in the measurement of vocational maturity

Problems posed by the measurement of vocational maturity are discussed. One is the choice of an appropriate approach to the construction of vocational maturity measures, and another is how to demonstrate that a developmental variable has been measured. A combined rational-empirical methodology is proposed as a possible solution to these problems, and a model of vocational maturity is formulated which can be used as a conceptual frame of reference for constructing theoretically meaningful and psychometrically valid measures of the variables.     

跨期决策中的维度差异偏好：眼动证据

在跨期决策研究领域,虽然基于维度的跨期模型得到了一些源自结果检验和过程检验的证据支持,但此类模型所假设的维度间差异比较的心理过程尚缺乏直接的过程证据。本研究通过两个眼动实验,系统考察了相关眼动指标对维度差异偏好的预测效应。结果发现,根据基于维度的权衡模型可有效拟合出个体在跨期决策中的维度差异偏好,并且反应时、眼跳注视熵和静态注视熵等指标均与维度差异偏好负相关,而基于维度的注意分配与维度差异判断正相关。这些研究发现支持了本研究所提出的跨期眼动模型的相关假设,证实了维度差异偏好与跨期决策的认知加工过程之间的联系,为基于维度的跨期模型提供了更直接的过程证据,并为今后跨期决策的眼动模型发展指明了新方向。