Quasi-dynamic choice models: Melioration and ratio invariance

There is continuing controversy about the behavioral process or processes that underlie the major regularities of free-operant choice such as molar matching and systematic deviations therefrom. A recent interchange between Vaughan and Silberberg and Ziriax concerned the relative merits of melioration, and a computer simulation of molecular maximizing. There are difficulties in evaluating theories expressed as computer programs because many arbitrary decisions must often be made in order to get the programs to operate. I therefore propose an alternative form of model that I term quasi-dynamic as a useful intermediate form of theory appropriate to our current state of knowledge about free-operant choice. Quasi-dynamic models resemble the game-theoretic analyses now commonplace in biology in that they can predict stable and unstable equilibria but not dynamic properties such as learning curves. It is possible to interpret melioration as a quasi-dynamic model. An alternative quasi-dynamic model for probabilistic choice, ratio invariance, has been proposed by Horner and Staddon. The present paper compares the predictions of melioration and ratio invariance for five experimental situations: concurrent variable-interval variable-interval schedules, concurrent variable-interval variable-ratio schedules, the two-armed bandit (concurrent random-ratio schedules), and two types of frequency-dependent schedule. Neither approach easily explains all the data, but ratio invariance seems to provide a better picture of pigeons' response to probabilistic choice procedures. Ratio invariance is also more adaptive (less susceptible to “traps”) and closer to the original expression of the law of effect than pure hill-climbing processes such as momentary maximizing and melioration, although such processes may come in to play on more complex procedures that provide opportunities for temporal discrimination.     

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.     

The effect of normative models on individual and group choice

Studied the effect of a normative model (maximization of expected value) upon group and individual choice. 109 MBA students in a Lain square research design chose between two alternatives differing in expected value and in range of outcomes. Group choices were significantly (p < .05) closer to those predicted by the normative model than were individual choices. This difference was not due only to information about the presence and applicability of the normative model but rather it was due to the persuasiveness of the model in a group as a cogent and correct solution to the choice dilemma. Task instructions emphasizing the rewards from risk taking produced significantly more choices (p < .05) of the riskier alternative, particularly by individuals as opposed to groups, than did instructions emphasizing the penalties of risk taking. ‘Risky’ and ‘conservative’ shifts in choice between groups and individuals were explicable through knowledge of the influence of the normative model in individual and group choice.     

Assessment and choice: an operant simulation of foraging in patches

Pigeons were presented with an operant simulation of two prey patches using concurrent random-ratio schedules of reinforcement. An unstable patch offered a higher initial reinforcement probability, which then declined unpredictably to a zero reinforcement probability in each session. A stable patch offered a low but unvarying reinforcement probability. When the reinforcement probability declined to zero in a single step, the birds displayed shorter giving-up times in the unstable patch when the ratio between the initial reinforcement probabilities in the unstable and stable patches was greater and when the combined magnitude of the reinforcement probabilities in the two patches was greater. When the unstable patch declined in two steps, the birds behaved as if their giving-up times were influenced heavily by events encountered during the most recent step of the double-step change. This effect was observed, however, only when the reinforcement probability in that step was .04, not when it was .06. All of these data agree with the predictions of a capture-probability model based on a comparison of the estimated probability of receiving a reinforcer in the current patch with that in alternative patches.     

Cognitive models of choice: comparing decision field theory to the proportional difference model

People often face preferential decisions under risk. To further our understanding of the cognitive processes underlying these preferential choices, two prominent cognitive models, decision field theory (DFT; Busemeyer & Townsend, 1993 ) and the proportional difference model (PD; González-Vallejo, 2002 ), were rigorously tested against each other. In two consecutive experiments, the participants repeatedly had to choose between monetary gambles. The first experiment provided the reference to estimate the models' free parameters. From these estimations, new gamble pairs were generated for the second experiment such that the two models made maximally divergent predictions. In the first experiment, both models explained the data equally well. However, in the second generalization experiment, the participants' choices were much closer to the predictions of DFT. The results indicate that the stochastic process assumed by DFT, in which evidence in favor of or against each option accumulates over time, described people's choice behavior better than the trade-offs between proportional differences assumed by PD.     

Goodness-of-fit tests for models of latency and choice

A goodness-of-fit test based on the maximum likelihood criterion is derived for use in evaluating models of choice reaction time that predict choice probabilities and means and variances of latency. Special cases of the test involving models that predict only one or two of these statistics are considered and shown to be asymptotically identical to the traditional goodness-of-fit tests appropriate for these special cases.     

Probabilistic models of set-dependent and attribute-level best-worst choice

We characterize a class of probabilistic choice models where the choice probabilities depend on two scales, one with a value for each available option and the other with a value for the set of available options. Then, we develop similar results for a task in which a person is presented with a profile of attributes, each at a pre-specified level, and chooses the best or the best and the worst of those attribute-levels. The latter design is an important variant on previous designs using best-worst choice to elicit preference information, and there is various evidence that it yields reliable interpretable data. Nonetheless, the data from a single such task cannot yield separate measures of the “importance” of an attribute and the “utility” of an attribute-level. We discuss various empirical designs, involving more than one task of the above general type, that may allow such separation of importance and utility.     

睡眠剥夺影响风险决策的双系统模型探讨

睡眠剥夺是指由于环境或自身原因无法满足正常睡眠时间的情况。大量实证研究发现, 睡眠剥夺会导致个体在风险决策中更倾向于风险寻求, 同时也有研究表明睡眠剥夺会导致个体风险规避, 而目前尚无统一结论。睡眠剥夺从风险感知、风险容忍、风险决策策略三个方面影响了风险决策, 其心理机制可由认知和情绪双路径模型进行解释, 且脑神经生理学研究也提供了相关证据。未来的研究应该进一步关注：(1)现实工作生活中的睡眠不足对风险决策的影响; (2)睡眠剥夺影响风险决策的理论模型建构。     

Person x situation interactions: choice of situations and congruence response models

Two models of Person x Situation interaction wee examined. The first model predicts that there is a relation between personality and the situations people naturally choose to be in; the second model predicts that when there is congruence between the situation and personality, a person will experience more positive and less negative affect. These models were investigated by using mood and activity reports gathered on 3,512 occasions sampled randomly from the everyday lives of 42 subjects. Situational dimensions were related to some but not all personality variables investigated. Need for order predicted choice of typical situations and extraversion correlated with time spent recreating socially. However, it was found that individuals did not spend more time in those settings where they experienced more positive emotions nor less time in those situations where they experienced more negative affect. In terms of the affect-congruence model, several predicted relations wee found, but several others did not reach significance. The failure of the affect-congruence model to be consistently supported was probably because the affect of individuals was relatively consistent across situations. The present results suggest that although some theoretically meaningful Person x Situation interactions do occur, they are not necessarily strong or easily predictable.     

Effects of auditory stimulus intensity on response force in simple, go/no-go, and choice RT tasks

In four experiments, increasing the intensities of both relevant and irrelevant auditory stimuli was found to increase response force (RF) in simple, go/no-go, and choice reaction time (RT) tasks. These results raise problems for models that localize the effects of auditory intensity on purely perceptual processes, indicating instead that intensity also affects motor output processes under many circumstances. In Experiment 1, simple RT, go/no-go, and choice RT tasks were compared, using the same stimuli for all tasks. Auditory stimulus intensity affected both RT and RF, and these effects were not modulated by task. In Experiments 2-4, an irrelevant auditory accessory stimulus accompanied a relevant visual stimulus, and the go/no-go and choice tasks were used. The intensity of the irrelevant auditory accessory stimulus was found to affect RT and RF, although the sizes of these effects depended somewhat on the temporal predictability of the accessory stimulus.     

Hyperbolic value addition and general models of animal choice

Three mathematical models of choice--the contextual-choice model (R. Grace, 1994), delay-reduction theory (N. Squires & E. Fantino, 1971), and a new model called the hyperbolic value-added model--were compared in their ability to predict the results from a wide variety of experiments with animal subjects. When supplied with 2 or 3 free parameters, all 3 models made fairly accurate predictions for a large set of experiments that used concurrent-chain procedures. One advantage of the hyperbolic value-added model is that it is derived from a simpler model that makes accurate predictions for many experiments using discrete-trial adjusting-delay procedures. Some results favor the hyperbolic value-added model and delay-reduction theory over the contextual-choice model, but more data are needed from choice situations for which the models make distinctly different predictions.     

Cognitive models of risky choice: parameter stability and predictive accuracy of prospect theory

In the behavioral sciences, a popular approach to describe and predict behavior is cognitive modeling with adjustable parameters (i.e., which can be fitted to data). Modeling with adjustable parameters allows, among other things, measuring differences between people. At the same time, parameter estimation also bears the risk of overfitting. Are individual differences as measured by model parameters stable enough to improve the ability to predict behavior as compared to modeling without adjustable parameters? We examined this issue in cumulative prospect theory (CPT), arguably the most widely used framework to model decisions under risk. Specifically, we examined (a) the temporal stability of CPT’s parameters; and (b) how well different implementations of CPT, varying in the number of adjustable parameters, predict individual choice relative to models with no adjustable parameters (such as CPT with fixed parameters, expected value theory, and various heuristics). We presented participants with risky choice problems and fitted CPT to each individual’s choices in two separate sessions (which were 1 week apart). All parameters were correlated across time, in particular when using a simple implementation of CPT. CPT allowing for individual variability in parameter values predicted individual choice better than CPT with fixed parameters, expected value theory, and the heuristics. CPT’s parameters thus seem to pick up stable individual differences that need to be considered when predicting risky choice.