ISSN 0439-755X
CN 11-1911/B

中国科学院心理研究所

## 风险决策和跨期决策的过程比较：以确定效应和即刻效应为例

1暨南大学管理学院, 广州 510632

2中国科学院行为科学重点实验室(中国科学院心理研究所), 北京 100101

3中国科学院大学心理学系, 北京 100049

4德国汉堡大学医学院系统神经科学系, 汉堡 20246

## Similarity in processes of risky choice and intertemporal choice: The case of certainty effect and immediacy effect

ZHOU Lei1,2,3, LI Ai-Mei1, ZHANG Lei4, LI Shu,2,3, LIANG Zhu-Yuan,2,3

1 Management School, Jinan University, Guangzhou 510632, China

2 CAS Key Laboratory of Behavioral Science, Institute of Psychology, Beijing 100101, China

3 Department of Psychology, University of Chinese Academy of Sciences, Beijing 100049, China

4 Institute for Systems Neuroscience, University Medical Center Hamburg-Eppendorf, Hamburg 20246, Germany

 基金资助: * 国家自然科学基金青年项目.  71801110国家自然科学基金面上项目.  71471171国家自然科学基金面上项目.  31471005国家自然科学基金面上项目.  71571087教育部人文社会科学研究青年基金项目.  18YJC630268中国博士后科学基金资助项目.  2018M633270中国科学院行为科学重点实验室自主研究课题项目.  Y5CX052003广东省自科重大培育项目资助.  2017A030308013

Abstract

Risky choice (RC) and intertemporal choice (IC) are two types of common decisions that are vital to human’s everyday life. RC and IC share similarities regarding theoretical development, behavioral effects, and neural basis. One critical challenge is that, although previous studies have revealed that RC and IC involve similar cognitive processes, results are mixed regarding what the exact mechanism might be. The mainstream discounting model hypothesizes that both RC and IC follow a compensatory and alternative-based rule. However, other models suggest that RC and IC commonly involve non-compensatory and attribute-based processing. Moreover, prior studies primarily based their findings on outcome data and few have attempted to determine whether RC and IC shared a common decision process at the cognitive computational level.
To fill this gap, the present study adopts a systematic approach to disentangle the exact mechanism of RC and IC. We considered two well-studied behavioral effects, namely, certainty effect of RC and immediacy effect of IC, respectively, and compared their underlying local and holistic process characteristics by using eye-tracking technique. Besides, we employed hierarchical Bayesian modeling to assess whether alternative- or attribute-based models better fit both RC and IC. We designed a 2×2 within-subject paradigm, with the choice task (RC vs. IC) and the construct of decision options (with vs. without certain/immediate option) as factors. Thirty-three postgraduate students participated in our study. As we were particularly interested in two pairs of decision rules, i.e., compensatory/non-compensatory rules and alternative-based/attribute-based rules, we included a series of decision attributes that reflected them, based on the local and holistic process characteristics derived from eye-movement data to test our hypotheses.
Our entire set of analyses aimed to (1) determine whether the decision processes of RC and IC are similar and (2) identify the best computational model that is more suitable for both decisions. For the first aim, results show that RC and IC indeed share comparable decision processes, albeit having a few differences in other aspects. Specifically, RC and IC differ in process characteristics, such as complexity and holistic eye-movement dynamics, and IC is processed in a relatively more deliberate, deeper fashion than RC. However, they are similar in other characteristics, such as search direction, which is more relevant to making decisions. For the second aim, computational modeling of process characteristics suggests that both types of decisions are consistent with non-discounting models. In particular, results of search direction, in light of Bayesian model comparison, reveals that participants are more likely to follow the non-compensatory, attribute-based rule rather than the alternative-based/attribute-based rule when deciding for both RC and IC. Furthermore, different task constructs of decision options, i.e., with or without certain/immediate option, show distinct process characteristics, such as direction, complexity, and depth in both RC and IC.
To conclude, the present study shows that although differences exist between RC and IC, they indeed have shared cognitive mechanisms at the core of the decision processes. In both types of decisions, contrary to classic discounting models, individuals seem not to follow compensatory, attribute-based rules, which undergoes a “weighting and summing” or “delay discounting” process. Instead, they are more likely to use simple heuristic rules hypothesized by non-discounting models. Moreover, when including certain or immediate options, individuals tend to follow less compensatory and non-dominant (neither attribute-based nor alternative-based) rules. In sum, our findings not only provide a theoretical and empirical basis for the establishment of a common framework for RC and IC, but also provide a novel direction for thorough theoretical and methodological comparisons between variant decision tasks.

Keywords： risky choice ; intertemporal choice ; eye-tracking ; hierarchical Bayesian modeling ; certainty effect ; immediacy effect

ZHOU Lei, LI Ai-Mei, ZHANG Lei, LI Shu, LIANG Zhu-Yuan. Similarity in processes of risky choice and intertemporal choice: The case of certainty effect and immediacy effect. Acta Psychologica Sinica[J], 2019, 51(3): 337-352 doi:10.3724/SP.J.1041.2019.00337

## 1 前言

### 1.1 风险和跨期决策的相似性

1.1.1 理论发展

1.1.2 风险和跨期决策类比关系的研究

1.1.3 确定效应和即刻效应

### 1.4 研究目的与假设

H1 (反应时)：二者决策时间无显著差异。

H2 (选择偏好)：风险决策存在确定效应, 跨期决策存在即刻效应。

H3 (加工复杂程度)：二者加工复杂程度无显著差异。

H4a (加工深度)：二者在决策前注视信息量百分比无显著差异。

H4b (加工深度)：二者在决策前均无需注视所有选项特征。

H5 (加工方向)：二者基于选项的眼跳和基于维度眼跳的频数分布无显著差异。

H6 ：二者眼动轨迹无显著差异。

H7 ：相对于折扣模型, 二者能更好地被非折扣模型拟合。

## 2 方法

### 图2

2.4.1 局部过程特征比较

$SM=\frac{\sqrt{N}\left( \frac{AD}{N} \right)({{r}_{a}}-{{r}_{d}})-(A-D)}{\sqrt{{{A}^{2}}(D-1)+{{D}^{2}}(A-1)}}$

SM值服从标准正态分布, 已被广泛应用于决策的眼动研究(Konstantinidis, van Ravenzwaaij, & Newell, 2017; Schulte-Mecklenbeck, Kühberger, Gagl, & Hutzler, 2017; Su et al., 2013)。以SM值为搜索模式的测量指标适用于检验基于选项和维度的决策模型：操纵选项和维度数量时, 其均值稳定, 得到极端数值的概率极低(Böckenholt & Hynan, 1994)。相对于其他指标, 它对搜索模式的变化更敏感：如操纵搜索策略, 使占优的搜索模式切换, SM值可敏感地探测出这种变化(Böckenholt & Hynan, 1994)。因此, 在本研究中, 如果个体依据补偿性规则加工, 其决策的主要加工方向是基于选项, SM值应相对较大; 反之, 更可能是基于维度加工。

2.4.2 整体过程特征比较

2.4.3 模型拟合的比较

WAIC的计算公式如下：

$WAIC=-2(\widehat{\text{lpd}}-{{\hat{p}}_{waic}})$

$\widehat{\text{lpd}}=\sum\limits_{i=1}^{n}{\log \left( \frac{1}{S}\sum\limits_{S=1}^{S}{p({{y}_{i}}|{{\theta }^{S}})} \right)}$

${{\hat{p}}_{\text{waic}}}$表示估计出的参数的有效数量(estimated effective number of parameters), 对应模型的复杂程度：

${{\hat{p}}_{\text{waic}}}=\sum\limits_{i=1}^{n}{Var_{S=1}^{S}(\log (p({{y}_{i}}|{{\theta }^{S}})))}$

V = A * e-kD (5)

V = A / (1 + kD) (6)

$\begin{matrix} & p(LL)=L\left( \left( \begin{matrix} \begin{matrix}& {{\beta }_{I}} \\ & {{\beta }_{xA}} \\ \end{matrix} \\ {{\beta }_{xR}} \\ {{\beta }_{dR}} \\ {{\beta }_{dR}} \\\end{matrix} \right)*\left( \begin{matrix} \begin{matrix} & \ \ \ \ \ \ 1 \\ & {{X}_{LL}}-{{X}_{SS}} \\ \end{matrix} \\ ({{X}_{LL}}-{{X}_{SS}})/{{X}^{*}} \\ {{D}_{LL}}-{{D}_{SS}} \\ ({{D}_{LL}}-{{D}_{SS}})/{{D}^{*}} \\\end{matrix} \right) \right) \\ & \ \ \ \ {{X}^{*}}=\frac{({{X}_{LL}}+{{X}_{SS}})}{2}\ \ \ \ {{D}^{*}}=\frac{({{D}_{LL}}+{{D}_{SS}})}{2} \\ \end{matrix}$ (7)

## 3 结果

3.1.1 决策时间

3.1.2 选择偏好

3.2.1 加工复杂程度

3.2.2 加工深度

3.2.3 加工方向

### 图7

(左：不含确定/即刻条件, 右：包含确定/即刻条件)

WAIC预测率WAIC预测率

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An interesting phenomenon, which we dub the ‘pseudo‐immediacy effect’, was detected in intertemporal choices. The majority of our participants preferred the smaller but sooner (SS) outcome to the larger but later (LL) outcome when a pseudo‐immediacy reward was framed, but a higher proportion of participants preferred the LL outcome to the SS outcome when the pseudo‐immediate format was removed. Such a shift violated the invariance principle which requires that the preference order between options does not depend on the manner in which they are described. With reference to the pseudo‐certainty effect reported by Kahneman and Tversky in 1984, our findings typically support the notion that risk and delay are psychologically equivalent and that the same psychological process underlies risk and intertemporal choice.

Liang Z-Y., Zhou L., &Su Y . ( 2016, Aug.).

The hidden-zero effect in risky choice: An eye-tracking study

Paper presented at the 31th International Congress of Psychology, Yokohama, JAPAN.

Luckman A., Donkin C., &Newell B. R . ( 2017).

Can a single model account for both risky choices and inter-temporal choices? Testing the assumptions underlying models of risky inter-temporal choice

Psychonomic Bulletin & Review, 25, 785-792. doi: 10.3758/s13423-017-1330-8

URL     PMID:28600719

There is growing interest in modelling how people make choices that involve both risks and delays, i.e., risky inter-temporal choices. We investigated an untested assumption underlying several proposed risky inter-temporal choice models: that pure risky choices and pure inter-temporal choices are special cases of risky inter-temporal choice. We tested this assumption by presenting a single group of participants with risky choices and inter-temporal choices. We then compared the performance of a model that is fit to both choice types simultaneously, with the performance of separate models fit to the risky choice and inter-temporal choice data. We find, using Bayesian model comparison, that the majority of participants are best fit by a single model that incorporates both risky and inter-temporal choices. This result supports the assumption that risky choices and inter-temporal choices may be special cases of risky inter-temporal choice. Our results also suggest that, under the conditions of our experiment, interpretation of monetary value is very similar in risky choices and inter-temporal choices.

Loewenstein G., &Prelec D. ( 1992).

Anomalies in intertemporal choice: Evidence and an interpretation

The Quarterly Journal of Economics, 107( 2), 573-597. doi: 10.1006/obhd.1996.0028

Research on decision making under uncertainty has been strongly influenced by the documentation of numerous expected utility (EU) anomalies--behaviors that violate the expected utility axioms. The relative lack of progress on the closely related topic of intertemporal choice is partly due to the absence of an analogous set of discounted utility (DU) anomalies. We enumerate a set of DU anomalies analogous to the EU anomalies and propose a model that accounts for the anomalies, as well as other intertemporal choice phenomena incompatible with DU. We discuss implications for savings behavior, estimation of discount rates, and choice framing effects.

Ly A., Verhagen J., &Wagenmakers E.-J . ( 2016 a).

An evaluation of alternative methods for testing hypotheses, from the perspective of Harold Jeffreys

Journal of Mathematical Psychology, 72, 43-55. doi: 10.1016/j.jmp.2016.01.003

61Reply to Robert (2016) The expected demise of the Bayes factor.61Reply to Chandramouli and Shiffrin (2016) Extending Bayesian induction.61Further elaboration on Jeffreys’s Bayes factors.

Ly A., Verhagen J., &Wagenmakers E-J . ( 2016 b).

Harold Jeffreys’s default Bayes factor hypothesis tests: Explanation, extension, and application in psychology

Journal of Mathematical Psychology, 72, 19-32. doi: 10.1016/j.jmp. 2015.06.004

61The Bayes factor follows logically from Jeffreys’s philosophy of model selection.61The ideas are illustrated with two examples: the Bayesian t-test and correlation test.61The Bayes factors are adapted to one-sided tests.61The Bayes factors are illustrated with various applications in psychological research.

Magen E., Dweck C., &Gross J. J . ( 2008).

The hidden-zero effect: Representing a single choice as an extended sequence reduces impulsive choice

Psychological Science, 19( 7), 648-649. doi: 10.1111/j.1467-9280.2008.02137.x

Marsman M., &Wagenmakers E-J . ( 2017).

Bayesian benefits with JASP

European Journal of Developmental Psychology, 14( 5), 545-555. doi: 10.1080/17405629.2016.1259614

Mazur J.E . ( 1987).

An adjusting procedure for studying delayed reinforcement

In M. L. Commons, J. E. Mazur, J. A. Nevin, & H. Rachlin(Eds.), Quantitative analyses of behavior: Vol. 5. The effect of delay and of intervening events on reinforcement value

Abstract [3] experiments showed that an adjusting procedure can provide useful information about choice between reinforcers, especially when delayed reinforcers are involved pigeon (PsycINFO Database Record (c) 2012 APA, all rights reserved)

McClure S. M., Laibson D. I., Loewenstein G., &Cohen J. D . ( 2004).

Separate neural systems value immediate and delayed monetary rewards

Science, 306( 5695), 503-507. doi: 10.1126/science.1100907

Myerson J., Green L., Hanson S. J., Holt D. D., &Estle S. J . ( 2003).

Discounting delayed and probabilistic rewards: Processes and traits

Journal of Economic Psychology, 24( 5), 619-635. doi: 10.1016/S0167-4870(03)00005-9

Noton D., &Stark L. ( 1971).

Scanpaths in eye movements during pattern perception

Science, 171( 3968), 308-311. doi: 10.1126/science.171.3968.308

URL     PMID:5538847

Subjects learned and recognized patterns which were marginally visible, requiring them to fixate directly each feature to which they wished to attend. Fixed "scanpaths," specific to subject and pattern, appeared in their saccadic eye movements, both intermittently during learning and in initial eye movements during recognition. A proposed theory of pattern perception explains these results.

Pascal B. ( 1670).

Pensées (W. F. Trotter, Trans.)

Retrieved Nov. 22, 2018, from

Rao L-L, &Li S. ( 2011).

Judgment and Decision Making, 6( 2), 122-129.

Rayner K. (Ed.) ( 2013).

Eye movements and visual cognition: Scene perception and reading.

New York:Springer-Verlag. doi: 10.1007/978-1-4612-2852-3

Read D., Frederick S., &Scholten M . ( 2013).

DRIFT: An analysis of outcome framing in intertemporal choice

Journal of Experimental Psychology: Learning, Memory, and Cognition, 39( 2), 573-588. doi: 10.1037/a0029177

URL     PMID:22866891

People prefer to receive good outcomes immediately rather than wait, and they must be compensated for waiting. But what influences their decision about how much compensation is required for a given wait? To give a partial answer to this question, we develop the DRIFT model, a heuristic description of how framing influences intertemporal choice. We describe 4 experiments showing the implications of this model. In the experiments, we vary how the difference between a smaller sooner outcome and a larger later outcome is framed-either as total interest earned, as an interest rate, or as total amount earned (the conventional frame in studies of intertemporal choice)-and whether the larger later outcome is described as resulting from the investment of the smaller sooner one. These alternate frames have several effects. First, the investment language increases patience. Second, the explicit provision of the (otherwise implicit) experimental interest rate sharply reduces the magnitude effect. Correspondingly, we find that interest frames increase patience when the rewards are small, but they decrease patience when they are large. Third, the interest-rate frame induces somewhat greater discounting for longer time periods and, thus, reverses the common finding of "hyperbolic" discounting. Thus, many of the "stylized facts" implied by studies involving choices between a smaller sooner and a larger later amount are eliminated or reverse under alternate outcome frames.

Read D., Loewenstein G., &Kalyanaraman S . ( 1999).

Mixing virtue and vice: Combining the immediacy effect and the diversification heuristic

Journal of Behavioral Decision Making, 12( 4), 257-273. doi: 10.1002/(SICI)1099-0771 (199912)12:4%3C257::AID-BDM327%3E3.0.CO;2-6

Reeck C., Wall D., &Johnson E. J . ( 2017).

Search predicts and changes patience in intertemporal choice

Proceedings of the National Academy of Sciences, 114( 45), 11890-11895. doi: 10.1073/pnas.1707040114

URL     PMID:29078303

People often make decisions with consequences that unfold over time. When facing such intertemporal choices, people use different search strategies. We examine how these search strategies differ and how they relate to patience in intertemporal choice. We demonstrate that search varies substantially across individuals and identify two main search strategies omparative or integrative search. Importantly, comparative search correlates with greater patience and higher susceptibility to contextual influences on choice. We manipulated search using an unobtrusive technique, revealing a causal relationship between strategy and choice. Comparative searchers make more patient choices and exhibit larger framing effects than integrative searchers. An understanding of how differences in psychological processes change discounting can inform the design of behavioral interventions to improve consumer welfare. Intertemporal choice impacts many important outcomes, such as decisions about health, education, wealth, and the environment. However, the psychological processes underlying decisions involving outcomes at different points in time remain unclear, limiting opportunities to intervene and improve people patience. This research examines information-search strategies used during intertemporal choice and their impact on decisions. In experiment 1, we demonstrate that search strategies vary substantially across individuals. We subsequently identify two distinct search strategies across individuals. Comparative searchers, who compare features across options, discount future options less and are more susceptible to acceleration versus delay framing than integrative searchers, who integrate the features of an option. Experiment 2 manipulates search using an unobtrusive method to establish a causal relationship between strategy and choice, randomly assigning participants to conditions promoting either comparative or integrative search. Again, comparative search promotes greater patience than integrative search. Additionally, when participants adopt a comparative search strategy, they also exhibit greater effects of acceleration versus delay framing. Although most participants reported that the manipulation did not change their behavior, promoting comparative search decreased discounting of future rewards substantially and speeded patient choices. These findings highlight the central role that heterogeneity in psychological processes plays in shaping intertemporal choice. Importantly, these results indicate that theories that ignore variability in search strategies may be inadvertently aggregating over different subpopulations that use very different processes. The findings also inform interventions in choice architecture to increase patience and improve consumer welfare.

Rouder J. N., Speckman P. L., Sun D. C., Morey R. D., &Iverson G . ( 2009).

Bayesian t-tests for accepting and rejecting the null hypothesis

Psychonomic Bulletin & Review, 16, 225-237. doi: 10.3758/PBR.16.2.225

URL     PMID:19293088

Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the null hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easy-to-use, Web-based program that performs the necessary calculations.

Samuelson P.A . ( 1937).

A note on measurement of utility

The Review of Economic Studies, 4( 2), 155-161.

No abstract is available for this item.

Scheibehenne B., &Pachur T. ( 2015).

Using Bayesian hierarchical parameter estimation to assess the generalizability of cognitive models of choice

Psychonomic Bulletin & Review, 22( 2), 391-407. doi: 10.3758/s13423-014-0684-4

URL     PMID:25134469

To be useful, cognitive models with fitted parameters should show generalizability across time and allow accurate predictions of future observations. It has been proposed that hierarchical procedures yield better estimates of model parameters than do nonhierarchical, independent approaches, because the formers’ estimates for individuals within a group can mutually inform each other. Here, we examine Bayesian hierarchical approaches to evaluating model generalizability in the context of two prominent models of risky choice—cumulative prospect theory (Tversky & Kahneman, 1992 ) and the transfer-of-attention-exchange model (Birnbaum & Chavez, 1997 ). Using empirical data of risky choices collected for each individual at two time points, we compared the use of hierarchical versus independent, nonhierarchical Bayesian estimation techniques to assess two aspects of model generalizability: parameter stability (across time) and predictive accuracy. The relative performance of hierarchical versus independent estimation varied across the different measures of generalizability. The hierarchical approach improved parameter stability (in terms of a lower absolute discrepancy of parameter values across time) and predictive accuracy (in terms of deviance; i.e., likelihood). With respect to test–retest correlations and posterior predictive accuracy, however, the hierarchical approach did not outperform the independent approach. Further analyses suggested that this was due to strong correlations between some parameters within both models. Such intercorrelations make it difficult to identify and interpret single parameters and can induce high degrees of shrinkage in hierarchical models. Similar findings may also occur in the context of other cognitive models of choice.

Schneider E., Streicher B., Lermer E., Sachs R., &Frey D . ( 2017).

Measuring the zero-risk bias: Methodological artefact or decision-making strategy?

Zeitschrift für Psychologie, 225, 31-44. doi: 10.1027/2151-2604/a000284

Schulte-Mecklenbeck M., Johnson J. G., Böckenholt U., Goldstein D. G., Russo J. E., Sullivan N. J., &Willemsen M. C . ( 2017).

Process-tracing methods in decision making: On growing up in the 70s

Current Directions in Psychological Science, 26( 5), 442-450. doi: 10.1177/0963721417708229

Decision research has experienced a shift from simple algebraic theories of choice to an appreciation of mental processes underlying choice. A variety of process-tracing methods has helped researchers test these process explanations. Here, we provide a survey of these methods, including specific examples for subject reports, movement-based measures, peripheral psychophysiology, and neural techniques. We show how these methods can inform phenomena as varied as attention, emotion, strategy use, and understanding neural correlates. Two important future developments are identified: broadening the number of explicit tests of proposed processes through formal modeling and determining standards and best practices for data collection.

Schulte-Mecklenbeck M., Kühberger A., Gagl B., &Hutzler F . ( 2017).

Inducing thought processes: Bringing process measures and cognitive processes closer together

Journal of Behavioral Decision Making, 30( 5), 1001-1013. doi: 10.1002/bdm.2007

The challenge in inferring cognitive processes from observational data is to correctly matrix overt behavior with its covert cognitive process. To improve our understanding of the overt-covert mapping in the domain of decision making, we collected eye-movement data during decisions between gamble-problems. Participants were either free to choose or instructed to use a specific choice strategy (maximizing expected value or a choice heuristic). We found large differences in looking patterns between free and instructed choices. Looking patterns provided no support for the common assumption that attention is equally distributed between outcomes and probabilities, even when participants were instructed to maximize expected value. Eye-movement data are to some extent ambiguous with respect to underlying cognitive processes. Copyright (c) 2017 John Wiley & Sons, Ltd.

Scholten M., &Read D. ( 2010).

Psychological Review, 117( 3), 925-944. doi: 10.1037/a001

URL     PMID:20658858

Abstract It is commonly assumed that people make intertemporal choices by "discounting" the value of delayed outcomes, assigning discounted values independently to all options, and comparing the discounted values. We identify a class of anomalies to this assumption of alternative-based discounting, which collectively shows that options are not treated independently but rather comparatively: The time difference, or interval, between the options sometimes counts more and sometimes counts less if it is taken as a whole than if it is divided into shorter subintervals (superadditivity and subadditivity, respectively), and whether the interval counts more or less depends on the money difference, or compensation, involved (inseparability). We develop a model that replaces alternative-based discounting with attribute-based tradeoffs. In our model, people make intertemporal choices by weighing how much more they will receive or pay if they wait longer against how much longer the wait will be, or, conversely, how much less they will receive or pay if they do not wait longer against how much shorter the wait will be. This model, called the tradeoff model, accommodates, in a psychologically plausible way, all anomalies that the discounting approach can and cannot address. (c) 2010 APA, all rights reserved.

Simon H. A. ( 1982). Models of Bounded Rationality: Empirically grounded economic reason. Cambridge, US: MIT Press.

Stewart N., Hermens F., &Matthews W. J . ( 2015).

Eye movements in risky choice

Journal of Behavioral Decision Making, 29( 2-3), 116-136. doi: 10.1002/bdm.1854

We asked participants to make simple risky choices while we recorded their eye movements. We built a complete statistical model of the eye movements and found very little systematic variation in eye movements over the time course of a choice or across the different choices. The only exceptions were finding more (of the same) eye movements when choice options were similar, and an emerging gaze bias in which people looked more at the gamble they ultimately chose. These findings are inconsistent with prospect theory, the priority heuristic, or decision field theory. However, the eye movements made during a choice have a large relationship with the final choice, and this is mostly independent from the contribution of the actual attribute values in the choice options. That is, eye movements tell us not just about the processing of attribute values but also are independently associated with choice. The pattern is simple—people choose the gamble they look at more often, independently of the actual numbers they see—and this pattern is simpler than predicted by decision field theory, decision by sampling, and the parallel constraint satisfaction model. 08 2015 The Authors.Journal of Behavioral Decision Makingpublished by John Wiley & Sons Ltd.

Stevens J. R. ( 2011). Mechanisms for decisions about the future. In R. Menzel, & J. Fischer (Eds.) Animal thinking: Contemporary issues in comparative cognition (pp. 93- 104) . Cambridge, MA: MIT Press.

Stevenson M. K., Busemeyer J. R., &Naylor, J. C.. , ( 1990) . Judgment and decision-making theory. In D. M. Dunnette, & L. M. Hough (Eds.) Handbook of industrial and organizational psychology (pp. 283-374) . CA, US: Consulting Psychologists Press.

Su Y., Rao L. L., Sun H. Y., Du X. L., Li X., &Li S . ( 2013).

Is making a risky choice based on a weighting and adding process? An eye-tracking investigation

Journal of Experimental Psychology: Learning, Memory, and Cognition, 39( 6), 1765-1780. doi: 10.1037/a0032861

URL     PMID:23687917

Vehtari A., Gelman A., &Gabry J . ( 2015).

Efficient implementation of leave-one-out cross-validation and WAIC for evaluating fitted Bayesian models

ArXiv Preprint ArXiv:1507.04544. doi: 1007/s11222-016-9696-4

Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the posterior simulations of the parameter values. LOO and WAIC have various advantages over simpler estimates of predictive error such as AIC and DIC but are less used in practice because they involve additional computational steps. Here we lay out fast and stable computations for LOO and WAIC that can be performed using existing simulation draws. We compute LOO using Pareto smoothed importance sampling (PSIS), a new procedure for regularizing importance weights. As a byproduct of our calculations, we also obtain approximate standard errors for estimated predictive errors and for comparing of predictive errors between two models. We implement the computations in an R package called 'loo' and demonstrate using models fit with the Bayesian inference package Stan.

Vincent B.T . ( 2016).

Hierarchical Bayesian estimation and hypothesis testing for delay discounting tasks

Behavior Research Methods, 48, 1608-1620. doi: 10.3758/s13428-015- 0672-2

URL     PMID:26542975

A state-of-the-art data analysis procedure is presented to conduct hierarchical Bayesian inference and hypothesis testing on delay discounting data. The delay discounting task is a key experimental paradigm used across a wide range of disciplines from economics, cognitive science, and neuroscience, all of which seek to understand how humans or animals trade off the immediacy verses the magnitude of a reward. Bayesian estimation allows rich inferences to be drawn, along with measures of confidence, based upon limited and noisy behavioural data. Hierarchical modelling allows more precise inferences to be made, thus using sometimes expensive or difficult to obtain data in the most efficient way. The proposed probabilistic generative model describes how participants compare the present subjective value of reward choices on a trial-to-trial basis, estimates participant- and group-level parameters. We infer discount rate as a function of reward size, allowing the magnitude effect to be measured. Demonstrations are provided to show how this analysis approach can aid hypothesis testing. The analysis is demonstrated on data from the popular 27-item monetary choice questionnaire (Kirby, Psychonomic Bulletin & Review, 16 (3), 457 462 2009 ), but will accept data from a range of protocols, including adaptive procedures. The software is made freely available to researchers.

Wagenmakers E-J., Love J., Marsman M., Jamil T., Ly A., Verhagen J., … van Doorn J . ( 2018 a).

Bayesian inference for psychology. Part II : Example applications with JASP

Psychonomic Bulletin & Review, 25( 1), 58-76. doi: 10.3758/s13423-017-1323-7

URL     PMID:28685272

Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t -test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder 檚 BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

Wagenmakers E.- J., Marsman M., Jamil T., Ly A., Verhagen J., Love J., … Morey R. D . ( 2018 b).

Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications

Psychonomic Bulletin & Review, 25( 1), 35-57. doi: 10.3758/s13423-017-1343-3

Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al. this issue ).

Wang Z-J., &Li S . ( 2012).

Tests of the integrative model and priority heuristic model from the point of view of choice process: Evidence from an eye-tracking study

Acta Psychologica Sinica, 44( 2), 179-198. doi: 10.3724/SP.J.1041.2012.00179

[ 汪祚军, 李纾 . ( 2012).

Weber B.J., &Chapman G.B . ( 2005).

The combined effects of risk and time on choice: Does uncertainty eliminate the immediacy effect? Does delay eliminate the certainty effect?

Organizational Behavior and Human Decision Processes, 96( 2), 104-118. doi: 10.1016/j.obhdp.2005.01.001

No abstract is available for this item.

Weber B.J., &Huettel S.A . ( 2008).

The neural substrates of probabilistic and intertemporal decision making

Brain Research, 1234, 104-115. doi: 10.1016/j.brainres.2008.07.105

URL     PMID:2629583

Many important decisions involve outcomes that are either probabilistic or delayed. Based on similarities in decision preferences, models of decision making have postulated that the same psychological processes may underlie decisions involving probabilities (i.e., risky choice) and decisions involving delay (i.e., intertemporal choice). Equivocal behavioral evidence has made this hypothesis difficult to evaluate. However, a combination of functional neuroimaging and behavioral data may allow identification of differences between these forms of decision making. Here, we used functional magnetic resonance imaging (fMRI) to examine brain activation in subjects making a series of choices between pairs of real monetary rewards that differed either in their relative risk or their relative delay. While both sorts of choices evoked activation in brain systems previously implicated in executive control, we observed clear distinctions between these forms of decision making. Notably, choices involving risk evoked greater activation in posterior parietal and lateral prefrontal cortices, whereas choices involving delay evoked greater activation in the posterior cingulate cortex and the striatum. Moreover, activation of regions associated with reward evaluation predicted choices of a more-risky option, whereas activation of control regions predicted choices of more-delayed or less-risky options. These results indicate that there are differences in the patterns of brain activation evoked by risky and intertemporal choices, suggesting that the two domains utilize at least partially distinct sets of cognitive processes.

Wei Z-H., &Li X.S . ( 2015).

Decision process tracing: Evidence from eye-movement data

Advances in Psychological Science, 23( 12), 2029-2041. doi: 10.3724/SP.J.1042.2015.02029

[ 魏子晗, 李兴珊 . ( 2015).

Wu F., Gu Q., Shi Z-H., Gao Z-F., &Shen M-W . ( 2018).

Striding over the “classical statistical inference trap” —Application of Bayes factors in psychological studies

Chinese Journal of Applied Psychology, 24(3), 195-202.

[ 吴凡, 顾全, 施壮华, 高在峰, 沈模卫 . ( 2018).

Wu Y., Zhou X-L., &Luo Y-J . ( 2010).

The neuroscience of intertemporal choices and decision-making under risk and uncertainty

Studies of Psychology and Behavior, 84( 1), 76-80.

[ 吴燕, 周晓林, 罗跃嘉 . ( 2010).

Economic decision-making consists of two traditional problems: Intertemporal choices and Decision-making under risk and uncertainty. Intertemporal choice is divided into impulsivity and self-control. Paralimbic cortex, are preferentially activated by decisions involving impulsivity, including nucleus accumbens, orbitofrontal cortex in the central and middle prefrontal cortex; and regions of the lateral prefrontal cortex and posterior parietal cortex show enhanced changes in activity by self-controlled decisions. Cerebral cortex and amygdala are associated with the deciong-making under risk and uncertainty.

Zhang Y-Y., Xu L-J., Rao L-L., Zhou L., Zhou, Y, Jiang, T-Z, Li, S., &Liang Z-Y . ( 2016).

Gain-loss asymmetry in neural correlates of temporal discounting: An approach-avoidance motivation perspective

Scientific Reports, 6, 31902. doi: 10.1038/srep31902

URL     PMID:4997255

Gain-loss asymmetry in temporal discounting (i.e., when individuals discount gains more than losses) has been implicated in numerous problematic and addictive behaviors, resulting in enormous personal and societal costs. On the basis of findings from a previous study, we speculated that approach-avoidance motivation would modulate gain-loss asymmetry. To test this speculation, we examined the effects of motivation on gain-loss asymmetry by analyzing functional connectivity. We found that approach and avoidance motivation were negatively associated with functional connectivity between the medial orbitofrontal cortex (MOFC) and the dorsolateral prefrontal cortex and functional connectivity between the MOFC and the posterior parietal cortex (PPC) in the gain domain. Only avoidance motivation was found to be positively associated with functional connectivity between the medial prefrontal cortex (MPFC) and the posterior cingulate cortex (PCC) as well as between the MPFC and the insula in the loss domain. Our findings suggest that the relationships of approach-avoidance motivation and neural correlates yielded an asymmetrical pattern between the gain and loss domains in temporal discounting. Thus, we provide new insight into understanding gain-loss asymmetry in temporal discounting.

Zhou L . ( 2017).

Process comparison of risky choice and intertemporal choice: Evidence from eye-tracking method (Unpublished Doctoral dissertation).

University of Chinese Academy of Sciences, Beijing, China.

[ 周蕾 ( 2017).

Zhou L., Zhang Y-Y., Li S., &Liang, Z-Y .( 2018).

New paradigms for the old question: Challenge the expectation rule held by risky decision-making theories

Journal of Pacific Rim Psychology, 12, e17. doi: 10.1017/prp.2018.4

Zhou L., Zhang Y-Y., Wang Z-J., Rao L-L., Wang W., Li S., Li X. S., &Liang Z-Y . ( 2016).

A scanpath analysis of the risky decision-making process

Journal of Behavioral Decision Making. 29( 2-3), 169-182. doi: 10.1002/bdm.1943

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