Beyond process tracing response dynamic in preferential choice case study

Beyond process tracing: Response dynamics in preferential choice Gregory J Koop Miami University Joseph G Johnson Miami University The ubiquity of process models of decision making requires an increased degree of sophistication in the methods and metrics that we use to evaluate models In this paper, we capitalize on recent work in cognitive science on analyzing response dynamics (or action dynamics) We propose that, as information processing unfolds over the course of a decision, the bearing this has on intended action is also revealed in the motor system This decidedly “embodied” view suggests that researchers are missing out on potential dependent variables with which to evaluate their models—those associated with the motor response that produces a choice The current work develops a method for collecting and analyzing such data in the domain of decision making generally, and preferential choice specifically We first validate this method using widely normed stimuli from the International Affective Picture System (Experiment 1) After demonstrating that curvature in response trajectories provides a metric of the competition between choice options, we further extend the method to risky decision making (Experiment 2) In this second study, both choice (discrete) and response (continuous) data correspond to the well-known idea of risk-seeking in losses, and risk-aversion in gains, but the continuous data also demonstrate that choices contrary to this maxim may be the product of at least one online preference reversal In sum, we validate response dynamics for use in preferential choice tasks and demonstrate the unique conclusions afforded by response dynamics over and above traditional methods Keywords: Decision making, response dynamics, methodology, process models, preference reversals, risky decision making Introduction Recent theoretical work in judgment and decision making can be characterized, in part, by a newfound emphasis on the underlying mental processes that result in behavior That is, rather than simply trying to predict or describe the overt choices people make, researchers are increasingly interested in forming specific models about the latent cognitive and emotional processes that produce those decisions Broadly, we might classify these as computational or process models, which consist specifically of production rule systems (Payne, Bettman, & Johnson, 1992, 1993), heuristic “toolboxes” (Gigerenzer, Todd, & The ABC Research Group, 1999), neural network models (Usher & McClelland, 2001; Simon, Krawczyk, Holyoak, 2004; Glöckner & Betsch, 2008), sampling models (Busemeyer & Townsend, 1993; Diederich, 1997; Roe, Busemeyer, & Townsend, 2001; Stewart, Chater, & Brown, 2006), and more To many, including the present authors, this is a welcome and exciting evolution of theorizing in our field With an increase in the explanatory scope of these process models comes the need for advancement in the methodological tools and analytic techniques by which we evaluate them (Johnson, Schulte-Mecklenbeck, & Willemsen, 2008) Traditional algebraic models, such as Savage’s (1954) instantiation of expected utility, were assumed to be paramorphic representations, not necessarily describing the exact underlying mental process of how individuals make choices, but rather what choices people make Therefore, researchers were content—and it was theoretically sufficient—to only examine choice outcomes and the maintenance (or not) of principles such as transitivity and independence (e.g., Rieskamp, Busemeyer, & Mellers, 2006) However, contemporary emphasis on process modeling requires more sophisticated means of model evaluation In the past couple decades, process-tracing techniques such as mouse- and eye-tracking have become popular for drawing inferences about the information acquisition process in decision making (Franco-Watkins & Johnson, 2011; Payne, 1976; Payne et al., 1993; Wedell & Koop & Johnson (2012) Senter, 1997; Wedel & Pieters, 2008; and many more) This large body of work seeks to verify the patterns of information acquisition that decision makers employ, and compare these to the predictions of various process models This represents a boon in the ability to critically assess and compare different theoretical processing accounts Granted, there are some strong assumptions that need to be made when using this paradigm, and some limitations in the resulting inferences (Bröder & Schiffer, 2003, and the references therein; Franco-Watkins & Johnson, 2011; Johnson & Koop, in preparation) Still, this paradigm has proven valuable in acknowledging the importance of bringing multiple dependent variables to bear on scientific inquiry in decision research In the current work, we are not disparaging the contribution of process-tracing techniques to our understanding of decision processes However, we are concerned with a singular shortcoming of this approach In particular, the process-tracing paradigm is focused on patterns of information acquisition, but not necessarily the direct impact this information has en route to making a decision That is, even though this approach is able to monitor the dynamics of information collection, it does not dynamically assess how this information influences preferences or “online” behavioral intentions In fact, it cannot so: the only indication of preference in these tasks remains discrete, in the form of a single button press or mouse click to indicate selection of a preferred option at the conclusion of each trial At best, then, processtracing paradigms can only draw inferences about how aggregate measures (such as number of acquisitions or time per acquisition) relate to the ultimately chosen option, or the strategy assumed to produce that option In response, we would simply propose to dynamically monitor the response selection action as well Just as process-tracing has been used as a proxy for dynamic attention in decision tasks, we propose that response-tracing can be used as a dynamic indicator of preference We begin with some theoretical context and a brief survey of this paradigm’s success in cognitive science before presenting a validation, extension, and application of this approach to preferential choice 1.1 Embodied cognition Our basic premise rests on the assumption that cognitive processes can be revealed in the motor system responsible for producing relevant actions This proposition can be cast as an element of embodied cognition, which is already theoretically popular in behavioral research (for overviews, see Clark, 2002; Wilson, 1999) For example, recent work on the hot topics of “embodied” and “situated” cognition—even now “embodied economics” (Oullier & Basso, 2010)—suggests that our cognitive, conceptual frameworks are driven by metaphorical relations (at least) to our perceptual and motoric structures Indeed, the recent trend in social sciences has been away from classical theories and towards embodiment theories (Gallagher, 2005) Whereas classical theories separate the body from mental operations, theories of embodiment maintain the importance of the body and its movements for cognitive processes The theoretical perspective of embodied cognition can take several forms (see Goldman & de Vignemont, 2009; and Wilson, 2002, for two possible classifications) One strong interpretation assumes that the neural machinery of thought and action are singular and inseparable, whereas a milder assumption, adopted here, is that cognitive operations produce systematic and reliable physical manifestations In general this approach appreciates the close interaction between cognition and the motor system, and questions the reductionistic tendency to study either in isolation (see Raab, Johnson, & Heekeren, 2009, for a collection of papers in the context of decision making) Embodiment theories have been spreading within and beyond cognitive sciences—they have been applied to the fields of learning, development, and education and have found their way into specialized domains such as sports, robotics and virtual environments Contemporary decision models, in contrast, still explicitly (Glimcher, 2009, p 506) or implicitly assume that the motor component of Koop & Johnson (2012) the decision is the final consequence of cognition; at best, they are silent on this relationship This is problematic as it ignores a number of empirical phenomena such as cognitive tuning (or motor congruence) that suggest the potential for motoric inputs to cognitive processing (Förster & Strack, 1997; Friedman & Förster, 2002; Raab & Green, 2005; Strack, Martin, & Stepper, 1988) For instance, Strack, et al (1988) showed how inducing facial muscles to perform the action required of smiling or frowning affected the assessment of a stimulus’ valence accordingly (e.g., cartoons rated as funnier when facial muscles were in a position related to smiling) Förster and Strack (1997) and Raab and Green (2005) found similar effects for gross motor movements such as the flexion or extension of the arm on categorization and association tasks Proprioceptive and motor information may also be directly relevant for decision making in other ways, such as by constraining the set of available options, or altering the perception of available options or their attributes (see Johnson, 2009, for elaboration within the context of a computational model) Some of the processtracing work in decision research is also beginning to acknowledge these connections, such as work that shows the influence of visual attention (measured via eye-tracking) on preference (Shimojo, Simion, Shimojo, & Scheier, 2008) and problem solving (Thomas & Lleras, 2007) Just as the existing work has identified a robust connection from the motor system to cognitive processes, the current work introduces evidence for the reciprocal connection of cognitive processes to the motor system It does so by capitalizing on a recent development in other fields that have employed continuous response tracking paradigms 1.2 Mental operations revealed in response dynamics Most recently, continuous online response tracking has been used in cognitive science as evidence for the “continuity of mind” (Spivey, 2008) This work, here referred to as the study of response dynamics, simply involves spatial separation of response options for simple tasks to allow for continuous recording of the motor trajectory required to produce a response Substantial evidence suggests this trajectory reveals approach tendencies for the associated response options (see Spivey et al., 2005; Dale, Kehoe, & Spivey, 2007; Duran, Dale, & McNamara, 2010, for methodological details) Such recordings have been successfully applied to gross motor movements, such as lifting the arm to point a response device at a large screen (Koop & Johnson, 2011; Duran et al., 2010), as well as the fine motor movements associated with using a computer mouse (Spivey et al., 2005, among others) Essentially, the major innovation is to monitor the online formation of a response, rather than simply the discrete or ballistic production of a response that is typically collected in experimental settings (a single button press, or mouse click) The validity of this research paradigm is supported by work that correlates the neural activity across the cognitive and motor brain regions for several tasks (Cisek & Kalaska, 2005; Freeman, Ambady, Midgley, & Holcomb, 2011), including perceptual decision making (see Schall, 2004, for a review) Response dynamics research has revealed new insights about behaviors such as categorization (Dale et al., 2007), evaluation of information (McKinstry, Dale, & Spivey, 2008), speech perception (Spivey et al., 2005), deceptive intentions (Duran et al., 2010), stereotyping (Freeman & Ambady, 2009), and learning (Dale, Roche, Snyder, & McCall, 2008; Koop & Johnson, 2011) Additional related work has been conducted within the “rapid reach” paradigm (see Song & Nakayama, 2009, for an overview) A concrete example may help to illustrate the basic paradigm (Figure 1) Spivey et al (2005) asked participants to simply click with a computer mouse the image of an object (e.g., “candle,” in Figure 1) that was identified through headphones The correct object was paired either with a phonologically similar distractor (e.g., “candy”), or with a dissimilar control object (e.g., “jacket”) Their results (Figure 1) show the curvature of the response trajectories is affected by the similarity of the paired object—the similar distractor produced an increase in curvature, suggesting a competitive “pull” during the response move- Koop & Johnson (2012) Figure Example of response dynamics paradigm results from Spivey et al (2005) Increased response attraction from a phonologically similar distractor produces greater curvature in the response trajectory (gray line), relative to a dissimilar control distractor (black line) ment caused by an implicit desire to select the phonologically similar distractor The current work presents the first (to our knowledge) true extension of this body of research to the domain within decision research dealing with preferential choice Previous research using this paradigm has focused on tasks such as identification and categorization where objectively correct responses could be determined a priori In contrast, the remainder of the current work will seek to validate the method to situations where preferences are more subjective, and extend it to a traditional risky decision making task among gambles Anecdotal support (e.g., your finger’s movements when selecting a cut of meat in the grocer’s display case) and informal applications (e.g., the online tracking of focus groups’ perceptions during presidential debates) to preferential choice may abound Here, however, we hope to establish the scientific use of this paradigm for decisions in a controlled experimental design We present two experiments using this paradigm that establish its validity and ability to address theoretical predictions We also provide enough detail for researchers to consult as a sort of primer in applying these methods and metrics in their own research Experiment Because this is the first extension of the response dynamics method to preferential choice, our first task is to demonstrate the validity of the method within this domain In order to so, we utilized an extremely wellstudied set of stimuli, the International Affective Picture System (IAPS; Lang, Bradley, & Cuthbert, 2008) The IAPS consists of over 1000 photographs that have been well normed (by approximately 100 participants for each picture) on three dimensions of emotion: affective valence (or pleasantness), arousal, and dominance We focused on the dimensions of pleasantness and arousal under the assumption that preference would be roughly analogous to ratings of pleasantness, given equal levels of arousal Thus we were able to directly test the claim that measures of response dynamics can accurately represent the development of preference 2.1 Methods 2.1.1 General paradigm The general paradigm simply involves participants making choices on a screen as depicted in Figure Participants began each trial by clicking on a box at the bottom-center of the screen Once they did so, this box disappeared and the picture stimuli (described below) appeared in boxes at the upper-left and upper-right of the screen In this way, it was possible to achieve a considerable distance between the initiation and termination of the response, as well as sufficient distance between Figure The general response dynamics paradigm Participants are initially presented with a “Start” button and two empty response boxes, which are then populated with response options once the “Start” button has been clicked 5 Koop & Johnson (2012) the two response options Clicking in the box of their preferred picture recorded their choice, removed the picture response boxes from the display, and began the next trial Immediate, complete, and unadulterated preference for one option would suggest that the response trajectory proceeds in a straight line from the point of initiation to the point of response Deviation from this direct path is interpreted as an attraction to the competing (unchosen) response option (e.g., Spivey & Dale, 2006) In our case, this would suggest that even if a participant selects Picture A, the degree of curvature in the associated response trajectory serves as an indication of implicit and concurrent attraction towards Picture B during the formation of the response—an online measure of relative preference 2.1.2 Participants We recruited 98 employees at a corporate business park to complete the experiment (59 female; age, M = 40.03 years, SD = 11.97; 13 left-handed) Between-subjects analyses did not reveal any effects of handedness Participants signed-up for the experiment at a table in a common area, where other experiment options were also present For their participation, participants received product vouchers worth approximately $10 for use at a company store 2.1.3 Stimuli All stimuli were drawn from the IAPS based off of their previous ratings of average pleasantness and arousal on nine-point scales (Lang, et al, 2008) We selected 140 pictures that ranged from very unpleasant (pleasantness = 1.66) to very pleasant (pleasantness = 8.34), and paired pictures based on their similarity in pleasantness ratings to create 70 trials Arousal rating was held constant (difference < 0.45) within trial pairs These 70 trials were further divided into trial classes (10 pairs per class) depending on similarity in pleasantness ratings between the pictures, ranging from similar (difference ≈ 0) to dissimilar (difference ≈ 6) The experiment was conducted in a professional setting, which resulted in 10 picture pairs being removed at the behest of the employer due to their graphic content The removed trials were more likely to have come from more dissimilar classes because these classes required more strongly negative pictures to achieve such large differences in pleasantness This left slightly unequal numbers of trials in each trial class (see Table 1) Thus, we were left with a total of 60 picture pairs that varied in pleasantness ratings but were each roughly matched for arousal 2.1.4 Procedure After providing informed consent, participants were led to individual testing booths and provided with instruction slides on the nature of the task Participants were told that they were going to be shown two pictures, and they simply had to click on the picture they preferred To insure that the response trajectories reflected the natural accumulation of preference rather than demand characteristics, participants were not told their mouse movements would be recorded, and were given no special instructions or motivations regarding mouse movements Prior to beginning the main task, participants completed a practice trial without stimuli to ensure familiarity with the response process Next, each participant completed five practice trials with increasingly unpleasant stimuli The purpose of these trials was to acclimatize participants to the range of pleasantness they would see in the task and were not included in analyses Following these five acclimatization trials, participants completed the main block of 60 trials The main block was randomized for each participant both for left/right picture presentation, as well as for trial order Immediately following the experiment, participants were given their payment vouchers and thanked for their participation 2.2 Results 2.2.1 Aggregate-level data analysis Our goal for Experiment is to explore whether the response dynamics methodology was valid for a typical preference task Therefore, we will focus on those analyses that we feel are best suited to achieving this end, but are by no means exhaustive We refer the reader to previous work for additional details about the rationale and procedural steps for Koop & Johnson (2012) many of the analyses we perform (in particular, Spivey et al., 2005; Dale et al., 2007; and Duran et al., 2010) The choice data show that participants were globally more likely to choose the picture in each pair that was rated as more pleasant (Table 1)1, and a repeated-measures ANOVA revealed an effect of Similarity on individual choice proportions, F(5, 485) = 184.67, p < 01 These outcome data represent an initial validation of our assumption that the pleasantness ratings in IAPS are an appropriate normed analogue to preference Furthermore, the data suggest that the presentation format and procedure did not have an idiosyncratic effect on choice behavior, and we can dive more deeply into the response trajectories without concern Rather than merely interpreting discrete choices, response dynamics allows us to observe the process underlying these choices Because we recorded mouse position at a rate of 100 Hz, each trial necessarily produces a different number of measurements based on response time For ease of direct comparison, we timenormalized the complete trajectory for each trial of each participant into a series of 101 ordered (x,y) pairs These were calculated by including the initial and terminal x,y-coordinates, followed by linear interpolation of the positional data stream at 99 equally-spaced time intervals (Spivey et al., 2005, established this precedent for all subsequent work) Next, we explored whether the degree of curvature was indeed indicative of increased “competition” from the foregone option In the context of the current task, it stands to reason that selections among pairs of similar stimuli should produce more competition, and less direct response paths, whereas choices made among dissimilar stimuli should contain more unequivocally preferred options and thus more direct paths To assess this claim, we examined those trials in which participants chose the more positive option In highly dissimilar trials (difference > 3), most participants never selected the more unpleasant option This is understandable given the nature of the stimuli, but unfortunately causes a substantial loss of power in within-subjects analyses Most likely, the majority of these selections could be considered “error” trials For example, choice of the less pleasant option within the Difference ≈ trial class may have entailed choosing a picture entitled “Starving Child” over one entitled “Wedding.” Thus, we choose to focus only on those trials where participants selected the more pleasant option, and can therefore quantify the competitive pull of non-chosen, less pleasant options That is, we address the question of whether, given choice of the more pleasant option in a pair, increased pleasantness of the foregone option is associated with increased “pull” revealed by curvature in the response trajectory The resulting aggregate trajectories suggest an effect of Similarity via the predicted ordinal relationships in curvature between trajectories (Figure 3) Choices of the more pleasant option were most direct in the Difference ≈ trial class, where the more pleasant option is most easily identifiable With each successive increase in pleasantness similarity, curvature in the response trajectory also increased This trend culminated in the Difference ≈ trial class, which appears to be subject to the most competitive pull from the non-chosen, less pleasant option As predicted, this pattern indeed suggests increasing preference for the non-chosen option, and an increasingly powerful competitive pull therefrom, as pictures become more similarly pleasant 2.2.2 Individual-level data analysis Trials where difference = were not included in these analyses because there was no meaningful way to divide those trials on the basis of response That is, they were excluded because there is no More Pleasant or Less Pleasant response when pleasantness is held constant The plots shown in Figure necessarily aggregate across participants for clarity and power, but it is important to consider metrics calculated on the level of the individual Figure Response trajectories for selections of the more positive option by difference class Plots are time-normalized to 101 time steps, plotted as offset (in pixels) from trial initiation point Placement of response box is approximate Solid lines (moving from dark to light) represent the Difference = 1, Difference = 2, and Difference = trial classes respectively Dashed lines (again moving from dark to light) represent the Difference = 4, Difference = 5, and Difference = trial classes respectively participant as well Response dynamics provides a number of methods for quantifying such differences visible in the aggregate trajectory plots One benefit of such metrics is that they are done on each individual trajectory, and then averaged across trials within each condition for each participant, which is important given the dangers inherent in working solely with aggregate data (e.g., Estes, 1956; Estes & Maddox, 2005) For example, we calculated measures of absolute deviation (Euclidean distance) from a hypothetical direct response path at each of the 101 time-normalized bins mentioned above Maximum absolute deviation (MAD) is simply the maximum value in this set, whereas average absolute deviation (AAD) is the mathematical average across the entire timenormalized trajectory MAD is better at highlighting differences occurring in the “heart” of each trial, whereas AAD is less susceptible to spurious outliers but constrained by endpoints held in common by each trial We calculated MAD and AAD for each trial, for each participant, and then calculated each participant’s average of these metrics across all trials within each condition where the more pleasant option was selected As expected based on the aggregate response trajectories shown in Figure 3, the analysis of individual data show the six trajectories differ in both MAD, F(5,470) = 34.60, p < 001, and AAD, F(5,470) = 25.60, p < 001 Furthermore, the linear contrast for each metric was also significant (Figure a,b; p < 001), which confirms that the trend visible in the aggregate trajectories was not merely an artifact of averaging Figure Absolute deviation from a direct path in pixels for Experiment (a) Maximum absolute deviation (MAD) and (b) average absolute deviation (AAD) were computed for each trial class in Experiment Similarity in pleasantness was highest in the Difference = trial class and lowest in the Difference = trial class 2.3 Discussion: Experiment The results of Experiment represent an important validation of the response dynamics paradigm within the domain of preferential choice To provide this validation, we utilized extremely well-normed stimuli drawn from the International Affective Picture System (IAPS; Lang, Bradley, & Cuthbert, 2008), and instructed participants to simply select the picture that they preferred in a pair The analyses performed above suggest that response dynamics can be effectively utilized to more fully elucidate the preferential choice process We contend that the curvature in participants’ response trajectories was the product of the similarity in preference between the choice options, as operationalized by normed pleasantness ratings The ordinal relationships in similarity between the six trial classes were manifested in the aggregate response trajectories Selections of the more pleasant options on the most dissimilar trials (Difference ≈ 6) were subject to the least competitive pull, and with each successive increase in similarity, competitive pull (i.e., curvature) increased as well These data support the fundamental response dynamics assumption previously validated in other domains (e.g., Spivey, Grosjean, & Knoblich, 2005): curvature produced in the motor response is the product of competition between response options The general paradigm has been wellestablished in cognitive science, but the key validation provided uniquely by this study is the use of response dynamics in the domain of preferential choice, where responses are based on subjective evaluation rather than objective criteria Given this validation, we can now proceed to apply the method to a traditional risky decision-making task of gamble selection—almost certainly the most common task in decision research over the past few decades Because these stimuli are more complex, it is possible that participants will all of their assessment “offline” before initiating the response movement However, if response dynamics are again able to record the process of preference development, they will offer a substantial increase in resolution relative to the simple outcome analyses (i.e., discrete choice) that have typically been performed on this type of stimuli Experiment We imported the response dynamics paradigm into a standard laboratory risky decision-making task of gamble selection In short, we utilized the same method as Experiment 1, but populated the response Koop & Johnson (2012) Figure Presentation of gambles in Experiment boxes with economic gambles rather than pictures (Figure 5) We conducted Experiment to further the primary goal of establishing the response dynamics paradigm in the field of preferential choice To this end, we will explore several quantitative measures, in addition to those utilized in Experiment 1, that have been reported in the previous literature using this paradigm We will then evaluate how these new metrics contribute to our understanding of risky choice behavior above and beyond existing techniques 3.1 Method 3.1.1 Participants We recruited 197 undergraduate students enrolled in an introductory psychology course to participate in one of two conditions: a Gain condition (N = 110) and a Loss condition (N = 87) Students selected the experiment from an online sign-up site that included a number of experiment options For their participation, students received course credit and a monetary reward based on their performance in the task (as described in section 3.1.3) 3.1.2 Stimuli Stimuli in the form of single (nonzero) outcome gambles were created as follows First, we created one gamble for each success probability of 0.90, 0.80, 0.70, and 0.60 We assigned outcome values to these success probabilities in an attempt to approximately equate EV; we attached outcome values of $60, $70, $80, and $90, respectively, to the success probabilities (e.g., win $60 with probability 0.90, else nothing) Next, we subtracted $10 from the outcome values of these four gambles to create four additional stimuli (e.g., win $50 with probability 0.90), then subtracted $10 from each of those to create our final four stimuli (e.g., win $40 with probability 0.90) Finally, we created by hand every possible pairwise comparison among these twelve stimuli where one gamble had a higher success probability, but the other had a higher outcome value This resulted in a total of 43 trials, to which we also added three trials with a dominant option We then attached negative signs to all of the outcomes in these 46 Gain condition pairs to create a second set of 46 gambles for the Loss condition Note that some of these trials were ultimately excluded from analyses (section 3.2); complete pairings (shown for the Gain condition) can be found in the Appendix 3.1.3 Procedure After providing informed consent, participants were informed that they would earn money based on their responses during the experiment The nature of the experiment required extra time to process the response data and calculate final payments—thus, participants also filled out payment vouchers that linked them to their choice data so that they could be paid at the end of the week in which they took the experiment This process was thoroughly explained to participants by the experimenter and repeated on instruction slides After filling out the payment voucher, participants read through computerized instruction slides that explained the nature of the task Participants were told that they would be playing a series of gambles for real money and that every gamble they selected would be simulated in order to determine a final payment amount The two conditions varied in regards to the exact method used to calculate a final payment in order to avoid the clearly undesirable potential to have students “owing” us money in the Loss condition In the Gain condition, we calculated final payment by taking each participant’s average earnings per trial and dividing that value by ten In the Loss condition, participants were truthfully told that they had received a $10 “endowment” for the 10 Koop & Johnson (2012) task and that every gamble they played would subtract from this amount The same formula used to determine payment in the Gains condition was also used in the Loss condition, only rather than simply taking the average of all gamble outcomes divided by ten, this amount was then subtracted from the initial “endowment” of $10 Participants in both conditions were provided with their respective method and told that, on average, they could expect to earn around $5 Finally, in order to ensure that they understood the manner in which they were expected to indicate a choice, they were shown animated example trials and completed an example trial prior to the main task As in Experiment 1, participants were not informed that their mouse movements were being recorded, and were given no special instructions about mouse movement whatsoever All participants used their right hands to complete the task All participants completed all 46 trials in their respective conditions The order in which gambles appeared was randomized once (for both conditions), and then this single order was reversed for counterbalancing across participants The left/right presentation order of gambles within a pair was also counterbalanced between participants Following completion of all experimental trials, participants were reminded of the date and location of their payment collection window before being dismissed 3.2 Results Experiment represents an increase in the complexity of stimuli relative to Experiment 1, which allows us to ask more complex questions about the psychological processes underlying participants’ decisions This increased complexity also allows us to showcase the diversity of analytic techniques made possible by continuous response tracking, including derivative measures such as velocity and acceleration We will base our analyses on a simple comparison of risk attitudes, which is a pervasive construct in decision research using gamble stimuli such as these In particular, we will compare trials where the “safer” option was chosen to those trials where the “riskier” option was chosen, where risk is operationalized by gamble variance, per convention in the field For these comparisons, we excluded the three trials with a dominant option to keep such “obvious” choices from inflating any measures 3.2.1 Aggregate-level data analysis As in Experiment 1, the choice data (Table 2) provide an initial assessment of whether either the method or the stimuli are idiosyncratic in a way that prevents further generalization These data show that participants preferred the Safe gamble in the domain of Gains, by a margin of three to one In the Loss domain, participants preferred the Risky option, although the relative strength of this preference was not quite as extreme These results are in line with typical risk attitudes across gains and losses (Tversky & Kahneman, 1981), and again affirm that the methodology did not adversely affect behavior, and that the stimuli created for this task were not abnormal Again as in Experiment 1, we first plotted the time-normalized trajectories aggregated across trials and participants (Figure 6) Specfically, to produce Figure 6, we separated an individual’s trials into Risky and Safe choices For each participant, we then averaged across the corresponding trajectories within each Response condition At this point, each participant is represented by a single Risky trajectory and a single Safe trajectory, unless they did not make a single choice of one type across all trials For example, a participant who made all Safe choices would have a Safe trajectory aggregated across 43 trials but would Because most of our stimulus pairs did not differ greatly in expected value, we assumed that gamble variance was an appropriate measure, rather than requiring use of the coefficient of variation (see Weber, Shafir, & Blais, 2004) To prepare the data for subsequent analyses, we recoded the xcoordinates of the mouse movement trajectories as necessary to remove the artifact of left-right presentation order counterbalancing Figure Response trajectories for Gain and Loss domains Plots are time-normalized to 101 time steps, plotted as offset (in pixels) from trial initiation point Placement of response box is approximate Total y-distance of all trajectories is approximately 300 pixels Dashed lines show aggregated trajectories for choice of Risky option, and solid lines show aggregated trajectories for choice of Safe option, separately for Loss trials (gray lines) and Gain trials (dark lines) not have a Risky trajectory Finally, the plots shown in Figure were generated by then aggregating these individual x- and y-vectors across all participants within the associated Domain-Response combination to produce each plotted trajectory, and negating the xcoordinates for all Risky choices Because a few participants in each Domain had fully consistent revealed risk attitudes and never made one type of choice (Risky or Safe), sample sizes varied slightly across conditions (Table for sample sizes) Closer inspection of Figure reveals a number of interesting phenomena For the Gain condition (dark lines), the response trajectories are clearly more direct for the Safe choices (solid lines) compared to the Risky choices (dotted lines) In fact, the Safe choice trajectories never tend towards the Risky option, but the Risky choice trajectories suggest participants briefly consider the Safe option before changing course towards the Risky option they ultimately choose In the Loss condition (light lines), the relative curvature across Risky and Safe choice trajectories is reversed—greater curvature is associated with selection of the Safe option Comparisons across Gains and Losses makes clear that the easiest and most definite choice, as inferred from the directness of the response trajectory, was selection of a Safe Gain, whereas the most difficult and conflicted choice was selection of the Risky Gain Any choice in the Loss domain produced conflict between these two relative extremes, with selection of the Risky Loss seeming slightly easier and less equivocal This interaction between Domain and Response is especially noteworthy in that it parallels the choice data in the current experiment as well as an abundance of previous research (cf prospect theory’s risk-seeking for losses and risk-aversion for gains; Kahneman & Tversky, 1979) Another distinct advantage of collecting continuous positional data is the ability to Figure Velocity of trajectories shown in Figure 6, calculated as average pixel distance per time step across a moving window of seven time steps for Gains (a) and Losses (b) The first time step of the associated window is shown on the x-axis Dashed lines show aggregated trajectories for choice of Risky option, and solid lines show aggregated trajectories for choice of Safe option Bars along x-axis approximate periods of significant divergence (p