1 Introduction

Over the last decades, economists have become increasingly interested in attention. For instance, on the microeconomic level, researchers have proposed that attention may explain behavioral biases such as the endowment effect, the attraction effect or the phenomenon of motivated cognition (e.g., Amasino et al, Reference Amasino, Pace and van der Weele2021; Gabaix, Reference Gabaix2019). On the macroeconomic level, limits to attention may explain how economic agents react to news shocks, form expectations about future prices and how this affects business cycles (e.g., Sims, Reference Sims2003). Alongside these applications, several prominent new theories try to incorporate the role of attention in economic behavior. “Salience theory” explains how prominent features among potential payoffs attract attention and sway decisions, leading to behavioral biases (Bordalo et al., Reference Bordalo, Gennaioli and Shleifer2012, Reference Bordalo, Gennaioli and Shleifer2013). Theories of “Rational Inattention” propose that decision makers direct limited attentional resources to information that is deemed to be most useful (Gabaix, Reference Gabaix2019; Sims, Reference Sims, Friedman and Woodford2010). Finally, sequential sampling models offer a descriptive framework of how processes of information acquisition translate into decision making (Fudenberg et al., Reference Fudenberg, Strack and Strzalecki2018; Krajbich et al., Reference Krajbich, Lu and Camerer2012; Ratcliff, Reference Ratcliff1978).

These theoretical approaches differ fundamentally in their description of economic agents. Some theories, like rational inattention, emphasize personal factors such as individual preferences as a source of attention. Others, like salience theory, stress external contextual influences. This discrepancy mirrors a prominent distinction in psychology and neuroscience, where researchers distinguish between “goal-directed” (also referred to as “top-down" or “endogenous”) and “stimulus-driven” (also referred to as “bottom-up” or “exogenous”) attention processes (Corbetta & Shulman, Reference Corbetta and Shulman2002; Egeth & Yantis, Reference Egeth and Yantis1997; Posner et al., Reference Posner, Snyder and Davidson1980). It is clear from both the neuroscientific literature and everyday experience that both these forces affect attention. As an example, consider going to the supermarket with a prepared shopping list that guides your search, while simultaneously being tempted to make unplanned purchases of highly salient or advertised items.

The distinction between personal and contextual drivers of attention matters for both theoretical modeling and for practical applications. Yet, while some papers in psychology and neuroscience have tried to quantify the influence of these different channels on behavior, as we discuss in more detail below, there has been little work to understand their relative importance. In particular, we aim to identify here how much these attentional variations are predictive of choice, and consequently, how useful they are to the toolkit of empirical economists. These questions become more important as attention measurements such as eye-tracking become cheaper and less challenging to implement. For instance, there have been multiple advances on how to measure attention online, e.g., via mouselabweb (Willemsen & Johnson, Reference Willemsen and Johnson2011), or similar applications in oTree (Hirmas & Engelmann, Reference Hirmas and Engelmann2024), and attention can be even measured via internet-connected webcams (Yang & Krajbich, Reference Yang and Krajbich2021).

In this paper, we propose a novel empirical method to approximate personal and context-driven variation in attention, and illustrate our method in two original experiments on risky choice. Over multiple trials, subjects choose to accept or reject lotteries with equiprobable losses and gains, which vary between trials. While subjects make choices, we record their attention patterns to potential gains and losses using eye-tracking. Our method decomposes attentional variation into two orthogonal dimensions: (1) between-subject variation in attention, measured as the individuals' average attention to specific attributes, and (2) within-subject variation in attention across trials, which is measured as the deviations from the individual-specific average on each trial. We argue that these measures proxy for personal and contextual drivers in our setting: option attributes vary across trials, but not across decision makers, so between-subject variation in average attention should be mostly associated with personal differences. By contrast, within-subject variation in attention, which keeps personal characteristics of the decision maker constant, proxies for contextual influences.

We first show that attention is not well explained by individual characteristics like age or gender, or contextual elements like the size or screen location of gains and losses. This underlines the additional explanatory power that attention can have as a predictor of choice, which we test next. We find that both between-subject and within-subject variation in attention explain risky choices. Between-subject variations in attention to gains and losses correlates with a measure of individual loss aversion. Using standard random utility models, we show that including average individual variation in attention is a significant predictor of the weight allocated to gains and losses in the decision process. This effect is robustly observed across multiple model specifications and remains significant in the context of statistical methods that capture heterogeneous behavior. In addition, incorporating within-subject attentional variation explains an additional, if modest, amount of variation in choice, suggesting context also has an independent influence on choice. Out-of-sample predictions confirm this trend, showing highly consistent but modest improvements in predictive accuracy across subjects, particularly when average individual attention is additionally modeled.

As we explain in more detail in the next section, we contribute to the literature on attention in economic choice in various ways. First, we show how eye-tracking data can be decomposed into two channels that approximate the individual vs. contextual distinction in attentional control, which is commonplace in the neuroscience and psychology literature (and more recently in economics). We also contribute to the literature on risky choice, by showing that both individual and contextual attentional processes are linked with decisions involving risk. Our results show that risk taking is related to both personal, agent-related characteristics involved in deliberate choices, but also to situational factors such as the salience of specific choice options.

2 Related literature

The fields of psychology and cognitive (neuro-)science have long studied attention as a mechanism that reduces demands on limited visual and other cognitive systems by filtering relevant information from the large amounts of information entering our perceptual systems at any moment (e.g. Posner, Reference Posner2011). Recent key empirical findings that show a strong link between visual attention and decisions have attracted the interest of the field of decision science. Specifically, choice options that enter the attentional focus more often and for longer are more likely to be chosen (Krajbich et al., Reference Krajbich, Armel and Rangel2010, Reference Krajbich, Lu and Camerer2012; Lim et al., Reference Lim, O’Doherty and Rangel2011; Pachur et al., Reference Pachur, Schulte-Mecklenbeck and Murphy2018; Polonio et al., Reference Polonio, Di Guida and Coricelli2015) and choice options with higher values attract attention more than those with lower values (Anderson et al., Reference Anderson, Laurent and Yantis2011; Amasino et al., Reference Amasino, Sullivan and Kranton2019; Gluth et al., Reference Gluth, Spektor and Rieskamp2018; Gluth et al., Reference Gluth, Kern and Kortmann2020).

When it comes to characterizing the determinants of attention, the literature makes a fundamental distinction between goal-directed (top-down) and stimulus-driven (bottom-up) channels of attention, as defined in the introduction. Stimulus-driven attention is thought to have a larger influence on explorative decision processes, when individuals do not yet have a specific rule of choice (Fehr & Rangel, Reference Fehr and Rangel2011; Gottlieb et al., Reference Gottlieb, Oudeyer and Lopes2013). Nonetheless, a number of studies have provided evidence that both channels of attention play a role in decision-making (e.g. Corbetta and Shulman, Reference Corbetta and Shulman2002; Orquin and Lagerkvist, Reference Orquin and Lagerkvist2015; Orquin and Mueller Loose, Reference Orquin and Mueller Loose2013). Moreover, empirical and theoretical considerations in neuroscience suggest that the brain may process these types of attention in partially separable neural networks (e.g., Corbetta and Shulman, Reference Corbetta and Shulman2002; Kastner and Ungerleider, Reference Ungerleider2000).

In economic theory, similar distinctions have emerged. The importance of stimulus-driven attention for economic decisions is represented in “salience theory” proposed by Bordalo et al. (Reference Bordalo, Gennaioli and Shleifer2012, Reference Bordalo, Gennaioli and Shleifer2013) and related models like Kőszegi and Szeidl (Reference Kőszegi and Szeidl2013). These models propose functions that map different choice attributes into “salience”, which reflects the ease by which information is detected by the decision maker. Greater salience of an attribute translates into higher weights of said attribute in the decision. In these models, salience operates in a mechanical way, i.e. without any explicit optimization by the decision maker. It is therefore likely to lead to behavioral biases. Indeed, some of the key insights of these models are to account for a variety of behavioral biases such as the Allais' paradox or the endowment effect (Bordalo et al., Reference Bordalo, Gennaioli and Shleifer2012).

By contrast, the importance of goal-directed attention is reflected in economic models of rational inattention (Bartoš et al., Reference Bartoš, Bauer and Chytilová2016; Caplin & Dean, Reference Caplin and Dean2015; Gabaix, Reference Gabaix2019; Sims, Reference Sims2003, Reference Sims, Friedman and Woodford2010). In these theories, the decision maker optimally allocates scarce attention to those information sources or attributes that are most likely to affect the utility of choice. These models offer an answer to the question of how a decision maker can optimally allocate attention before actually knowing the value of the choice (Gabaix, Reference Gabaix2014). Applications have emerged in finance (Peng & Xiong, Reference Peng and Xiong2006), business cycle theory (Maćkowiak & Wiederholt, Reference Maćkowiak and Wiederholt2015), monetary policy (Mackowiak & Wiederholt, Reference Mackowiak and Wiederholt2009), industrial organisation (Dessein et al., Reference Dessein, Galeotti and Santos2016; Fosgerau et al., Reference Fosgerau, Sethi and Weibull2020), and consumer theory (Caplin & Dean, Reference Caplin and Dean2015; Matějka & McKay, Reference Matějka and McKay2015; Reis, Reference Reis2006).

Our exercise is motivated by the seemingly disparate views of the relative roles of agent and context that are inherent in these theoretical approaches. Our goal here is to approximate these attentional processes using readily available measures of attention in laboratory settings, namely eye-tracking, in combination with a novel econometric approach that separates average attention—reflecting individual-differences—from trial-wise deviations in attention—reflecting contextual influences on attention. Most closely related to this endeavor are papers that decompose attention using a number of different methodsFootnote ¹. Fisher (Reference Fisher2021) investigates the role of attention in intertemporal discounting, and shows that both within- and between-subject variation in attention allocation correlate with intertemporal decisions. In addition, random variations in exposure time to different attributes explain about 5% to 10% of intertemporal choices. Ghaffari and Fiedler (Reference Ghaffari and Fiedler2018) attempt to disentangle top-down and bottom-up attentional processes in moral choices. Adapting the well-established empirical result that choices are predicted by the last fixation, they experimentally manipulate the last fixation. Their results indicate that the attribute fixated last is predictive of choice, indicating an effect of bottom-up attention, which they estimate to be responsible for about 11% of the variance in decisions. Third, Towal et al. (Reference Towal, Mormann and Koch2013) perform an eye-tracking experiment on snacks, where they first elicited the value of snacks from participants. They calibrate the parameters of a modified drift-diffusion model (Ratcliff, Reference Ratcliff1978), where the drift rate can depend on the product's value and/or salience, a measure constructed from the perceptual features of the products appearance. Value appears as a more important predictor than salience, with a relative weight that is about 3 times higher. Finally, Navalpakkam et al. (Reference Navalpakkam, Koch and Rangel2010) ask their participants to choose between multiple targets that vary in value and salience, finding a significant effect of both on the decision.

Our paper adds to this literature by providing a statistical approach that decomposes attentional variation into (1) individual-average attention and (2) deviations from average attention on each trial using the same underlying eye-tracking data. This approach enables the researcher to assess to what extent each attention channel contributes to variance in choices using a single model. We adapt the traditionally used multi-attribute utility models to allow for both individual- and trial-wise variations in attention. In the context of our model, these attention channels can alter the weights for each attribute, thereby affecting decisions. In doing so, we elucidate the assumptions under which one can approximate goal-directed and stimulus-driven processes via between- versus within-subject variation in attention and choice.

Apart from our methodological insights, we contribute to a literature about the role of attention in risky choice (Fiedler & Glöckner, Reference Fiedler and Glöckner2012; Pachur et al., Reference Pachur, Schulte-Mecklenbeck and Murphy2018). In particular, we complement findings by Pachur et al. (Reference Pachur, Schulte-Mecklenbeck and Murphy2018), who show that loss aversion parameters are correlated with attention, and that exogenous variations in attention cause shifts in loss aversion. Our paper adds to this evidence, and shows that loss aversion is correlated with between-subject variation in attention. This is in line with our theoretical approach, which associates between-subject variation in attention with mechanisms that are internal to the agent. Additionally, our finding that within-subject variation in attention plays a role in risky choice may help explain the instability of decisions in risky choice across contexts (Bordalo et al., Reference Bordalo, Gennaioli and Shleifer2012; Johnson & Schkade, Reference Johnson and Schkade1989).

3 Experimental design

3.3 Main task

The main task in both experiments consisted of a series of 160 individual decisions involving risk. In each trial, participants were asked to accept or reject a mixed gamble with two equally likely outcomes. The outcomes were always a positive (“gains”) and a negative one (“losses”). Figure 1 shows the sequence of an example trial. At the beginning of the trial, participants were asked to focus on a fixation cross presented in the middle of the screen for a jittered period of time (300–1100 ms). This ensured that in each decision period eye fixations started from the same central position and that attention was not biased towards a single location. Then the two potential outcomes appeared at each side of the screen, with the left stimulus located at ( $x=480$ px, $y=580$ px), and the right one at ( $x=1420$ px, $y=580$ px). This wide separation between lottery options along the x-dimension (of approximately ${25}^{\circ }$ of visual angle) ensured that eye movement patterns can be well separated during the analysis stage (see Figure S1). The location of gains and losses was counterbalanced, such that they had an equal chance of appearing on the left or right in each trial.

The participants were asked to press the Up-Key on the keyboard to accept the gamble or the Down-Key to reject it. Subjects were given a period of 5 s to make the decision. If the subject did not respond within those 5 s, a message appeared on the screen reminding participants to ‘Respond Faster’. Participants were aware that if they did not respond within the 5-second period, they would receive the loss outcome of that trial in case it was selected at random at the end of the experiment. The limit on the decision time was implemented to ensure a predictable and swift experiment for each participant, and to avoid participant fatigue, which can lead to loss of eye-tracking data (e.g., due to closing eye-lids). To provide ample time for decisions while keeping the experiment reasonably short, we estimated the average decision times from prior research using an equivalent task setup (average decision time = 1400 ms; Engelmann and Tamir, Reference Engelmann and Tamir2009; Engelmann et al, Reference Engelmann, Meyer and Fehr2015; Reference Engelmann, Berns and Dunlop2017), which matches that of the current study (Mean RT = 1400 ms, SD = 712 ms). To allow for some deviations from the average time during more difficult trials we tripled the average estimate from previous studies and rounded up to 5 s. This approach was successful: In total, only 47 of the 14,372 trials included in the cleaned dataset exceeded the time limit; these ‘miss' trials were excluded from the analysis. Moreover, in 95.76% of the trials, participants made a decision within 3 s. This means that the time constraint was indeed not binding, and that it was unlikely to impact subjects' decision process. In experiment 2, the trial continued with a question of how confident the subject was about their decision, which was the only difference between the two experiments (see Fig. 1).

Fig. 1

Example of Experimental Trial Initially, a white fixation cross is shown for a random duration that is jittered between 300 and 1100 ms. The prospect is then presented. Participants then communicated their decision by pressing the up or down keys of the keyboard to accept or reject respectively. Feedback informed participants what option they had chosen before the next trial began in experiment 1. Experiment 2 differed only in that participants were asked to rate their confidence before the next trial

The attributes presented on the left and right were pseudo-randomized, such that the subject would never observe a loss or a gain more than three consecutive times on one side. The values of the Gains and Losses varied across trials. The gains fell between 20 and 38 ECU (experimental currency units) in steps of two units (10 cases). The losses ranged from − 13 to − 27 ECU in steps of two (8 cases). Gains and losses were independent from each other, and participants observed all possible combinations between gains and losses twice (80 trials per session in 2 sessions).

3.5 Eye-tracking data acquisition and pre-processing

Fixation points were carefully calibrated using a 9-point calibration at two time points in the experiment (before the start of the experiment and after 80/160 completed trials). Furthermore, throughout the experiment, gain and loss attributes were clearly separated by presenting one attribute on the left and another on the right of the center. This clear separation of lottery attributes on the screen allowed us to specify well-defined and non-overlapping regions of interest and thereby to improve the identification of fixations. Next, using k-means, we clustered the fixations along the horizontal axis representing fixation areas for left and right gamble attributes, and central fixation, which occurred only at the beginning of each trial. We ignore the vertical position for clustering, since all the stimuli were positioned at the same vertical location. This allowed us to discriminate between fixations for each outcome (left and right ROI) and central fixations (see Supplementary Fig. G4). Finally, K-means clustering was performed for each session separately, as separate calibrations were performed for each session.

Table 1 shows the number fixations for each region of interest by their order of occurrence. A large majority of the first fixations are on the centre (90%), indicating that subjects followed task-instructions to focus on the fixation cross between trials. Most subsequent fixations go to the left first (68.9%), reflecting a commonly observed upper-left location bias (Orquin & Mueller Loose, Reference Orquin and Mueller Loose2013).

Table 1

Number of fixations by order of Fixation and Region of Interest

Fixation	Left	Right	Total
1	10,463	3195	13,658
2	2859	9780	12,639
3	5265	2057	7322
4	922	1906	2828
$>5$	922	876	1798
Total	20,431	17,814	38,245

We focus our analyses of the eye-tracking data on the dwell times, defined as the period participants fixate on a lottery attribute throughout one trial. We do this, because dwell times are the dominant measure of attention in the literature. Another measure, the number of saccades or switches of gaze between options, are less informative for our purpose. As shown in Table 1, the majority of trials do not contain more than three fixations, hence this number has little variation across trials and participants.

4 Empirical strategy

Our empirical strategy proceeds in several steps. First, we aim to establish that attention is not a direct function of other observable variables like choice attributes or standard demographics, as this would make it unlikely that attention adds explanatory power as a predictor in choice models. Second, we aim to separate attentional variation into individual and contextual drivers to approximate the common distinction in cognitive science between goal-directed and stimulus-driven attention. To accomplish this, we decompose attention into between-subject and within-subject variation as proxies for these drivers. Third, we aim to understand the relation of both types of attentional channels with choice behavior. We model choice via a standard random utility model, which allows us to estimate the decision weights on positive and negative lottery payoffs. Decision weights, in turn, relate to loss aversion. We then correlate the individual average attention with these estimated weights. Finally, we compare how the addition of the two types of attention affects the fit of standard empirical models of risky choice. In the remainder of this section, we discuss these conceptual steps in turn.

Before we proceed it should be noted that, when it comes to attentional measures, eye-tracking provides a rich data set from which different measures of attention can be generated. The most commonly used measures, which are the focus of our analysis, are the number of fixations directed to an area of interest (AoI), the total or relative fixation duration on an area of interest, or which stimulus was attended first/last.Footnote ² For brevity, we focus on the dwell times (total time spent looking at an attribute, after log transformation) in our main analyses, but add supplementary analyses with alternative measures in the appendix when we cannot include these in a parsimonious manner in the main text.

4.2 Attention decomposition

As we argued in the introduction, attention may affect choice via both individual and contextual variation. To understand this better, we decompose attentional variation into two orthogonal measures. First, we calculate each individual's average attention for each specific stimulus/attribute (i.e., Gains and Losses). Let $a_{x,i,t}$ be the allocated attention to attribute $x\in \{Gain,Loss\}$ by individual i in trial $t\in \{1,...,T\}$ . We define the average-attention measure ${\overline{a}}_{x,i}$ as the standardized average attention to attribute x by individual i across all trials.

(1) $\begin{array}{cc}{\overline{a}}_{x,i}:=& \frac{\frac{1}{T}\left(\sum _{t=1}^T,a_{x,i,t}\right)-{\overline{a}}_x}{sd\left(a_x\right)}.\end{array}$

where ${\overline{a}}_x$ and $sd\left(a_x\right)$ are the sample mean and standard deviation of the attention measure for attribute x. Thus, this variable reflects how much more participant i attends to attribute x compared to the whole sample (measured in standard deviations).

Our second measure of attention captures the trial-wise deviations of attention from the individual averages for each attribute. The trial-wise deviation of attention, defined as ${\tilde{a}}_{x,i,t}$ , is calculated as in Eq. (2). This variable reflects how much more participant i attends to attribute x in trial t compared to the participants' average behaviour (measured in standard deviations).

(2) $\begin{array}{cc}{\tilde{a}}_{x,i,t}:=& \frac{a_{x,i,t}-\frac{1}{T}\sum _{t=1}^T{a}_{x,i,t}}{sd\left(a_x\right)}.\end{array}$

In our study, participants do not receive any feedback about their decisions until the end of the experiment. The only variables that vary across the trials are the values of the lottery outcomes and where they are presented. All participants undergo the same trials but in a different order. This implies that between-subject variation in attention reflects personal differences, and can thus be considered a proxy for attention driven by personal goals and characteristics, which is often associated with goal-directed or top-down attention. By contrast, within-subject variation in attention keeps individual characteristics constant, and hence reflects elements of the decision context, such as the location of gains and losses on the screen (which was randomized). Note that this interpretation of our decomposition relies on some untested assumptions, most notably the absence of interactions between contextual variables and the goals or preferences of individuals. An example for the presence of such interactions is when participants differentially attend to an attribute once the attribute value crosses a threshold (e.g., losses become more important if they have a value that is higher than some reference point). In such a case, this individual effect will be partially captured by trial-wise deviations of attention instead of the average attention. If such interactions exist, the model will overestimate the importance of contextual factors, as individual variations will be wrongfully attributed to context.

4.3 Modeling the decision process

The key part of our analysis concerns the role of attention in decision making. To conceptualize the decision making progress, we use a standard random utility model (RUM; McFadden, Reference McFadden1980). The general specification of our model is described by Eqs. (3) and (4).

(3) $\begin{array}{cc}P(D_{i,t}=accept)=& {(1+exp\left\{V_{i,t}\right\})}^{-1},\end{array}$

(4) $\begin{array}{cc}{V}_{i,t}=& {\alpha }_i+{\omega }_{G,i}{G}_t+{\omega }_{L,i}{L}_t.\end{array}$

Here, ${\omega }_{G,i}$ , and ${\omega }_{L,i}$ can be interpreted as weights on the potential gains and losses that determine the value of the lottery and hence the probability to accept it.

We estimate the RUM using a logit mixed model with random intercepts and slopes. We allow the covariance matrix of the random intercepts and slopes to be unstructured (i.e., non-zero covariance between errors). Additionally, we estimate the best linear unbiased predictors (BLUPs; Liu et al, Reference Liu, Rong and Liu2008) for ${\alpha }_i,{\omega }_{G,i}$ , and ${\omega }_{L,i}$ for each individual. Mixed models assume that each of the parameters is composed of a mean and an individual error term (i.e., random slopes and intercepts), which are not directly estimated but included in the covariance matrix of the decision models. Therefore, mixed models estimate the distribution of these individual errors. Based on these estimated distributions and the individual decision data, we can calculate the posterior expectation of these errors (i.e., BLUPs). BLUPs thus reflect predictions for the individual parameters that come from a common distribution, but also incorporate the components of the individual decisions.

The goal of our main analyses is to test whether the attention indices can capture the differences in the individual model parameters ( ${\alpha }_i,{\omega }_{G,i}$ and ${\omega }_{L,i}$ ). There are two components to this goal: first, on the behavioral level we wish to confirm that attention correlates with these individual parameters, which would indicate that attention is an important cognitive process that supports choice; second, on the modeling level we wish to demonstrate that we can credibly use attention as a proxy for the individual parameters reflecting heterogeneous behavior in contexts where these parameters are unidentifiable. This can occur for instance in the context of mixed regression models, which can increase in complexity to the point of becoming unidentifiable, especially when aiming to fulfill the common requirement of using maximal random effects structures (Barr et al., Reference Barr, Levy and Scheepers2013). We aim to test whether the use of attention variables offers a parsimonious solution for cases where the model complexity is high and these models are not identifiable.

To address the first goal, we correlate the individual parameters of choice with individual attention variables. We then ask how much of the variability in the individual parameters can be explained by individual average attention and other individual characteristics. To do so, we use a Shapley value analysis described above. The Shapley value regression analysis provides a fair and consistent estimation quantifying the contribution of each attention variable despite the potentially high degree of correlation between them. The Shapley-value analysis is performed using the SHAPLEY2 package in Stata17 (Wendelspiess Chávez Juárez, Reference Wendelspiess Chávez Juárez2015).

4.4 Effects of separate attention channels on choice

Finally, we analyse whether the different measures of attention can improve empirical models of choice. To accomplish this, we estimate the model defined in Eqs. (3) and (4) and incorporate the attentional measures as moderators for the weights on gain and loss values, as follows:

(5) $\begin{array}{cc}{V}_{i,t}=& {\alpha }_i+{\omega }_{G,i}{G}_t+{\pi }_{G,\overline{a}}{\overline{a}}_{G,i}+{\pi }_{G,\tilde{a}}{\tilde{a}}_{G,i,t}+{\omega }_{L,i}{L}_t+{\pi }_{L,\overline{a}}{\overline{a}}_{L,i}+{\pi }_{L,\tilde{a}}{\tilde{a}}_{L,i,t}+{ϵ}_{i,t}\end{array}$

where the main effects of the gains and losses are represented by ${\omega }_{G,i}$ and ${\omega }_{L,i}$ respectively. The moderating effects of individual-average attention are captured by ${\pi }_{G,\overline{a}}$ for the gain values and ${\pi }_{L,\overline{a}}$ for the loss values. Similarly, the parameters ${\pi }_{G,\tilde{a}}$ and ${\pi }_{L,\tilde{a}}$ capture the moderating effects of the trial-wise deviations of attention to gain and loss values respectively.

To evaluate the contribution of attention to explaining decisions, we consider two types of often-used logit models. First, we consider models that have random intercepts but a common slope, i.e. ${\omega }_i=\omega$ , which is a standard approach in economics. To evaluate the role of attention, we estimate the model with and without interactions of individual attention and trial-wise attention to the attributes (gains and losses), and compare standard measures of model fit.

Second, we address our second main goal outlined in Sect. 4.3 and consider more elaborate mixed models (Barr et al., Reference Barr, Levy and Scheepers2013) that include random effects for the coefficients of the attributes (slopes). These models benefit from a large number of observations per person that are typically elicited in neuroscientific experiments, but not economic ones. We can exploit the large dataset we have collected (up to 160 observations per participant), which enables us to estimate these types of models. Importantly, this approach allows us to test the contribution of attention to the model fit after including the individual heterogeneity.

6 Discussion and conclusion

In this study, we investigate the relationship between attention and the decision process. Participants take part in an incentivized experiment involving lotteries with positive and negative outcomes, while their eye movements are recorded using eye-tracking. We analyze: (1) the factors influencing attention, (2) how attention patterns relate to individual differences in decision-making, (3) whether including attention in commonly used models for decision-making processes can enhance model fit, and (4) whether a single attention measure or a decomposition into two attention channels reflecting individual average attention and trial-wise deviations of attention further improves model fit.

Our results show that attention is weakly associated with both contextual factors, such as the position of the information, and individual factors, such as gender and age. Importantly, while some factors are significantly correlated with variations in attention, their contribution is small, leaving most of the variance in attention unexplained. These results suggest that measures of attention share little variance with common measures related to individual and contextual factors, and are therefore in a position to explain components of the variance of decision making processes above and beyond these measures.

This is exactly what our subsequent results show. Specifically, we first demonstrate significant correlations between decisional and attentional loss aversion. We subsequently show that attention is a significant moderator of decision weights that relate attribute size to choices in the context of a modified random utility model. Most importantly, we show that a decomposition of the attention data into individual average attention and trial-wise differences in attention to a given attribute adds explanatory power to models of the decision process. Specifically, when considering individual average attention, our findings show that when participants spend more time than the average person looking at an outcome, this increases the importance of this outcome for the decision. In addition, trial-wise deviations in attention also matter: if a subjects spends more time looking at a particular outcome in a given trial (compared to their experiment-wide average focus time on that attribute reflected by the individual average attention), our results indicate that a higher weight is assigned to that outcome during that trial. This result mirrors prior work on the causal effects of attention, showing that manipulating presentation times for a given attribute and on a given trial, leads to a greater influence of that attribute on the decision process (e.g., Hirmas and Engelmann, Reference Hirmas and Engelmann2023; Olschewski et al, Reference Olschewski, Rieskamp and Scheibehenne2018; Pachur et al, Reference Pachur, Schulte-Mecklenbeck and Murphy2018). Although the sample size of our study is comparable with many other studies involving eye-tracking (e.g., Alós-Ferrer and Ritschel, Reference Alós-Ferrer and Ritschel2022; Devetag et al, Reference Devetag, Di Guida and Polonio2016; Hausfeld et al, Reference Hausfeld, von Hesler and Goldlücke2021), we nonetheless perform a number of robustness checks. We perform two analyses to explore whether the sample size might affect our results. First, we perform a Monte-Carlo simulation, where we randomly pick sub-samples of different sizes from our total sample and estimate the parameters of our decision model. The results displayed in Appendix section D show that after 60–70 participants or more, the results become stable and stay within the 95% confidence intervals of the full-sample estimations. Moreover, we also inspect whether using only the data from Experiments 1 and 2 generate different results. In Appendix table E, we show that the results remain relatively stable across experimental samples. Specifically, attention remains a significant moderator for the influence of value on choice when using the samples of each experiment, as originally reported for the whole sample.

Since we have established that the attention models produce robust results and have better descriptive power, we next ask whether the attention models also generate better out-of-sample predictions. In order to analyze the predictive power of our models, we perform a simulation exercise in which we randomly select 80% of the trials for each participant, estimate the decision models (baseline and our attention-based models) with that data and predict the decisions of the remaining 20% of the trials. Our results (reported in Appendix F) show that the models including only individual-average attention and the model including both individual and trial-wise attention outperform the baseline model (without attention) in out-of-sample predictions. In addition, we find that individual average attention shows a consistent improvement in predictive power, outperforming the baseline model in 90.5% of the simulations; while the full model, that includes trial-wise deviations only outperforms it in 72.6% of the cases. It is important to note that even though the out-of-sample predictions of the model with individual-average attention are consistently superior, the marginal improvement in the predictions is rather small (from 87.7% correct predictions in the baseline model to 88.0% correct in the individual-average attention model, F3, panel A). We attribute the small differences to the already strong predictive power of the baseline model. When comparing the out-of-sample predictions across participants (F3, panel B), we find that including attention in the model increases the predictive accuracy by up to 2.84 percentage points (individual attention model) and 5.9 percentage points (full model) for those individuals for which the baseline predictions are relatively low. These results show that adding individual average attention to the baseline model leads to modest but consistent improvements in out-of-sample predictions, while the inclusion of trial-wise deviations leads to specific improvements for some of the most volatile participants.

Finally, we would like to point out a number of methodological advances brought forward by our modeling exercise: (1) our rich eye-tracking data gave us an opportunity to compare different attention measures and make inferences on their relative suitability for decision models. We find that a decomposition of the attention data into individual average attention and trial-wise differences in attention leads to superior model fits and modest improvements in predictive power. Our current recommendation for the analyses of attention data obtained via eye-tracking is to use the richer data obtained from the attention channel decomposition outlined here, but future research is required to develop a more nuanced understanding of the different contexts in which each of the attention measures is superior. (2) We compare different modeling approaches from economics and other fields. We find that the inclusion of random slopes can reduce the predictive power of some attention measures as a moderator, but does not eliminate it. In such cases, relative measures, like the proportion of time spent looking at an attribute, are likely the best predictors of individual differences in attribute relevance, consistent with the existing literature (Rahal & Fiedler, Reference Rahal and Fiedler2019). While random slope models are the preferred model type in some fields (e.g., Meteyard & Davies, Reference Meteyard and Davies2020; Hoven et al, Reference Hoven, Hirmas and Engelmann2023), they increase the complexity of mixed models often to the point of non-convergence (Barr et al., Reference Barr, Levy and Scheepers2013). Our results suggest that in cases when random slopes cannot be modeled—e.g., when the amount of data does not match model complexity—the inclusion of attention variables, specifically individual average attention, may compensate for some of the otherwise unexplained variance.

Among economists, there is some expectation that attention can be a “unifying” variable that ties together hitherto separate phenomena (Gabaix, Reference Gabaix2019). Similarly, the potential of attention and eye-tracking are attracting scholars from new research fields, such as management and organization science (e.g., Orquin and Mueller Loose, Reference Orquin and Mueller Loose2013; Meißner and Oll, Reference Meißner and Oll2019), and we expect this trend to increase both for researchers and in commerce as attention measurements such as eye-tracking become cheaper and less challenging to implement, e.g., via advances in online measures of attention via mouselabweb (Willemsen & Johnson, Reference Willemsen and Johnson2011), similar applications in oTree (Hirmas & Engelmann, Reference Hirmas and Engelmann2024), and internet-connected webcams (Yang & Krajbich, Reference Yang and Krajbich2021). Overall, our results support attention as a useful variable to understand the decision making process. We show here that both individual and contextual variation matter, suggesting a role for modeling approaches that emphasize individual agency and salience.

Moreover, the framework we propose here can be flexibly applied to different experimental contexts and can help answer a number of questions that are crucial to fulfill this promise of attention research. For instance, future research should address how the relative influence of contextual versus individual drivers of attention varies across environments? Moreover, how do various aspects of salience affect stimulus-driven attention and the occurrence of behavioral biases? Finally, how do individual differences in attention correlate with personal characteristics and decision parameters? Answering these questions will be valuable to both theorists and policy makers alike. More generally, our approach demonstrates the fruitful interaction between cognitive (neuro-)science and economic analysis.