Previous studies of strategic social interaction in game theory have predominantly used games with clearly-defined turns and limited choices. Yet, most real-world social behaviors involve dynamic, coevolving decisions by interacting agents, which poses challenges for creating tractable models of behavior. Here, using a game in which humans competed against both real and artificial opponents, we show that it is possible to quantify the instantaneous dynamic coupling between agents. Adopting a reinforcement learning approach, we use Gaussian Processes to model the policy and value functions of participants as a function of both game state and opponent identity. We found that higher-scoring participants timed their final change in direction to moments when the opponent’s counter-strategy was weaker, while lower-scoring participants less precisely timed their final moves. This approach offers a natural set of metrics for facilitating analysis at multiple timescales and suggests new classes of experimental paradigms for assessing behavior. Game theory typically models strategic human behavior using scenarios with decision constraints that poorly represent real-world social interactions. Here, the authors show it is possible to model dynamic, real-world strategic interactions using Bayesian and reinforcement learning principles. Paradigms like Matching Pennies, Trust/Ultimatum Games, and Prisoner’s Dilemma have used simple choices in highly standardized contexts to yield key insights into social decision-making in humans and animals12. These game theory paradigms draw upon a vast literature detailing how rational players would behave15, yet studies comparing human behavior to these normative solutions have found that humans often violate rational predictions16.Over the last 15 years, game theory has been foundational in establishing cognitive and biological mechanisms of strategic decision making18. Moreover, while game theory has made progress in generalizing optimal strategies for games in continuous time and space, such as duels and auction bidding22, considerably less has been done to quantify highly dynamic behavior in cases where optimal strategies remain challenging to compute. While game theory has proven highly successful in analyzing various sorts of equilibria players might settle into, considerably less is known about the processes by which these equilibria are reached24. As a result, it is desirable to develop analytical tools capable of quantifying strategic dynamics while maintaining the mathematical rigor that has made game theory such a productive framework.While a central aim of game theory is to describe how people should make decisions, describing how humans actually make decisions is of particular interest to social scientists. Indeed, many of the features that have made game theory paradigms analytically attractive—discrete choices, turn-taking, known payouts—are abstractions away from real-world social interactions. For instance, when buyers haggle over the price of a good, they interact in real time, using a combination of nonverbal cues, strategic planning, perspective taking, and value judgment. Their continuous, dynamic interaction thus poses a challenge to any computational framework for the study of social decisions31, game theory21, and nonparametric Bayesian modeling34 to capture these social dynamics. Our approach produces models of behavior that are both flexible enough to capture the variability present in a continuously evolving strategic setting and powerful enough to quantify strategic differences across participants, trials, and even individual moments within trials. Our testbed for these ideas is a competitive task in which human participants played against both a human opponent and a computer opponent in a real time, movement-based game. This paradigm generates a rich complexity in individuals’ behavior that can be succinctly described by individualized, instantaneous policy and value functions, facilitating analysis at multiple timescales of interest. This approach quantifies complex interactions between multiple agents in a parsimonious manner and suggests new classes of tractable paradigms for studying human behavior and decision making.Here, we introduce a computational modeling framework that borrows from recent advances in reinforcement learning18. The task was viewed on a computer screen and played by two players: an experimental participant (N = 82) who controlled an on-screen circle, or puck, and another long-term participant who controlled an on-screen bar, acting as the goalie. Hereafter, we will refer to these players as the participant and the opponent, respectively. The puck began each trial at the left of the screen and moved rightward at a constant horizontal speed. The participant’s objective was to score by crossing a goal line located at the right end of the screen behind the opponent. The opponent’s task was to block the puck from reaching the goal line. Each player moved his or her avatar using a joystick. Both players were only able to control the vertical velocities of their respective avatars, though the puck and bar had distinct game physics  reported that they thought the human opponent was better, and the other half reported that the computer algorithm was better, suggesting that the computer algorithm did, in fact, play at a level comparable to both human opponents.Participants played the penalty shot task in an fMRI scanner. Here, we report only the behavioral data from this experiment. On each trial, participants played against a randomly selected opponent. On half of the trials, this was a human opponent, located outside the scanner . On the other half of trials, the opponent was a computer algorithm. This opponent followed a track-then-guess heuristic in which it attempted to match the puck’s vertical position (with a variable reaction time) before randomly choosing a direction to move at maximal speed near the end of the trial. This choice was motivated not only by pilot data that showed such a strategy was difficult for participants to exploit, but also by past work analyzing the anticipatory strategies of goalkeepersy-axis). For example, Participant 3 . While it is possible to model these time series directlynts Fig. . That ist is an action, at, and the probability of this action given a state of the world st is given by the policy function: Π = p, where we let st denote a vector of predictors at each timepoint and ω is a binary variable indicating the opponent’s identity 25. In our case, we define the action space as a single binary variable, with 1 indicating a change in direction and a 0 indicating continuation along the current trajectory. However, the state s remains continuous and includes 7 predictor variables: the x and y positions of the puck, the y position of the bar, their respective vertical velocities, the time since the occurrence of the last change point , and an opponent experience variable that ranged from 0  to 1  that was specific to each opponent and reflected potential strategic adaptation over the course of the experiment. Finally, we simplify our notation, defining π = p. Because our input space is of moderate dimension, a model for π will be a continuous function of s instead of a large matrix, as it would be for a model with a discrete state space. Our contribution is to show that nonparametric methods allow us to address the challenge of modeling π using only sparsely sampled data.Viewed through the lens of reinforcement learning, the decision of whether to switch direction at time 38. Our model selection was guided by three requirements: First, the model should be flexible enough to capture the rich diversity of player behavior. Second, the model should appropriately handle a small number of change points (≈4.6%) with an input space of moderate dimension. Third, the model should avoid overfitting while providing a principled estimate of uncertainty. For these reasons, we fit each participant’s data using a Gaussian Process (GP) classification model.Our decision to model change point probabilities as a function only of states and opponents means that the data at each time are independent of each other given these variables. Thus, our approach is also equivalent to a binary classification problem. Binary classification is well-studied, with many methods available, including logistic regression, support vector machines, and neural networks39. In the same way that a sample from a normal distribution is a real number and a sample from a Bernoulli distribution is a binary variable, a sample from a GP is an entire function  or spatial density (d = 2)). Gaussian Processes have the advantage of providing a principled, Bayesian measure of uncertainty over functions32, and while some types of GPs are equivalent to infinitely-wide, single-layer neural networks, they have been shown to outperform neural networks in avoiding overfitting on small to moderate datasets42. Moreover, they are the method of choice when modeling time courses based on sparse or irregularly-sampled data44. Thus, GPs offer competitive modeling performance with the added benefits of uncertainty estimation and differentiability.A Gaussian Process (GP) is a distribution over functions. GPs are widely used in spatial and time series modeling for their combination of flexibility and ability to generalize from even modest datam(x)  and a covariance function k that defines the correlation between values of f at different input points32:f(x) is a random function drawn from the GP. By definition, the joint distribution of the observed dataset d, mean μi = m(xi), and covariance More formally, a GP is fully characterized by a mean function s and opponent identity ω. Following standard techniques45, we assumed that binary change point observations ai were Bernoulli distributed according to the policy π and that the policy itself was related to an underlying GP:−1 is the inverse cumulative normal distribution  and f with mean 0 and kernel function k. Because we assume that f is a smooth function of its inputs, we choose the common radial basis function (RBF) kernel32:i indexing input variables and σi and λi hyperparameters setting the overall magnitude of the covariance and the length scale of correlations along each dimension, respectively. Here, x includes both s and ω. Even though ω is a discrete parameter, we approximate it as a continuous variable, as is often done in Bayesian modeling using GPs46.As stated above, we chose to model players’ policies via a GP classification model that predicted an upcoming change in the puck’s direction from the current state We found that our GP classification model accurately captured the diverse patterns present in participants’ data Fig. . That isModel fits revealed that participant policies were most strongly affected by the participant’s own velocity, followed by the time since the previous change point and the participant’s own vertical position . That is, participants were more weakly influenced by their opponent’s position and velocity than by their own movements, suggesting that their strategies were only secondarily reactive. Moreover, hyperparameters for the opponent experience variable, which captured changes in strategy over the course of the experiment, were large, indicating that their strategies quickly stabilized and remained consistent throughout play. In fact, trajectories for most players did not differ markedly in shape between the first and last ten trials  with respect to the opponent’s position and velocity (see Methods). We then used these gradients to define a moment-by-moment sensitivity index. Since the gradients of the GP measure the degree to which small changes in the current game state affect the participant’s probability of changing course, gradients with respect to the opponent’s position and velocity capture the degree to which the participant’s current behavior is sensitive to the opponent’s actions.We next sought to quantify how much participants’ switching behavior changed as a function of the opponent’s actions. Because our change point policy model is based on a smooth Gaussian Process, we can quantify this sensitivity using gradients of the GP Just as switch probability changes dynamically with game state, sensitivity to opponent action varies throughout the trial. Figure The sensitivity metric defined above represents a particular moment-by-moment measure of the degree to which one player (the participant) is coupled to the actions of the other (the opponent). Based on our prior expectation, we chose a combination of sensitivities to opponent position and velocity, but other combinations are equally plausible. In fact, one could define a sensitivity metric to each input variable individually. Here, we show that such an approach produces a principled characterization of participants’ behavior across multiple timescales. Indeed, when aggregated at the participant level, these indices fully characterize the policy model.We defined one sensitivity for each input variable equal to the square of the gradient along each input direction (see Methods). This yielded eight new sensitivity indices (seven for state plus one for opponent identity) in addition to the opponent action sensitivity defined above. However, our previous index can be defined in terms of these new indices, so there are only eight unique values in the set. The most important feature of these new indices is that, like the policy, they are defined moment-by-moment, but can be aggregated across multiple levels of granularity, including trial and participant averages. As in classic analysis of variance (ANOVA), we can consider each index value at each data point as the sum of three terms: a participant-level mean, a trial-level offset from this mean, and a residual specific to the data point. Likewise, we can estimate variances within trial , across trials, and across our participant population. As in ANOVA, the sum of these variances, appropriately weighted, equals the total variance in the data. Normalizing by this total variance yields a set of three positive terms that sums to 1:σ2 is indeed correlated with the variance in probability of switching across timepoints for each participant . Likewise, Fig. R = −0.64, t = 7.43, p < 0.0001). In both cases, this is exactly what we expect: the noise hyperparameter for a classification model is related to the variance in its predictions, while low sensitivities correspond to long correlation length scales. Thus, our gradient-based sensitivity metrics naturally extend GP hyperparameters to the timepoint level, providing a principled characterization of strategy suitable for analysis at multiple timescales.Finally, we note an important relationship between participant-level sensitivities and model hyperparameters. Because Gaussian Processes, like Gaussian distributions, are completely characterized by their mean and covariance, summaries of a Gaussian Process taken over the data can only be functions of the hyperparameters that define the mean and covariance. That is, we expect on mathematical grounds that our sensitivities, when averaged across an entire participant’s data, should be related to the model’s hyperparameters : the expected value of taking action a in state s against opponent ω and playing according to policy π thereafter. As indicated by notation, this value is policy-dependent. That is, each policy π uniquely determines a value function Qπ . The action value model took as inputs the instantaneous state, opponent, and observed action at that time and attempted to predict from those data whether the participant subsequently won the trial. We used the same Gaussian Process classification approach as before, only this time predicting the trial outcome and using the participant’s observed action  as an additional input. Results from this model are discussed in Supplementary Note To capture this distinction, we also modeled each subject’s empirical action value function 22, in which players continuously evaluate options but choose only a single action. Along similar lines, we chose to analyze the expected value of the participant changing direction a final time and continuing on a straight-line trajectory thereafter. In keeping with the hockey analogy, this is equivalent to the instantaneous value of shooting the puck: the puck changes direction and moves under inertia thereafter. We estimated this value using the final change point of each trial as training data, with each opponent  modeled by a separate GP. This is justified by our assumption that, once participants have made their final move, all participant strategies are identical and trivial: the participant has no choices remaining. In reality, opponents in our game have imperfect information about whether participants have in fact committed to a final move, and so opponent beliefs about individual participants may be relevant in principle. Nonetheless, given the speed of the game and the following results, such an assumption serves as a useful baseline against which more elaborate assumptions about opponents’ beliefs might be tested.While our empirical expected value model successfully predicts each player’s instantaneous prospects, it suffers from a key drawback: because it is conditioned on both players’ observed (and coupled) strategies, it does little to disentangle the effects of each player’s decisions on the trial’s outcome. However, our task bears a strong resemblance to the class of differential games known as duelss against opponent ω. Here again, state s includes the positions and vertical velocities of both players, as well as the normalized time since the subject’s last change point. Note the primary distinction between our action value models: The empirical EV model estimates the value of action a to the participant at a particular moment, assuming both players follows their usual strategies π thereafter. The final move EV again also estimates the value to the participant of changing direction, but assumes no change points thereafter.More formally, we estimated R = 0.31, p = 0.004; trials against human opponent #1: R = 0.665, p < 0.0001; trials against human opponent #2: R = 0.65, p < 0.0001), demonstrating that this value is a good proxy for both win rate and shooter skill. Furthermore, when we plotted participants’ estimated EV as a function of time within trial, we found that higher-scoring participants were more likely to locate their final change points during periods of high final move EV. Conversely, worse subjects showed the opposite pattern: they timed their final moves during periods of relatively low expected value . In other words, the most successful participants were those who better concentrated their final change points within an optimal temporal window against each opponent.Unsurprisingly, we found that there was a strong correlation between each subject’s average expected value at final move and win rate against each opponent  are shown in Fig. 49, which seeks to estimate, rather than learn, policies and value functions capable of generating observed behavior and also the recent surge of interest in multi-agent reinforcement learning systems52. Our problem can be viewed as a limit of the game theory context in which decisions take place simultaneously in continuous time as well as dynamically against another opponent53. Our work stands to complement those results by focusing on the dynamics that describe players’ various decisions made throughout the task (in the policy model) as well as how valuable these actions are . This emphasis on the dynamic coupling of agents also bring us closer to real-world social interactions, in which decisions are based on coevolving exchanges.Increasing interest in dynamic social interactions has necessitated a commensurate increase in the complexity of behavioral studies, but the methods used to analyze these new paradigms often lack the flexibility to handle the data produced. Here, we have shown that Gaussian Processes make it possible both to fit complex behavioral strategies and to forge links with the literature on reinforcement learning and game theory. Thus, our work is related to ideas in both inverse reinforcement learning32. The resulting statistical inferences are better indicators of model fit than point estimates obtained from maximum likelihood methods. Second, differentiability of policies and value functions allows us to derive sensitivity estimates that quantify the coupling between agents, which we have shown can characterize individual differences in play on a variety of timescales. Third, modeling the joint distribution of both players allows us to perform counterfactual analyses  is comparatively small. Nevertheless, the specific Gaussian Process formulation we have chosen has several limits. First, we have assumed that policies can be described as functions of instantaneous game state, which precludes situations where current behavior may depend on recent history. Second, as the number of agents grows, the required number of state variables grows exponentially. In this case, the data necessarily become even sparser and inferences more uncertain. Finally, even approximate GP methods can struggle when scaling to very large datasets. As a result, when data are abundant, parametric models like neural networks, which can be trained efficiently on subsets of data, may be more appropriate.Importantly, our approach of using flexible models like Gaussian Processes that capture the richness observed in real data is not limited to a specific task. It generalizes readily to more than two agents, both cooperative and competitive contexts, and a wide variety of reward structures. All of these variants can be captured by simply enlarging the state space to accommodate the additional variables characterizing each agent, as is done in joint action learning algorithms59. For our task, in which within-trial dynamics are more variable than across-trial changes in strategy, an analysis of variance showed that many sensitivities, including the baseline probability of switching and our sensitivity to opponent action metric, were relatively more trait-like than state-like, consistent with the idea that the underlying variability in our participant population is not in strategic heuristics but in the degree to which players’ actions are coupled to one another. This decomposition of variance for continuous, task-related predictors can be used in future studies for systematically determining whether a given covariate characterizes a trait-like or state-like process, which is particularly important when investigating individual differences in the social sciences.Our specific application yielded significant insights into humans’ dynamic strategic interaction with both human and computer opponents. We found that participants exhibited a large variety of trajectories against both opponents, yet a majority of our participants demonstrated a heightened opponent sensitivity toward one particular goalie throughout the trial, and that subjects’ sensitivity to opponent actions demonstrated substantial subject-level variability. The importance of these policy-derived metrics, particularly the sensitivities, is consistent with the findings of many groups that an ability to model the intentions of another agent plays a central role in human social interaction60, as well as work which frames many common decisions in terms of foraging or search problems63.Finally, we showed that an analysis of participants’ evolving prospects of winning easily distinguished between the track-then-guess heuristic of the computer opponent and the more complex human opponents. Such an analysis allows us not only to assess the degree to which a given moment in the trial is critical to a player’s future prospects, but also how successful players are in seizing these opportunities. This is a result of the fact that action values are functions of both players’ strategies. More specifically, by characterizing our task as a stopping problem, in which participants’ objective was to time a single decision, we showed that an ability to accurately time one’s final change point during periods of high expected value differentiated high-scoring from low-scoring participants. That effective players capitalize on momentary advantage is intuitive and relates to empirical work showing that expected value plays a role in strategic decision-making65. The key advantage of our approach lies in an ability to identify both behavioral tipping points (high sensitivity of policy) and reward tipping points  and distinguish between the two. This is particularly crucial in the analysis of neural data, where one wishes to designate different types of cognitive events in addition to observational events 67. Taken together, our results and overall approach offer a new path to the use of more naturalistic paradigms in the study and modeling of social interaction.Perhaps most important for studies of social and decision neuroscience, our models suggest a natural set of variables of interest at a hierarchy of temporal scales. While the policies and action values we derive offer instantaneous regressors at the tens of milliseconds resolution of electrophysiology, including EEG and ECoG, these metrics can also be averaged at the trial and participant level for use with fMRI and PET. Providing computational frameworks for capturing complex temporal dynamics is crucial in learning and decision makingThis study was approved by the Institutional Review Board of Duke University Medical Center. Data from 82 healthy volunteers  were included in the behavioral analyses. All participants gave written informed consent to participate in this experiment and were informed that no deception would be used throughout the experiment. Two long-term participants played the role of the human opponent in the penalty shot task, but each participant played against only one human opponent. The human opponents were not members of the study team and had no stake in the outcome of the study apart from maximizing their own compensation. Participants were told that on each trial they would play against either the human opponent they had met with during the consenting process, or against a computer algorithm. We emphasized to participants that deception would not be used in our task regarding who they were in fact playing against . Our task was incentive-compatible: both the experimental participant and the human opponent were rewarded in monetary bonuses that were dependent on how frequently each player won.Participants began the experiment with a 4 min practice block followed by three experimental blocks, each ~12 min long. Participants played as many trials as they could within each 12 min block, resulting in roughly 200 trials in total for each participant . At the beginning of each trial, each participant was prompted to center the joystick in order for the next trial to begin. A centered fixation cross was then presented for a jittered amount of time, ranging from 1.0 to 7.5 s. Following the fixation cross, the identity of the opponent on the upcoming trial (either “Computer” or the name of the human opponent) was displayed in centered text for 2 s. Each trial lasted roughly 1.5 s. Following the end of a trial, centered text displaying “WIN” or “LOSS” would appear on-screen, indicating the previous trial’s outcome. Following the experiment, participants completed a post-task survey, were debriefed, and compensated.x = 0.77. The puck moved with constant horizontal velocity vp and vertical velocity vput, where ut ∈  was the vertical joystick input at time t. The participant controlled only the vertical velocity of the puck. The puck was constrained to remain onscreen. At each time t, the coordinates of the puck were updated according to:The puck was represented as a colored circle  for three consecutive time steps, the bar’s maximal velocity began to increase on the third step. That is, at each time stepBoth the human and computer opponents were identically represented on-screen by a vertical bar. The bar began each trial at , immediately to the left of the goal line, and could only move up or down. Unlike the puck, the opponent was able to accelerate: If the opponent maintained direction at near-maximal input  norm of the GP gradient along that direction:i = 1 … 8 indexing each predictor variable in  and σi the local uncertainty in ∇i f. This can be motivated by noting that since f is a GP, ∇f is as well . This is equivalent to combining the gradients for opponent position and velocity by first performing a PCA on these two coordinates and weighting each principal component equally in the calculation. As with the νi above, it can be shown that this index has a known distribution , allowing us to calculate uncertainty in the action sensitivity metric at each timepoint (see Supplementary Note When we consider a total sensitivity to opponent actions, we combine sensitivities to opponent action and velocity into a single metric:Further information on research design is available in the Supplementary InformationPeer Review FileReporting SummaryDescription of Additional Supplementary FilesSupplementary Movie 1


These models are often applied to empirical data as “measurement tools”, with different theoretical accounts being contrasted within the framework of the model. Some method is then needed to decide between these competing theoretical accounts, as only assessing the models on their ability to fit trends in the empirical data ignores model flexibility, and therefore, creates a bias towards more flexible models. However, there is no objectively optimal method to select between models, with methods varying in both their computational tractability and theoretical basis. I provide a systematic comparison between nine different model selection methods using a popular EAM—the linear ballistic accumulator  contains supplementary material, which is available to authorized users. Over the past several decades, formalized cognitive models have become a dominant way of expressing theoretical explanations and analyzing empirical data. These formalized models take the verbal explanations of theories of cognitive processes, and express them as precise mathematical functions that make exact quantitative predictions about empirical data. Formalized cognitive models have been largely adopted within the area of rapid decision-making, with the evidence accumulation models (EAM) forming the most dominant class of models , as more flexible models can predict a wider range of potential data patterns, and are able to “over-fit” to the noise in the sample data, which can often result in a more flexible model more closely matching the data than a simpler, but more correct, model . However, parameter counting ignores “functional form flexibility”: how the model’s specific function alters the amount of flexibility provided by each parameter, and therefore, the model overall ) over the entire posterior, and flexibility being calculated by some measure of variability of the likelihood over the posterior. In addition, recent research has highlighted methods that can provide accurate approximations of the Bayes factor in complex cognitive models within a reasonable time-frame p(𝜃)) over the entire parameter space, rewarding models for having a high posterior probability, but penalizing models for having an overly wide set of a priori predictions , I focused my assessment on a single, widely applied EAM: the linear ballistic accumulator , the standard deviation in drift rate over trials (s), the decision threshold (b), the upper bound of the uniform starting point distribution (A), and the non-decision time (t0). As is commonly the case in applications, I constrained the t0, A, and b parameters to be the same across accumulators, with each accumulator having a different mean drift rate  and standard deviation in drift rate (svc and sve). Per convention, svc was fixed to 1 to satisfy a scaling property within the model  differs randomly between trials according to a truncated normal distribution (lower bound of 0), and the amount of starting evidence for each alternative differs randomly between trials according to a uniform distribution (lower bound of 0). In addition, some amount of time is assumed to be dedicated to non-decision related processes, such as perception and motor function . The LBA contains five parameters per accumulator : the mean drift rate over trials (vc) was allowed to have different values across conditions, (3) a “threshold” model where the threshold parameter  was allowed to have different values between conditions, and (4) a “complex” model, where both vc and b were allowed to have different values across conditions. Formally, the null model was defined as:i indexes the condition, the threshold model was defined as:To create different theoretical accounts within the LBA to compare in each data set, I defined four sub-models that allowed for different changes in parameter values across “within-subjects” experimental conditions. These were (1) a “null” model where all parameters were constrained to have the same values across conditions, (2) a “drift” model where the correct mean drift rate parameter . AIC uses the maximum likelihood as a measure of goodness-of-fit, and the number of free parameters as a measure of flexibility, with more parameters resulting in harsher penalties. DIC uses the average log-likelihood over the posterior distribution as a measure of goodness-of-fit, and the difference between this average and the log-likelihood at some fixed, central point of the posterior as a measure of flexibility, with greater differences resulting in harsher penalties. Although the mean of the parameter values over the joint posterior is often used as the point estimate in this calculation ), and k is the number of free parameters in the model. DIC can be written as:S is the number of posterior samples, and max is the maximum function over all posterior samples. WAIC can be written as:n is the number of data points, and var is the variance function over the posterior samples.Formally, AIC can be written as:p(y|𝜃)t). To obtain the marginal likelihood, a series of power posteriors must be estimated with powers  between 0 and 1, which forms a discrete approximation of a continuous integration curve between 0 and 1. Integrating over this area with a simple integration rule provides the marginal likelihood. The TIDE method estimates all power posteriors simultaneously, with each temperature being a different chain in a single run of the Different Evolution Markov chain Monte Carlo  containing a natural penalty for flexibility through the integration of the unnormalized posterior probability over the entire parameter space. BF-BS uses the bridge sampling algorithm to estimate the marginal likelihood for each model, requiring (1) samples from the posterior distribution, (2) the definition of a proposal distribution and samples from this distribution, and (3) the definition of a bridge function. I use the recommendations of Gronau et al.,  for the Formally, BIC can be written as: et al.,  and Anni et al., , respectp), the augmented ROPE (ROPEa), and the χ2 test of relative deviance, do not clearly fit into either category above. DICp is calculated in an identical manner to DIC, but with the deviance calculation based on the unnormalized posterior probability. ROPEa is calculated in the same fashion as regular ROPE, where the selection process is purely based on the parameter posterior densities; however, in cases that would usually be ruled as “indeterminate”, ROPEa chooses based on the largest posterior density. Note that as with ROPE, ROPEa makes decisions on parameters as separate, binary cases. Therefore, to select the model with both drift rate and threshold varying over condition, ROPEa would require the posterior distributions for the change in drift rate and threshold over condition to each mostly fall outside their respective ROPE. The χ2 method uses a significance test to decide whether additional parameters are required to explain the data in the case of nested models. Specifically, the difference in deviance—with the “deviance” in this case being the maximum log-likelihood multiplied by negative 2—is approximately distributed as a χ2 with degrees of freedom equal to the difference in the number of parameters. Significant values indicate that the more complex model is required, whereas non-significant values indicate that the simpler model is satisfactory. In order to use the χ2 test to compare all four models, I firstly assessed which “single effect” model  had the better deviance score , and then compared the better model to the null model. If this test was significant, then the single effect model was compared to the drift and threshold model to determine the best model, and if the test was non-significant, then the null model was compared to the complex model to determine the best model.The other three methods, DIC with the prior probability included , 1,000 samples per chain discarded as burn-in, and 1000 samples per chain taken from the joint posterior. For AIC, BIC, and the χ2 test of relative deviance, which all require the maximum likelihood, I used the maximum likelihood contained within the posterior distribution ), which is equivalent to the maximum likelihood obtained through maximum likelihood estimation in situations where data are plentiful and the prior is relatively uninformative. For BF-BS, I took 3k× 1000 samples from the proposal distribution. For BF-TI, I fit each model with 40 temperatures, meaning that 40 chains were used instead of 3k. For ROPEa, the same value used to define a “small” effect size for each parameter in simulating the data was used to define the size of the ROPE .All models were fit using Bayesian parameter estimation, as most of the model selection metrics assessed in this study require posterior distributions. The posterior distributions were estimated through Differential Evolution Markov chain Monte Carlo , and the consistent between metrics. Note that I say “correct” , as although the data generating model is known, the data generating model is not necessarily the model that best explains each specific sample of randomly generated data. Therefore, assessing the selection of the correct model is strictly an “inversion” based test . All possible Brier scores fall between 0 and 2, where 0 indicates the best possible performance and 2 indicates the worst possible performance. However, I adjusted the resulting Brier scores to a scale that provides a more intuitive interpretation, where scores are between − 1 and 1, − 1 indicates the worst possible performance, 1 indicates the best possible performance, and 0 indicates chance performance. In order to obtain the probability assigned to each outcome for each model in a specific data set, I calculated probability weights for each model. For models on the deviance scale , the probability weight for model i was calculated as:MSMi is the model selection method deviance for model i, and N in the number of models being evaluated. For models on the log-likelihood scale  the probability weight for model i was calculated as:a, the same concept was used as above, except instead of a likelihood being used to calculate the weights, it was the relative posterior density. However, the Brier score cannot be easily calculated for the χ2 test of relative deviance, as the choice is determined through a significance test, which cannot be directly interpreted as a level of evidence , and not the consistency between the selection of separate drift and threshold effects.I simulated 2500 total data sets, with each being a single simulated “participant” with two “experimental” conditions, and 300 simulated trials per condition. My choice of two experimental conditions, rather than a larger number, was to (1) minimize the potential sources of variability in the design to allow comparisons to be as robust as possible, and (2) mimic the pseudo-experiment design of Dutilh et al., , which mand a decrease in threshold for the same condition, creating a more extreme difference between the conditions in response time than a single effect. The “drift and threshold balanced” data sets were using an increase in drift rate for one condition, and a decrease in threshold for the other condition , with the effects in response time balancing each other out to some extent.The 2500 data sets fell into one of five different qualitative types of effects: “null”, “drift”, “threshold”, “drift and threshold extreme”, and “drift and threshold balanced”. The “null” data sets were simulated using the same parameter values for both conditions, meaning that there was no underlying difference between the two conditions. The “drift” and “threshold” data sets were simulated with an increased (decreased) drift rate (threshold) parameter value for the second condition, respectively. The amount of change in the parameter for each data set was set to be either “small”, “moderate”, or “large”, with these different sizes decided by a priori simulations that found what amount of change resulted in 0.2, 0.5, and 0.8 effect size differences between conditions in the response time distributions. This created six different categories of one-way effects: drift rate and threshold, with each having small, moderate, or large differences in the parameter value. The “drift and threshold extreme” data sets were simulated using an increase in drift rate I simulated 100 “participants”  for each of these 25 categories of effects, which served as replicates of the effects to assess the consistency of inferences. To minimize the potential sources of variability that could causes inconsistencies, these simulated replicates were each generated with identical parameter values. In addition, across the 25 categories of effect, the same parameter values were used for non-manipulated parameters. These “baseline”, non-manipulated parameter values were:Figure p, and ROPEa show near-optimal performance when either no effect is present  or a single moderate/large effect is present, but show poor performance when one or both of the effects are small. This suggests that (1) no method appears to perform “better” than all others under all potential conditions, and (2) some methods are more consistent in their selection accuracy across the different potential combinations of effects, whereas others are more polarizing.There appear to be two overarching trends in the correct selections. Firstly, all methods correctly identify almost every replicate when both effects are part of the data generating model and each effect is either moderate or large. This suggests that (1) the methods are indistinguishable in these circumstances, and (2) by inversion standards, all methods show near-optimal performance in these circumstances. Secondly, the performance of the methods appears to be clearly separated in the small effect and null data sets. In general, AIC, DIC, and WAIC appear to show good performance in each of these cells of the design, whereas BIC, BF-BS, BF-TI, DICp) has a similar pattern of performance across the cells of the design to the Bayes factor methods, as opposed to the predictive accuracy methods that the standard DIC method belongs to. The performance of DIC and DICp deviate from one another a great deal, suggesting a large influence of including the prior probability. Secondly, the conceptually simple ROPEa method performs very well, even though augmentations were made to the standard ROPE method to force it to select a model in every instance. In general, the augmented ROPE seems to perform as well as, if not better than, the Bayes factor. Lastly, and perhaps most importantly, the simpler parameter-counting methods perform extremely well. In each cell of the design, AIC performs about as well as both of its more complex counterparts, DIC and WAIC, and BIC performs about as well as its more complex Bayes factor counterparts. This is extremely important, as the use of more complex metrics is commonly advocated on theoretical bases, but in this practical context, their performance does not seem to be any better than the simpler methods. The simple χ2 deviance test (DEV) also shows good performance, though it does not seem to clearly map onto either class of selection method.In addition to these general trends, there appear to be three other important, and potentially surprising, more specific results. Firstly, when including the prior probability, the DIC method  of similar effect sizes, with drift and threshold being selected fairly similar amounts in equivalent cell of the design. Secondly, the “Bayes factor” type methods are much more conservative than the “predictive accuracy” type methods. The clear distinction here is in cases where the effect does not exist  appears to be largely independent of whether or not the other effect  is non-existent, small, moderate, or large. For example, when looking at Fig. As the relationship between methods was extremely similar in many cells of the design, I collapsed over several for ease of communication. Firstly, as there was little difference between the methods in previous assessments when both effects were present and moderate or large in size, I collapse over these 8 cells. Secondly, as there was generally little difference between the impact of moderate and large effects in previous assessments, I collapse over those cells in all instances. Lastly, as there was little difference between drift rate and threshold of effects in previous assessments, I collapse over these two types of generated effects. This leaves eight collapsed cells to assess the consistency of the methods over, which can be seen in Fig. There appear to be two key general trends in the consistency assessment. First and foremost, all methods are extremely consistent with one another when both effects are present and moderate-to-large in size. This further re-iterates that the choice in model selection method makes little difference in situations with sizable effects. Secondly, there appears to become a much greater distinction between the predictive accuracy and Bayes factor methods in the other cells of the design, where one or both of the effects are small or non-existent. The difference appears to be least prevalent when one effect is large and the other does not exist, and most prevalent when both effects exist, are small, and are “balanced”, further showing that the key distinction between the methods is for small effects. However, in all cases, the consistency within each class of method is very high, with AIC, DIC, and WAIC all being consistent with one another, and BIC, BF-BS, and BF-TI also being consistent with one another.In addition, there appear to be two specific, but important, points to note here. Firstly, DIC and WAIC are extremely consistent with one another in every cell of the design. Although this may seem like a minor point, the lack of difference between these methods is of key importance. Specifically, WAIC has been suggested as a major theoretical improvement to DIC, and the assessment of the variance in the posterior likelihood is thought to be a superior assessment of flexibility than DIC’s more simple flexibility assessment. However, there appears to be little practical difference between the methods, suggesting that WAIC is of little-to-no benefit over the more simple DIC. Secondly, although the consistency between the two Bayes factor approximations of BF-BS and BF-TI is extremely high, they do not show perfect agreement. This is potentially concerning, as both methods are intended to estimate the exact same quantity  in an unbiased manner, and have been shown to do so accurately in models where the marginal likelihood is analytically solvable  than the predictive accuracy. Thirdly, the augmented version of ROPE performed very similarly to the Bayes factor. However, ROPEa was not always in perfect agreement with the Bayes factor, showing closer agreement to the predictive accuracy methods in the “small balanced” cell, which resulted in it having “better” performance than the Bayes factor in this cell. Lastly, the simpler methods of model selection showed a very close relationship to their more complex counterparts. In most cells of the design, AIC is extremely consistent with DIC and WAIC, and BIC is extremely consistent with the BF-BS and BF-TI. This suggests that although there are many theoretical advantages to using these more complex methods of model selection, the practical advantages of using them over more simple approximations may be limited, and therefore, many users may wish to opt for the simpler alternatives.This section also re-enforces several previous key points regarding the relationships between the different methods. Firstly, there appears to be a practical distinction between the “predictive accuracy” methods and the “Bayes factor” methods, with these classes of methods only providing largely consistent inferences when all effects evaluated exist and are sizable. This is very important to showcase, as researchers often use these different classes of methods interchangeably as general “model selection metrics”. However, the classes of methods are theoretically very different, and as shown here, can come to very different practical inferences. Secondly, DICOne key finding of the simulation study was that both BIC and Bayes factors performed conservatively when compared to AIC, DIC, and WAIC. As mentioned above, this is probably not surprising given that Bayes factors with uninformative priors are known to be conservative. Specifically, when applying Bayes factors to simple, statistical models, previous research has shown that effects are less likely to be detected when uninformed priors are placed on the “effect size” parameter , compared to when using more informed priors Lindley, .X in conditions 1 and 2 were given by:Xmean is the parameter mean over conditions, and Xdiff is the parameter difference between conditions. For the parameter reflecting the mean over conditions, I used the same priors as the previous analysis:UP is a completely uninformative prior , WIP is a weakly informative prior , MIP is a moderately informative prior, and HIP is a highly informative prior. As the focus of this assessment was only on the impact of informative priors, I only applied one of the methods (bridge sampling) of approximating the Bayes factor.Here, I provide a follow-up assessment to evaluate how more informative priors practically impact the LBA models selected by the Bayes factor. As the Bayes factor provided near-optimal selection for moderate and large effects even with uninformative priors, I focus this assessment on the 5 cells of the design that are most likely to be impacted by using informed priors: the no effect, small drift rate effect, small threshold effect, small drift rate and threshold “extreme” effect, and small drift rate and threshold “balanced” effect. In order to place more informative priors on the difference in the parameter values between conditions,WIP shows extremely similar performance to the priors used in the previous analysis, showing near-optimal performance when no effect is present, poorer performance when a single, small sized effect is present, and extremely poor performance when both effects are present and small in size. The UP shows even more conservative performance, selecting optimally when no effect is present, but poorly for a single effect, and misidentifying almost every data set when both effects are present. In contrast, the MIP shows more balanced performance, with selection no longer being optimal when no effect is present, but drastically improving when either one or both effects are present. However, the HIP appears to become overly liberal, showing poorer performance in all cells of the design except the case where both effects are present and combined in an “extreme” manner.Figure UP and WIP very rarely select an effect when it is not present, though often do not select effects that are present. The MIP performs better in this regard, mostly selecting effects when they are present and failing to select effects when they are not present, except for in the “balance” cell where selection is poorer. The HIP provides the opposite performance to the UP and WIP, often selecting effects regardless of whether they are present, except for in the “balance” cell, where selection is at approximately chance.The correct selection of specific effects (middle and right panels) supports the previous insights. The HIP in this case) can have detrimental effects on the selection process, resulting in many effects that are not present being detected, and other strange patterns of selection . Therefore, the use of informed priors can provide advantages for model selection with Bayes factors, though to provide sensible results these priors must be sensibly informed.Importantly, these results show that the level of informativeness within the prior has a practical impact in the selection of psychological theory within the LBA when using Bayes factors, and using more informed priors can result in better performance. However, making these priors overly narrow , which reflected an approximate number of rapid decisions that participants make in a short experiment. However, the number of trials can differ greatly between studies that apply EAMs, with some studies having as few as 40 trials per condition , and 900. As with the first simulation study, I simulated 100 data sets  for each of these 20 cells. As there seemed to be general agreement within each class of methods in the previous simulation study, I only use four methods within this assessment: AIC , DIC , BIC , and bridge sampling .Figure However, the performance of the different classes of methods in each cell of the design differed between the numbers of trials. For the smaller numbers of trials (30 and 100), the Bayes factor methods very rarely suggest that an effect is present, regardless of the true generating model. This results in near-perfect performance when no effect is present, but poor performance when either one or both of the effects are present. The predictive accuracy methods suggest that an effect is present slightly more often than the Bayes factor methods for smaller numbers of trials, resulting in slightly better performance when effects are present, and slightly poorer performance when they are not. However, it should be noted that at an absolute level, the predictive accuracy methods still perform poorly  in detecting these effects when the number of trials are small. For the largest number of trials (900), the predictive accuracy methods are near-perfect in detecting effects when they are present, resulting in near-perfect performance for the cells of the design where both effects are present. However, these methods also suggest that effects are present in some cases when they are not, resulting in poorer performance for the single effect and null cells. In contrast, the Bayes factor methods are near-perfect for the null and single effect cells, but fail to detect both effects in many cases for the “balance” and “extreme” data sets.Interestingly, both Bayes factor methods show similar performance in all cells of the design, throughout all sample sizes. This again suggests that BIC provides an adequate approximation to the Bayes factor with uninformative priors for comparing different theories within the LBA framework. However, this is not the case for the predictive accuracy methods. Although AIC and DIC perform similarly when the number of trials are small, their performance continues to diverge as the number of trials increases. Specifically, as the number of trials increases, both AIC and DIC improve at detecting when effects are present, increasing their overall performance. However, as the number of trials increases AIC remains fairly stable at detecting when effects are not present, whereas DIC begins to false alarm increasingly often, resulting in DIC having poorer performance than AIC for single effect and null cells. This is likely due to DIC providing a more accurate approximation of leave-one-out cross validation than AIC. When using cross validation in cases where the null model is true, the estimated difference in parameter value between conditions in the more flexible model will become increasingly closer to zero  as the amount of data increases, which will result the more flexible model being identical to the simpler model in predicting the left out data  a failing of the simple parameter counting approximation of AIC, or (2) the limited number of replicates with these data (20). However, in an overall sense, the simple approximation of AIC and BIC again show close agreement with the more complex methods that they aim to approximate, suggesting their adequacy in these types of comparisons between models.Figure The current study provided a systematic assessment of how different model selection methods perform in practical situations for the analysis of response time data using evidence accumulation models (EAMs). Specifically, I used the Linear Ballistic Accumulator  and the “Bayes factor” methods  in the models selected, with the predictive accuracy methods generally being more liberal, and the Bayes factor methods generally being more conservative. Theoretically this result is not particularly surprising, as predictive accuracy methods will favor the more flexible model as the amount of data approaches infinite, and Bayes factors with uniformed priors are considered to be conservative. However, in practice these theoretical differences are often ignored, with a convenient method being applied as a general “model selection metric”, with the class of model selection method chosen rarely justified. These findings suggest that the theoretical difference is quite meaningful, and can often make a meaningful difference to the inferences about the data. In addition, one potentially interesting sub-finding is that these inconsistencies are only present when the effect of interest  is non-existent or small, and that methods show extremely high consistency when the effect is moderate or large. Therefore, although there are inconsistencies between the classes of methods when any potential effects are small, when all potential effects are large then all methods provide equivalent results.Secondly, there appeared to be few differences between the simple “parameter counting” methods of model selection, and the more complex variants that accounted for functional form flexibility. Specifically, within each class of methods discussed above, the simple approximations showed high levels of consistency with the more complex methods. AIC showed a high level of agreement with both DIC and WAIC, and BIC showed a high level of agreement with both Bayes factor approximation methods. Although it is known that the flexibility of the model is more than simply the sum of its free parameters, with the way that they are functionally combined also impacting upon the flexibility of the model, my findings appear to suggest that the parameter counting heuristic provides a fairly accurate approximation of flexibility when applying the LBA. These two general findings both appeared to be robust across both simulated and empirical data, suggesting that these findings should extrapolate to similar experimental context that the LBA might be applied to.p(y|𝜃)p(𝜃) instead of p(y|𝜃)) greatly changed its inferences, with DICp showing a closer relationship to the Bayes factor than to the standard DIC calculation. This suggests that when a researcher wants a measure of predictive accuracy, they should use the standard DIC calculation; however, if they are looking for a simple Bayesian method that provides a similar result to the Bayes factor, then DICp may be an interesting alternative. Thirdly, the augmentation of the estimation method ROPE appeared to perform quite well, and showed similar performance in many instances to the Bayes factor. Therefore, when the “zero region” for ROPE is chosen in a principled manner, the method appears to provide a promising method of practically comparing models. Fourthly, although bridge sampling and thermodynamic integration both provide an unbiased approximation of the marginal likelihood that has been shown to be accurate for simpler models where the marginal likelihood is solvable, there were some minor inconsistencies in their selections. This could potentially be due to either one or both methods having too greater approximation error in the limited number of samples that were used, or the fact that the TIDE method is a further approximation of the TI method . Although both classes of methods show near-perfect agreement when a moderate or large effect is present, with both always selecting in favor of the effect, the classes diverge in the cases of small or null effects. However, the choice between the classes of methods may be difficult for many users of the LBA, as they may not have a theoretical preference for either “predictive accuracy” or “the best account of these data”, and the Bayes factor can also be thought of in terms of a different type of “predictive accuracy”  by expressing the selection metric as relative probability weights for each model . Therefore, it is important that researchers consider both which model is chosen as the best model by the model selection method, as well as the strength of evidence in favor of the winning model over the other models. Previous applications of the LBA have largely focused on only which model was selected as the best model, and have mostly ignored the strength of evidence in the selection. However, this study found that performance was improved for all model selection methods when accounting for the probability assigned to each model, suggesting that the methods are more likely to show high confidence in selecting correct models than incorrect models. The strength of evidence in favor of each model can be easily obtained for all of the methods used within this manuscript , meaning that the assessment likely would have had to be less comprehensive to fit into a reasonable computational time frame. Therefore, I chose to perform a more comprehensive and robust assessment on non-hierarchical models, rather than a lesser version involving hierarchical models.Secondly, and most importantly, there are many potential theoretical difficulties when performing comparisons between nested hierarchical models , which are still largely unresolved within the literature. Previous research has already highlighted the issues with “two-stage” approaches, where model parameters are estimated with hierarchical cognitive models and then placed into a subsequent statistical test , as this will lead to biases in favor of an effect , having some amount of between-person variability in the exact drift rate difference between conditions will result in the “drift” model being the superior model. However, it is not clear whether this strong assumption is a reasonable one to make, and researchers may differ on their opinions of whether or not the null model should include random slopes. In addition, if random slopes are deemed to be necessary for null models, then assessments still need to be made on the best way to define this new hierarchical null model. The “random slopes” issue is also not restricted to comparisons made using Bayesian hierarchical model selection; the same logic and strong constraints  applies to group-based comparisons made using non-hierarchical models, such as summing the AIC or BIC values over participants Below is the link to the electronic supplementary material.


In the context of chronic illness, the individual’s social and relational environment plays a critical role as it can provide the informal support and care over time, beyond healthcare and social welfare institutions. Social Network Analysis represents an appropriate theoretical and methodological approach to study and understand social support since it provides measures of personal network structure, composition and functional content. The aim of this mixed method study is to present the usefulness of Personal Network Analysis to explore social support in the context of chronic pain. Personal and support network data of 30 people with chronic pain  were collected, obtaining measures of personal network structure and composition as well as information about social support characteristics. Also, semi-structured interviews with participants were conducted to identify the context of their experience of pain, their limitations as regards leading an autonomous life, their social support needs and other aspects concerning the effect of pain on their social and relational lives. This approach shows the importance of non-kin social support providers and the significant role of non-providers in the personal networks of people suffering chronic pain. Chronic pain is a major public health problem due to both its prevalence and its significant effects on patients, their families and the social and professional environment, leading to a deterioration in the quality of life . PrevaleOne of the resources derived from social ties is social support, a concept that has attracted considerable attention and has been explored from a variety of perspectives, with particular emphasis on different dimensions, components and mechanisms of action. A widely used definition of this concept was proposed by Cobb in 1976: “Social support is […] information leading the subject to believe that he is cared for and loved, esteemed, and a member of a network of mutual obligation” , who estThe impact of social relationships that provide support on health has been well established in the literature. Researchers have used many general and interchangeable terms, including social networks, social ties, social integration and other constructs such as social support . NeverthAs part of the development of social support as a concept, it needs to be highlighted the operationalisation of various dimensions such as types of support ,13,14, tA substantial increase in health studies that use Social Network Analysis approaches has witnessed in the last decade ,21,22,23Many instruments have been developed for the measurement and assessment of social support since it was first defined over four decades ago. These instruments explore the presence of varied types of social support and social network characteristics , focusing mainly on the significant ties that provide support for the individual ,37,38. NCross-sectional design with mixed methodology combining Personal Network Analysis and semi-structured interviews.Participants comprised 30 people (15 men and 15 women) diagnosed with chronic pain and receiving care at Marqués de Valdecilla University Hospital Pain Unit . Fieldwork and analyses were conducted between July 2014 and July 2015. Participants were selected through convenience sampling during visits or outpatient treatment for pain. Data were collected at the hospital or informants’ homes following their health status and personal preferences. Results on the personal networks of the 30 cases studied and 600 personal relationships (20 relationships per ego) were obtained.(a)Personal network structure: unlike sociocentric or complete networks, in which each member is considered to contribute equally to shaping the network structure, personal networks examine the influence on the informant (ego) of each member of a network, based on the principle that not all network members contribute equally to the phenomenon under study , be thatDensity: the percentage of ties that exist in a network out of all possible ties.Degree centrality : number of vertices adjacent to a given vertex in an asymmetric graph or the number of relations of a given person. It is a measure of network activity. An alter is highly degree central to the extent that he or she is directly connected to many other alters.Betweenness centrality : number of times a vertex occurs on a geodesic  connecting every other pairs in a graph. A single alter is highly between central to the extent that they lie on many geodesics (shortest paths) between alters. In this sense, they act as a bridge between alters and thus, potentially, control information, for example.Components: set of alters who are connected to one another directly or indirectly.Isolates: actors who are not connected to any other actors.(b)Personal network composition : age, sex, type of tie with ego, place of residence and proximity.(c)Social support (function): type, satisfaction, reciprocity, variation over time, frequency and channel of transmission. In this specific context of chronic pain, support was considered generally: emotional support, such as the interpersonal transactions that make a person feel understood and accompanied in his or her pain; instrumental support, such as the help of other people in activities that the individual either cannot perform or for which others are required as a result of pain ; and informational support, such as advice or information about chronic pain that helps the subject deal with the pain .Personal network:https://sourceforge.net/projects/egonet/ v.2014) was used to collect and analyse each ego’s personal network data. Also, UCInet software  You can’t plan or do anything, it’s … it tortures you, you get depressed, you … well I was begging them to amputate my leg as soon as I knew nothing could be done […], it’s devastating to be in so much pain, not knowing what to do, not knowing how to act … it destroys you: as a person, as a woman, as a worker, as a mother, as a wife … it completely annihilates you. Woman, 46 years old.When I have one of my very bad days I, I … how can I say it? I don’t want to be with them. I don’t, because I feel so unwell, nothing feels good, everything looks black, and I need to be alone […]. I’m very moody. It makes me feel so powerless, I can’t do anything and nobody can do anything for me. Woman, 66 years old.I used to go out, go walking with my friends, I looked after my daughter [cries] … it’s looking after my daughter that’s the worst thing because … I can’t give her a bath because I’d have to bend over and I can’t, fetch her from school … that’s the worst thing for me. Woman, 34 years old.I used to have a very wide circle but not now, not for some years now, there’s no circle. Only the very closest ones are left, the people at home. Things happen to you, as they did to me, and you lock yourself away with your pain and misery, because you can’t get around like you did before […]. It’s made me distance myself in the sense of not wanting to go out. Man, 60 years old.The informants’ accounts of their experience of pain showed that it affected several areas of life, including the social and relational dimension. Most of the informants’ accounts indicated reduced participation in social leisure activities, weakened social ties and a tendency towards social isolation both of themselves and of those closest to them:It affects everything around me, everything, absolutely everything. In general, friends … I don’t do much because I’m not up to it, because actually I have 8 brothers and sisters [cries], and I realise that I can’t spend an hour sitting down, I can’t lead a life like … I’d love to spend time with them. Woman, 52 years old.The people around me, mainly. I didn’t realise until I saw that they were suffering as much as I was when they saw the state I was in (…). Yes, those around me, I understand because somehow I get … I snap and don’t realise until later … I not as patient as I ought to be, sometimes I get aggressive and say things I wouldn’t normally say given my education and my way of being … (…) and then I feel like I’m someone else, I’m not myself, and that really upsets me. Man, 65 years old.[…] sometimes very bad, sometimes I realise that I’ve been taking it out on the first person to cross my path. And feeling ill, sometimes anything they said to me would set me off. Because I wasn’t well … you know? Yes, of course it changed me, of course it did. Woman, 66 years old.[…] Sometimes you have to say no to certain things, because I can’t, or I can but I don’t want to because I’ll suffer for it later, so of course you limit yourself a bit … you have less social life at times, and not just you but those closest to you as well because they’re not always going to say “Well you stay at home and we’ll go”, but … Man, 46 years old.Other accounts concerned the negative effects of pain on the family environment due to behavioural changes caused by pain, the consequences for family dynamics and the impact of pain on other members of the family:For the two months I was in bed, I was completely helpless because they had to pick me up, carry me to the shower, wash me and then dress me and put me back to bed. Once they gave me injections I could do it for myself, but they had to sit me on a seat in the shower in order for me to be able to wash myself. I couldn’t stand. Man, 47 years old.Housework: my husband has to help me make the bed or sometimes he has to do it himself because I can’t. Sometimes it’s the same for getting dressed, I have to tell him: help me tie this because I can’t, or get me that because I can’t, or do this because my hands aren’t strong enough. Woman, 66 years old.When I got ill they were the ones who really helped me. They helped me a lot because sometimes I couldn’t get out of bed, I couldn’t cook […], I couldn’t even dress myself, I couldn’t do anything because the pain was so strong, I wouldn’t wish this on anyone, honestly, it was so horrible that … Man, 30 years old.The effects of pain regarding limiting activities of daily living were also mentioned in the interviews, indicating the need for support or help from the personal environment:The accounts of pain that were collected clearly evidenced its multidimensional nature, rendering it a total experience. Similarly, its chronic nature, in which more stable periods alternated over time with periodic flare-ups, highlighted the importance of the personal environment in providing informal support and care.The personal contacts nominated by the informants consisted of 310 (51.7%) women and 290 (48.3%) men with a mean age of 48.3 years . By sex, women alters presented a mean age of 49.5 years old and men, 47.11. Sex was fairly evenly distributed, with women alters accounting for 51.67% (N = 310) and men, 48.33% (N = 290). According to the sex of the egos, women had more women in their networks (64%) than men (40%). The alters’ ties with the ego presented the following distribution: spouse , parent , sibling , child , other relative , friend , neighbour , co-worker  and relationship established because of the pain . Tie strength defined as a function of proximity presented the following distribution: very close , fairly close , close , not very close  and not close at all . With regard to the alters’ place of residence, most contacts lived in the same town as the ego  or in the same province , although some lived in another province  or in another country .The results for personal network structure see  did not These differences in personal network structure and composition together with other contextual variables might explain, at least in part, the social support content presented below.In the analysis of 600 relationships, 401 support providers (66.8%) and 199 non-providers (33.2%) were identified. The analysis of social support characteristics see  showed tDue to the chronic nature of the pain, variation in social support over time is particularly important. Most of the relationships analysed did not show variation in the social support they provided. Notably, the percentage of relationships where support had increased or decreased was similar. In addition, social support had been reciprocal in most of these relationships . In relationships providing social support (N = 401), this was primarily emotional or emotional and instrumental and was generally provided weekly or daily, in person or in person combined with telephone calls as the channel of transmission.The mean number of support providers in the networks studied was around 13 people, with a variable degree of satisfaction within the support that these relationships contained and transmitted, and 7 non-providers, with a similar percentage in women’s (31%) and men’s (36%) networks.Sex: more men  than women  were non-providers.Age: non-providers presented a mean age of 46.46 years old, but encompassed both ends of the life cycle (range 1–92 years).Type of tie: non-providers included friends , family , other relatives  and close family , including 3 spouses, 15 siblings and 10 children. Parents formed the only social tie not represented among non-providers. To a lesser extent, neighbours  and co-workers  appeared among the non-providers.Reciprocity: the non-provider group included a higher percentage of relationships in which the ego had provided support  than those in which the ego had not done so .Variation in support over time: the absence of support was maintained over time in almost all non-provider relationships , and support decreased in a small percentage of cases .Tie strength: non-providers of support presented a weak tie with the ego , although notably, the ego presented a strong tie with a similar percentage of these contacts .Place of residence of the alter: most non-providers of support resided in the same town as the ego  or in the same province . A smaller percentage resided in another province  or in another country .In terms of composition, relationships not providing support were characterised by:I’m a househusband and nurse because my wife is bedridden, she’s ill. […]. No, the children are only concerned with work, enjoying themselves, asking for something, but everything else? At least with me. […]. Man, 66 years old.Let’s see, he does help me a lot [her husband], because he’s there but in my heart I don’t think he understands either… I mean, he understands that I’m in pain but at the same time he’s also very like…: well, you’ll have to cope, there’s no alternative. […] I’d like more [referring to support], I’d like much more but I can’t force people … Women, 34 years old.[…] I’d have expected more support from her [her daughter]. She doesn’t understood me enough, either (…) I expected more support from her and more help. I think it might be because she doesn’t really believe me, because she’s also going through a bad patch […]. I’d like to think that she’s upset for me, I mean, that she doesn’t know how to help me but she does know how I am from the doctors, who’ve told her “your mother is very ill and so on”, but she doesn’t give me that impression. Maybe it’s because I don’t say anything and I need people to say it to me. Woman, 56 years old.Yes, there’s a relationship but it’s not support … it’s different, no. We’re family but… there isn’t a relationship of, of, of … you often have more contact, more support, with a neighbour than with a family member. […] We’re sisters and we see each other almost every day but it’s not to say: you’re ill and I’m going to support you … no, no, no. I’ve had several operations and she’s never been to visit and so on, no, no. Woman, 66 years old.Adding to these quantitative results, the qualitative information obtained indicated that the elderly and very young did not provide support due to characteristics associated with age. Illness of contacts was another reason for non-provision of support. In other cases, informants cited lack of understanding or empathy regarding their pain among the reasons given in their accounts for the non-provision of support, and this arose in personal relationships with close family members such as spouses, children or siblings.With regard to structure, the means for degree and betweenness centrality of non-providers and for all alters are given in These results identify non-providers of support as alters with fewer ties with other members of the network  and mediating or forming a bridge between other alters to a lesser extent than the alters as a whole . Thus, from a structural perspective, non-providers of support are located on the periphery and distant from the core of a network, although it is important to consider other contextual factors which in some cases might explain the non-provision of support .Graphs are visual representations of networks, displaying actors as nodes and the relational ties connecting actors as lines. By way of example, this section presents graphs of personal support networks, showing the diversity of relational and functional contexts of social support in the cases studied.The graphs below represent the personal support networks at ego level of two women  and two The results presented here regarding the structure, composition and social support function of all the personal networks studied, together with contextual factors obtained using a qualitative approach, show the relational and social reality of people with chronic pain.This paper has focused on demonstrating the usefulness of Personal Network Analysis to study social support in a specific context of illness: chronic pain. The study design enabled us to obtain data on the composition and structure of personal networks from which social support emerges, for all ties studied and at ego-level. It has proved equally relevant to obtain functional social support data on providers and to capture non-providers and their characteristics.Among the 600 relationships studied, emotional support was the most prevalent, being present in more than half of the ties analysed (63.6%), followed by this latter combined with instrumental support (21%). The most common channel of support was physical presence (47.9%), followed by this latter combined with telephone contact (33.4%) and telephone contact alone (15.7%). The most common frequency with which informants reported receiving support from their alters was weekly (36.2%) followed by daily (30.4%). As regards variations over time, the support provided by alters remained the same in the vast majority of cases (75%), while increases and decreases were observed in similar proportions . Reciprocal support relations  were present in the majority of the relationships (76.3%). In terms of satisfaction with support received (assessed through five categories ranging from very satisfactory to very unsatisfactory), 33.2% of unsatisfactory relationships corresponded to non-providers, and 12.3% were rated as very satisfactory.Many earlier studies on social support have paid most attention to family members as providers. Nevertheless, it is also necessary to consider other social roles such as friends and neighbours in the provision of certain types of support ,44,45. IOther authors have emphasised the importance of capturing qualitative aspects of social support networks , to helpAnother suitable social support resource is the working environment, considering the impact and consequences of chronic pain in this field. At European level, a total of 19% of people with chronic pain lost their job, 16% changed job responsibilities and 13% changed jobs entirely as a consequence of their pain ,61,62. OIn terms of structure and composition, the metrics of centrality studied at alter level between non-providers and the total number of alters indicate that the former occupy positions with less centrality  than the total. These results may reflect the informants’ long experience of chronic pain, which may have contributed to reducing social participation, weakening social ties and isolating them, as shown by the interviews, showing networks with fewer active and functionally operational contacts who offer support. Future research might consider the variables that influence the social support provided by social relationships considering both the size and the formal structure of the social networks in which it operates and its functional content  as well One limitation of the present study concerned the difficulty of obtaining data. The highly complex situation of general health and pain in some cases resulted in more refusals to participate in the study than expected at the outset. Regarding methodology, the number of cases and the type of sampling rendered it impossible to obtain results stratified by criteria such as age or sex, two key variables to consider in chronic pain, as shown in previous studies on prevalence.The analysis of personal networks combined with qualitative techniques represents a novel and useful approach to study social support. It allows a detailed examination of related variables from a network perspective, while visualisation and network interviews yield qualitative information on the individual’s social and relational reality in the context of chronic pain. This approach does not replace but rather complements the attributional measures that have traditionally been used to assess social support and for which there is empirical evidence. Thus, it helps to elucidate factors that explain the different contexts in which support is offered and received, mainly due to the emphasis placed on the structure and composition of personal networks from which social support emerges. Finally, varied social and relational environments of people with chronic pain must be considered especially in those cases in which informal support resources are insufficient or inadequate in order to complement them with the existing formal resources at the community level.