August 2021
Affective States
& Decision Strategies
by
Tobias Ballauff
13378228
Supervisor Federica Farolfi
Second Reader Dianna Amasino
Submitted in partial fulfilment of the requirements for the degree Masters of Science in Neuroeconomics - 15 EC
This document is written by Tobias Ballauff who declares to take full respon- sibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. UvA Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
This thesis aims to investigate the mechanisms of affective decision strategy selection to develop a functional understanding of affective states.
On the foundation of previous research it is argued that decisions are largely driven by dynamic neural affective states that lead to state specific behavioural patterns. While connected mechanisms have been previously suggested, the control exerted by affect in high level decision making is still inadequately understood. The author combines a digital foraging task with computational models of behaviour and affective induction. The re- sults show that choices in small stakes and limited time horizon events are better when humans experience more positive valence. Furthermore, it appears that complex affective states are central to the selection of de- cision strategies. Based on these findings, the author proposes a decision theoretic framework for the classification of affective states that encom- passes the role of affect in the mechanisms of evolutionarily sound meta decision making.
Contents
1 Introduction 1
1.1 Motivation . . . 1
1.2 Manuscript in Short . . . 1
2 Background 5 2.1 Perspectives on Affect . . . 5
2.2 Decision Strategies . . . 6
2.3 Affect in Decisions . . . 8
2.4 Unifying Affective States and Decision Strategies . . . 10
3 Methodology 14 3.1 Experimental Task . . . 14
3.2 Experimental Procedures . . . 16
3.3 Computational Framework. . . 17
4 Results 20 4.1 Induction . . . 20
4.2 Treatment Analysis. . . 22
4.3 Affect Analysis . . . 25
5 Discussion 33 5.1 Key Findings . . . 33
5.2 Limitations and Strengths . . . 35
5.3 Interpretation . . . 36
5.4 Outlook . . . 38
5.5 Concluding Remark . . . 41
References 42
Appendices 50
A Participant Instructions 50
B Additional Models 56
1 Introduction
1.1 Motivation
The experience of affect plays a central role in the way humans navigate their environments. Charles Darwin noted: “Joy quickens the circulation, and this stimulates the brain, which again reacts on the whole body.” (1872). This simplified illustration captures the intuition that emotions contribute to human cognition through distinct biochemical mechanisms. Until recently, however, the role of emotions or affect in key cognitive tasks like decision making has not been a central object of research (Loewenstein & Lerner, 2003).
The elusiveness of affect may have led behavioural scientists and especially economists to disregard the impact of emotions outright. Economic scholars have long favoured the well defined principles of rationality to derive self en- closed theories. However, as Darwin already noted, cognition and affect are not polar opposites, but rather tightly entangled concepts. Neuroscientific research supports this claim, as for example certain cognitive decision processes fail when brain areas linked to affect are lesioned (Fellows & Farah, 2003).
Humans also tend to use varying decision strategies (DSs), which are com- monly called heuristics and can be understood as high level or meta-decision making. DSs are used to successfully derive beneficial conclusions and actions in complex environments with repetitive patterns. These strategies filter infor- mation and compute preferences in a mostly fast and precise manner (Gigeren- zer, 2008). Given the central role of affect in how preferences are experienced, it seems apparent that affect must be integrated into meta-decision making paradigms.
However, given the significant ambiguity surrounding the definition of af- fect and the nature of complex meta-decision making, the threat of misleading conclusions being drawn is looming large. Nevertheless, only by taking on this challenge can researchers further advance the understanding of affect and its crucial role in the framework of human intelligence.
The field of affective neuroeconomics may well unveil the underlying reasons behind the effectiveness of human decision making. Darwin’s theory of evolution itself predicts that human emotions must be the result of generations of selective processes. While the importance of affect has been documented, it is now the time to truly understand its role in human decision-making processes. Therefore, this study aims to answer the following question: How do affective states interact with decision strategy mechanisms?
1.2 Manuscript in Short
Background
Human affect is a complex construct shaped by cultural developments, be- havioural studies and biological observations. Studying affect means to untangle these different perspectives. Neurological evidence suggests that affect exists on
multiple affective dimensions, rather than in distinct emotions (Lindquist et al., 2012).
Affective studies have attracted more interest recently, partly because they may hold the key to the understanding of meta-decision making. Cognitive sciences are on the verge of freeing themselves from traditional beliefs of op- timal behaviour and are exploring the phenomena underlying DS variability.
Heuristics researchers have moved the conversation from finding reasons why rationality in cognition fails, to how supposedly simple DSs can be so effective in cutting through the complexity of reality (Gigerenzer, 2008).
Affect appears to be fundamentally intertwined with the decision process and can not be dissected from it as a singular cause of certain biases (Loewenstein
& Lerner, 2003; Pfister & Boehm, 2008). Neurological evidence suggests that the reward system parametrically tracks valence during decision making (Tom et al., 2007), but arousal is also tracked in the vmPFC (Zhang et al., 2013).
Dynamic affective states, rather than affective impulses, appear to drive human behaviour in sequential decision events like foraging games (Spering et al., 2005).
Evidence suggests that affective states play a central role in taking in sen- sory information and computing a coherent outcome on a neural level (Bach
& Dayan, 2017). Regions linked to these strategic outcome computations are the dmPFC and the dlPFC (Korn & Bach, 2018, 2019). Results from repetitive transcranial magnetic stimulation (rTMS) studies have also indicated that these areas fulfill important functions in affect integration (Dunlop et al., 2020) and disengagement (De Raedt et al., 2010). These findings point to the importance of dynamic affective states for context coherent DSs in complex naturalistic environments.
Methodology
To simulate a naturalistic environment this study uses a sequential decision task based on an experiment by Korn & Bach (2019). Participants in the experiment are asked to digitally forage mushrooms for monetary reward, while avoiding an immediate threat of a predator attack. Both foraging success and predator attack have varying probabilities, which are known to the participant. For each decision node the choice is to risk foraging or to move on to the next decision without the risk of attack. An attack is associated with a potential loss of mushrooms and foraging opportunities, known to the participant. In between foraging situations participants’ affective states are altered through affect inducing videos, from the Database of Emotional Videos from Ottawa (DEVO) (Ack Baraly et al., 2020).
To study if DS selection is dependent on affect, three key DSs have been in- vestigated (1) The risk neutral payoff maximising DS (rnpmDS) or game optimal strategy. This strategy was computed through a Markov decision process (2) Focus on likelihood of foraging success DS (3) Focus on likelihood of a predator attack DS.
The task was developed to provide evidence for a dynamic affective states model. If the model and specifications derived from previous literature is correct,
this study should return evidence for the following three hypotheses.
I Experienced negative affective states lead to less desirable decision strate- gies during small stakes and limited time horizon events.
II Experienced positive affective states lead to more desirable decision strate- gies during small stakes and limited time horizon events.
III Complex affective states explain the use of targeted DSs.
Results
Affect measurements are a viable explanation for DS choices. Valence plays a key role in DS selection. Participants who experienced negative valence during the induction, are less likely to make foraging decisions according to the rnpmDS, lending support to hypothesis I. On the other hand, individuals that experienced the induction more positively are more likely to approximate the rnpmDS, which is evidence for the truthfulness of hypothesis II.
Other dimensions of affect also hold explanatory power for DS selection.
Combined effects of valence and arousal can also explain significant variations in DS utilisation. This finding lends some support to all three hypotheses.
Considering interactions for all three measured dimensions of affect with DSs provides the best fit for the observations. These effects are beyond interpreta- tion of specific affective influences. Nonetheless, this finding lends support to hypothesis III. Time taken for foraging decisions also appears to vary based on the interactions of stimuli and affective states.
Discussion
This study demonstrates that affective states shape the way decision strategies are used. In a foraging experiment that aims to simulate a naturalistic sequen- tial decision event, valence appears to significantly alter metacognitive decision making. Positive valence seems to be a good indicator for a better short term DS utilisation, whereas negative valence leads to less desirable monetary out- comes. A better explanation of the observations can be achieved by considering many dimensions of affect and how they act together to shape behaviour.
The experiment was conducted in an online fashion. Naturally this leads to less internal validity due lack of control over the participants and their envi- ronment, as well as limited options regarding the sensory experience during the experiment. On the other hand, the experiment is easily replicable and could with no additional effort be distributed to a significantly larger participant pool.
Results from this study have reinforced the authors’ belief that affect plays a key role in the way decisions are made. Humans are inconsistent in their choices, as they are guided by a dynamically changing affective state. The way affective states are shaped by incoming and memorised stimuli is hypothesised to be the result of an evolutionary selection process, expressed through neural population dynamics.
Given the promising findings from this study, it is proposed to conduct a rTMS study to further investigate the mechanisms underlying affective states.
Both the dmPFC, as well as the dlPFC lend themselves to such a study. Being able to directly influence DS use through brain stimulation could provide further insights about the way affective states are responsible for DS computations.
Given the rapid development of new precise methods for monitoring and altering neural activity, the author believes that cross disciplinary efforts may be a good option to extend the understanding of affective phenomena. Compu- tational models of affect in DSs, as used by this study, may not only be vital in predicting human behaviour, but may also accelerate the development of intelli- gent algorithms. Information theory with its high level concepts of information flows and processing may deliver new insights, just as quantum mechanics, the model for all particle interactions.
2 Background
2.1 Perspectives on Affect
”I shall limit myself ... to what may be called the coarser emotions, grief, fear, rage, love, in which every one recognizes a strong organic reverberation, and afterwards speak of the subtler emotions, or of those whose organic reverberation is less obvious and strong”
James (1890) Conceptual Affect
Most people can readily relate to feelings like “happy”, “scared”, “surprised“
or “angry” (Darwin, 1872), as they have personally experienced these. This commonly used terminology of emotions, though somewhat ambiguous, conveys the intended meaning.
Over recent decades researchers dealing with emotions have become more cautious of how to specify affective states (Loewenstein & Lerner, 2003). Qual- ifying complex concepts imprecisely can lead to incongruencies, when precise measurements aim to study these concepts. Describing modern neuroimaging data with a small set of emotional terms like those mentioned above, inadver- tently will lead to misspecifications.
Charles Darwin pioneered the study of affective states. He connected his understanding of emotions with his insights about life itself. The result was a theory of a fixed set of emotions, shared by humans and animals alike and fundamental to their nature (Darwin, 1872). This intuition of discrete emotions is supported by the finding that emotions are in fact recognised across indepen- dent cultures (Ekman et al., 1987). Describing affect in terms of discrete and basic emotions has hence a long standing tradition in the behavioural sciences.
An alternative model is the dimensional perspective, which can be inter- preted as both complementary or rivaling to basic emotions theory (Davidson et al., 1990). Defining affective states through a dimension like valence has the advantage of capturing positive and negative feelings on a spectrum. This positive negative scale does not only make emotions measurable, but also com- parable. Additionally, this approach can capture affect intensities well. What the valence model cannot do, is differentiate the intricacies between different emotional states. The addition of further dimensions like arousal and dom- inance improves the explanatory power of the continuous approach to affect (Mehrabian, 1996; Lindquist et al., 2012).
Another approach is to explain affect through its evolutionary functions.
Affect can be validly treated as a result of natural selection processes, where affect increases the likelihood of evolutionary beneficial decisions (Nesse, 1990).
An evolutionary view is a functional description of affect, though its power to conceptualise is limited.
Neurological Affect
Neuroimaging data opens up more detailed and data driven perspectives on the debate around affect. Behavioural principles can inspire the neurobiological perspectives on affect, but must not determine them.
The amygdala, for example, has been initially strongly linked with the basic emotion of fear (Breiter et al., 1996). However, more recently the consensus has emerged that the amygdala is involved in a wide range of affective states.
Hence a locationist approach with a limited set of basic emotions is unlikely to be a good model of affect (Lindquist et al., 2012).
There has been significantly stronger support for the dimensional view, show- ing evidence of affect dimensions being tracked in the brain. The Ventral Stria- tum (VS) (Schulz et al., 1997), and the ventromedial prefrontal cortex (vmPFC) (O’Doherty et al., 2001) have been identified as part of a reward system. Evi- dence shows that these brain areas parametrically track approach and avoidance decisions (i.e. valence). Similarly has physiological arousal been linked to para- metric activity in the vmPFC (Zhang et al., 2013). Dominance perception has been linked to multiple brain areas, most prominently the amygdala (Watanabe
& Yamamoto, 2015).
Summary - Perspectives on Affect
There is an apparent chasm between how humans intuitively and culturally experience emotions and how they can be measured in the brain. This differ- ence is not trivial. Current measures of affect usually require a self evaluation from individuals. During empirical studies it is therefore required to work with terminology every subject can clearly understand.
There is an agreement about the fundamental role affect plays in behaviour and that affective processes are reflected by tangible neural processes (Lindquist et al., 2012). Hence it is worth looking closer at what is commonly classified as affect and what are its key characteristics. Investigating why affect has sparked recent interest in the first place, can provide answers to these questions. The reason can be traced back to the shortcomings of economic models and variations in the use of decision strategies (DSs).
2.2 Decision Strategies
Heuristics as Decision Strategies
Traditionally cognitive decision making processes are often described in the con- trast between rationality (logic & Bayesian methods) and heuristics (Gigeren- zer, 2008). Classical economics has infamously neglected the importance of heuristics to construct its theories solely around the strong assumption that all interactions are performed by rational agents.
There is no doubt that economic theory and its axiom of rational decision making, originally postulated by Adam Smith (2003 [1776]), is a success story.
The premise of rationality has provided the basis for significant and precise
individual decision making theories like expected utility theory or game the- ory (Neumann & Morgenstern, 1944). However, experimental economists kept observing biases that could not be explained through logic or Bayesian method- ologies (Guth et al., 1982).
These deviations can be explained through what is known as bounded ra- tionality (Simon, 1955). Subsequently, prospect theory (Kahneman & Tver- sky, 1973, 1974, 1979) bridged the gap between psychology and economics.
Prospect theory mathematically outlines how individuals make seemingly ir- rational choices in simple economic games. Behavioural scientists have since adopted dual theories of decision making 1, to account for heuristic decision making as a parallel to rational thought (Evans, 2007).
However, varying DSs are more than just the occurrence of error prone heuristics. This can be summed up nicely in the metaphor of small and large worlds (Savage, 1954). In a small world, agents can estimate the values of all relevant parameters. From these values an optimal outcome can be computed through logic or Bayesian inference. In a large world, however, rational decisions are intractable problems. The information space has so many dynamic variables that they cannot be accounted for with limited computational resources. A heuristic or rather a simplifying DS is required to break down this complexity.
Conceptual Decision Strategies
To understand why this matters, it is helpful to understand where differing DSs come from. They tend to originate from evolutionary selection or learning (Gigerenzer I& Gaissmaier, 2011). Evolutionary DSs manifest themselves in a species through the fitness benefit they provide. An organism without risk averse tendencies for example, will likely go extinct due to premature death (McDermott et al., 2008). Risk averse tendencies are therefore favourable DSs for survival that account for ambiguity through trial and error — or survival and extinction.
Organisms use cue based DSs to build simplified models of their world, to narrow down the information space. In the end stands a manageable choice that can be optimised with rational thought alone (Simon, 1955). Affect has been identified as a key driver of such decision strategy variations (Slovic et al., 2007). However, the coined term affect heuristic is misleading, as will be elaborated on later in this study.
Neurological Decision Strategies
Neural dynamics that determine broader decision patterns are also called meta- control, as they are guiding the key parameters that shape DSs (Eppinger et al., 2021). Recent neuroscientific research implicates adjacent and overlapping regions in the medial prefrontal cortex (mPFC) in optimal and heuristic decision
1Dual theories often differentiate between a System 1 and a System 2. System 1 describes actions that are conducted automatically and unconsciously, whereas system 2 represents deliberate and effortful thought.
making (Korn & Bach, 2018). A follow-up study identified Blood-oxygen-level- dependent (BOLD) activity in the hippocampus, rather than the mPFC, during heuristics used in more aroused states (Korn & Bach, 2019). Hence there does not seem to be a single region in the brain, which could be linked to heuristic decision making. This suggests that the neural basis of different kinds of DSs’
is diverse and not linked to a specific heuristics region.
Summary - Decision Strategies
In conclusion, optimal computations in finite information spaces are as elegant and simple as they are effective. This rational thought appears to be our in- terface to reality. It is a simplified and overtly computable selection of an intractable stream of information at our exposure. Rationality in large worlds, however, is an illusion and any optimal policy can only be based on a filtered subset of the available information. The term heuristic, is used for a variety of cue based strategies with widely differing levels of sophistication. Rational thought is just a specific type of DS with a manageable information space. Neu- roscientific research also backs this conclusion, as DSs are computed throughout the brain. Furthermore, there is also neurobiological evidence for the role of af- fect in DS selection.
2.3 Affect in Decisions
Conceptual Affect in Decisions
The initial integration of affect into existing economic theory unified the concept of the behavioural decision value with expected utility theory (Loewenstein &
Lerner, 2003). A decision is described as an optimisation of the valence experi- enced, as a result of that decision, computed through Bayesian decision theory (Koerding & Wolpert, 2006). Pleasure is hence the common currency for utility maximisation and the goal of every decision (Cabanac, 1992).
Utility expressed as valence may be investigated through the decision affect theory (Mellers et al., 1997). According to decision affect theory, the utility of an outcome is not limited to the time independent value of the outcome.
Knowledge of alternative outcomes and unexpectedness influence the affective experience of outcomes as well. More evidence for the central role of affect can be found in individuals with clinical affective deficits. These conditions may elicit decisions that lead to suboptimal outcomes (Damasio, 1994). These findings extend the idea of economic utility maximisation without breaking it.
Another study, however, found that individuals who contemplate their rea- sons for making a consumer choice before making that choice are less satisfied than individuals that are not reflecting on their choice. This observation directly breaks with the idea that choices are rational maximisations of outcome valence.
It appears that the attributes that individuals consciously evaluate during the contemplation period may not be the most relevant. This implies that un- conscious preferences are getting crowded out by conscious evaluation. Hence,
individuals seem to be unaware of their true outcome preferences (Wilson et al., 1993). In return, affective states are important in evaluating attributes and are surprisingly effective in predicting the experienced utility of future states (Schwarz, 2013). For example, positive affect leads to different behaviours than negative affect, as the outcomes are evaluated with the help of the current mood (Clore & Huntslinger, 2007). Arousal as well has been indicated to impact deci- sions, increasing risk taking in ambiguous decisions (FeldmannHall et al., 2016).
The somatic marker hypothesis (Damasio et al., 1992) seeks to unify emo- tions with choice. Somatic markers are thought to be biochemical signals in the body that are in turn interpreted to guide choices. Affect is hence an innate property of decision making, expressed through somatic markers. The hypothe- sis further suggests that incidental affect also influences decision, as a distinction between related and unrelated markers is not always possible.
It can in fact be seen as established that the effect of affect is not bound to whatever has caused it, but will influence any decision, regardless if the affect holds relevant information. Affect does therefore shape decisions not solely through expected affect, but throughout the decision process, making the interaction significantly more dynamic than previously assumed (Loewenstein
& Lerner, 2003).
Affect or emotion does not serve a specific function for the decision pro- cess, but is rather dynamically modulating all stages of the process. From this, two key conclusions can be drawn: (1) The influence-on metaphor is mislead- ing. Affect is not an external influence on cognition, but rather a crucial part of it. Possibly due to the perceived superiority of rational thought, however, unconscious influences have been discarded as disturbances (2) Affect is not a homogeneous category with consistent paths of influence. Rather, it seems that a variety of modulations can be present or absent in affective states (Pfister &
Boehm, 2008).
Neurological Affect in Decisions
In neuroscience, converging evidence appears to confirm the existence of a com- mon currency. Outcome values of choices are represented in the reward system consisting of vmPFC (Peters & Buechel, 2009) and VS (Levy et al., 2010). Dam- age to parts of this affective reward system leads to individuals being unable to develop preferential decisions. This result clearly confirms the importance of affective brain regions in utility maximisation (Fellows & Farah, 2005). Relative coding as well has been observed in the reward system, establishing that value is always perceived within a context (Tremblay & Schultz, 1999; Knutson &
Greer, 2008). Interestingly, arousal has also been linked with activity in the vmPFC (Zhang et al., 2013) and latest research shows that valence and arousal do not seem to be separable in the vmPFC (Haj-Ali et al., 2020). This finding raises new questions about the relationship of affective dimensions.
Overall, evidence suggests that decision value as a model holds, when studied through a neuroscientific filter. Given the long development time and success in the disciplines of economics and psychology, this confirmation is vital but
unsurprising. It can be understood as established that valence in some form is tracked parametrically in the reward system (Tom et al., 2007), guiding decisions towards evolutionary benefits (Hoffman, 2019).
Regrettably, this consensus does not yet exist for the role of affect through- out the decision process. In fact, the neuroscientific literature explaining the behavioural observations earlier discussed in this manuscript is still scarce. How do seemingly unrelated valence, arousal, dominance and potentially other af- fective dimensions shape decisions? Accurate predictions of decisions will be impossible without a solution to these affect-in-decisions questions.
Additionally, the theory of expected utility and decision values must be an incomplete representation of affect. It can only partially explain how affective states integrate into decisions. It is also evident that without a holistic un- derstanding of affect in decisions the understanding of human cognition and intelligence is limited.
In the following, the author discusses promising approaches towards a com- plete theory of affective states and DSs. The aim is to remove the separation between expected and current affect and argue for a dynamic affect state ap- proach without the strict linear causal bounds utilised by previous theories.
2.4 Unifying Affective States and Decision Strategies
Temporal Inconsistencies of Utility Functions
Behavioural deviations from expected utility maximisation have been largely discussed. The evaluation of DSs has hinted at some underlying problems in this context. Applying the large world metaphor captures the intuition that real life optimisations must be intractable problems, given the limited computational resources available. The following account lays out a decision theoretic argument for why decision values need to be fundamentally reevaluated.
Having a utility function delivering the decision value for an approach- avoidance choice appears to be a mathematically sound approach. However, this isolationist view disregards the reality that an individual at any moment is confronted with a variety of long and short term goals that run parallel. Opti- misation might simultaneously happen over weekend plans as a long term goal, thirst as a fundamental need, fear of pain as continuous mode of self protection and many more (Bach & Dayan, 2017). While the utility of all these compet- ing goals could be theoretically summed up to determine the best course of action, practically this is impossible. The reason is that the utility maximisa- tion approach disregards neural system dynamics. Having all utilities computed simultaneously and adjusted to the dynamically changing environment is com- putationally intractable. This can be illustrated through the halting problem from computational theory. In essence, the problem states that there can be no such program to determine for all programs, if they will ever finish (Turing, 1937). To the best of our understanding, this property must hold true for neural computations as well. A general utility function is hence not applicable, as it can be uncomputable.
The solution must be to derive models that acknowledge the dynamic and continuous feedback cycle between goals and behaviour. In the following, a review of the key literature about (1) functional descriptions of ongoing affec- tive states and (2) computational underpinnings of affect is conducted. These two perspectives should not be seen as fundamentally separate, but rather as approximative models of the same substrate from different perspectives.
Affective States
Defining affect in terms of states that prompt the use of differing DSs, reconciles its definition with measurable neural results. Foraging tasks have been shown to be particularly suited to observe the interaction of affective states with deci- sions. These tasks appear to be a superior representation of reality, compared to the more common one-shot experiments, as they deliver less biased partici- pant behaviour (Carter et al., 2015). Foraging tasks have been shown to lead to the use of differing DSs between individuals with positive and negative affect (Spering et al., 2005).
Evidence for affect state dependent processing and decision making can be found across different neural sub-fields. Affect in the framework of mood has been linked to changes in memory recall and memory formation. Individuals will tend to recall memories that are congruent with the mood they are currently in. Similarly, more vibrant memories are formed, if the items to memorise align with an individual’s prevalent affective state (Bower, 1981). Given the crucial role memory plays for perception and behaviour, affective states can be expected to have a profound impact. Positive valence states for example, may lead to changes in content and context cue processing (Bohner et al., 1992), riskier behaviour due to focus on positive attributes (Stanton et al., 2014), as well as more focused and efficient DSs (Isen & Means, 1983).
The well studied phenomenon of priming (Weingarten et al., 2015), can be understood as a sub-phenomenon of affect state DS selection. During priming, an initial stimulus will shift the affective state, leading to more focused process- ing of related stimuli. These priming mechanisms manifest themselves not only in the visual brain regions, but also in the prefrontal cortex (PFC) (Schacter et al., 2004). The PFC and particularly the dorsolateral PFC (dlPFC) have also been linked with maintenance of working memory (Cohen et al., 1997). This suggests that information about a stimulus shifts the affective state through its impact on working memory encoding and working memory recall. An example can be found in health and taste related priming, before food selection. Individ- uals considering the health value of food items, show modulated value signals for specific foods in their vmPFC. Furthermore, individuals focusing on health benefits show stronger activation in the dlPFC than control subjects. This sug- gests that the neural representation of health concerns in the dlPFC modulates the affective state (Hare et al., 2011).
In conclusion, recent research points towards the importance of dynamic evaluations of internal states and their effect on decisions. The linear cause and effect models of affect and decisions proposed in the past, do not capture the
dynamic feedback cycles of affective states and sensory information. On the ex- ample of positive affect, it was discussed how affective states shape memory, per- ception and behaviour and in turn are shaped by these cognitive functions. The reason for this strong interaction is that affect is not an external phenomenon, but ingrained in the previously mentioned cognitive functions. Priming of the affective state will lead to altered decision values through controller modulation.
This in turn enables related associations and improved situational preparedness.
The affective state, however, is always present and constantly changing. These effects can be observed without defining the precise affective dimensions or af- fective states. In the following, it will be discussed how affect regulates neural computations and enables information processing.
State dependent Computations
Computationally, affect is hypothesised to be a response optimisation system that deploys algorithms to increase evolutionary fitness (Bach & Dayan, 2017).
Behaviour in foraging situations can indeed be explained through highly effective DSs, such as the normative optimal DS. Integration of different DSs can be traced back to activity in the dmPFC (Korn & Bach, 2018). Stimulation of the dmPFC with rTMS has also shown to be a potential treatment for depression, highlighting its importance in affective integration functions (Dunlop et al., 2020). Coupling of dmPFC and amygdala has been observed during situations of increased anxiety (Vytal et al., 2014).
Interestingly, when an immediate threat is introduced into the foraging sit- uation, threat focused DSs correlate with activity in the hippocampus, as well as the dlPFC (Korn & Bach, 2019). The dlPFC has been linked to mediating threat situations (Balderston et al., 2017) and rTMS stimulation to the area may lead to problems with emotional disengagement (De Raedt et al., 2010). It appears that key affective areas get deployed to develop stimulus specific DSs.
Further empirical evidence of how different affective states interact with DSs and their neural correlates in these situations is still outstanding.
The constant presence and influence of affective states can already be ob- served without any active manipulation. Monitoring of neural activity in mon- keys has shown that activity during a behavioural task shifted in the visual area V4 and the dlPFC. As expected, these state changes coincide with changes ob- served in animal behaviour. Specifically, these changes explain the disregard of sensory information in an impulsive way, determining monkey choices (Cowley et al., 2020).
The interaction of more salient affective states with decisions has been doc- umented on human subjects. Baseline activation in the vmPFC shifts with an individual’s affective state. This activity in turn determines the computational process that lies at the bottom of the decision making process. For example, the weighting of gains and losses may be influenced by these neuronal popula- tion dynamics (Vinckier et al., 2018). Contextual information as well has been shown to be simultaneously selected and integrated through a single dynamic process of neuronal populations in the PFC (Mante et al., 2013). This obser-
vation could be achieved through the trend of focusing on neural population dynamics (Kohn et al., 2016) and provides further evidence for the key role of dynamic and integrated affective states on a computational level.
The maintenance of homeostasis is a key principle that guides an individ- ual’s behaviour and hence its neural computations (Keramati & Gutkin, 2014).
Maintaining this balanced state prevents excessive internal and external stress to that organism. The importance of affective states in maintaining homeostasis can be illustrated through the need for hydration. If there is a need for hydra- tion, the Hypothalamus will cause neural population dynamics across the brain (Allen et al., 2019). This signal will hence dominate the affective state and its DSs will be focused towards resolving the threat of imbalance. The strongest form of affective influence is the reflex. The startling reflex for example is meant to protect from predator attack and readies the body for action. It elicits an affective state, significantly altering DSs towards stimuli like sounds or visual cues (Yeomas et al., 2002).
Summary - Unifying Affective States and Decision Strategies
Humans only have limited time and computational resources available to decide on behaviour. It is hypothesised that the brain maintains predictive models for certain behaviours by maintaining context appropriate affective states. These affective states can be understood as the root of decision strategies, which are pre-selecting the space for targeted neural population dynamics. Delivering further evidence for this dynamic affect DS model, as well as explaining the role of affective states, is the goal of the following experiment.
3 Methodology
The basis of this experiment is an approach-avoidance foraging task with sequen- tial decisions. The aim is to investigate the computations underlying foraging decisions, given specifically induced affective tendencies. This foraging task was selected for two reasons: (1) its capacity to yield more normative optimal par- ticipant behaviour than the one-shot version of the task (Carter et al., 2015) and (2) its ability to sample decisions for affective states in a coherent context (Spering et al., 2005). The main experimental task in this study has been de- veloped on the basis of the foraging task used in Korn & Bach (2019). The aim for the participants was to successfully forage mushrooms under the threat of predation. Affect inducing videos have been selected from the Database of Emo- tional Videos from Ottawa - DEVO (Ack Barlay et al., 2020). Participants were monetarily incentivised to maximise the amount of mushrooms they foraged.
The main experimental task consists of multiple passive induction parts and active foraging parts. The experimental design was developed to assess the interaction between changes in affective states (treatment/self-reported affect) and DS selection (foraging task). The aim of this investigation is to show on a behavioural level, how affect integrates into strategic cognitive computations.
If successful, the author hopes to lay the experimental ground work for a rTMS study.
3.1 Experimental Task
The experimental subjects participated in a sequential decision task. This task is designed as a digital foraging world, in which the goal is to gather as many mushrooms as possible (Appendix A) for the instructions).
During the task, participants enter 4 blocks of up to 4 trials. These blocks are referred to as forests and represent a closed event in the experiment, where foraging choices for the subjects are interdependent.
Mood-Induction Technique
Each forest begins with an induction phase, which is referred to as the trail to the forest. There are three different induction treatments, which were assigned to the subjects pseudo-randomly (by order of participation). The induction was conducted through affective videos. Videos were chosen as the method of induction, because of their proven effectiveness in inducing affect (Fernandez- Aguilar et al., 2019). Another factor is that videos are well suited for the repetitive induction technique this study uses. Different passages of the same video were shown to subjects. This technique of using only one coherent video was selected to simulate a continuous foraging environment, without letting participants adjust to a repeated stimulus (like one recurring affective image).
The videos are selected from the DEVO (Ack Baraly et al., 2020) for mood inducing videos, where their valence and arousal is rated on a 1-9 likert scale.
This study aims mainly to induce differing affect along the established valence
Figure 1: Induction Phase. Each block of trials, called for- est, starts with 10 sec- onds of an inductive video. Each partici- pant pseudo-randomly gets assigned the pos- itive (figure example), the negative or the neutral video, of which they see four clips.
dimension, with a level of arousal. Videos should induce (1) a positively aroused state through a video of a sloth orphanage (Figure 1), (2) a negatively aroused state through a wasp nest and (3) a neutral non aroused state as control, through birds on a pond.
The second criterion is that the videos show alive animals that had little or no resemblance of the predator icon in the foraging task. Animal videos are chosen because they fit well with the general frame of a foraging environment and are therefore not breaking the simulated context. Ultimately, the negative video was also selected on the basis of being rather threatening, whereas the positive video is rather non threatening. The induction video plays for 10 seconds before each forest.
Given the hypothesised constant presence of affective states (e.g. Bower, 1981; Cowley et al., 2020; Vinckier et al., 2018), the aim of the induction is not to generate a specific affective state, but to manipulate the present one towards a certain direction.
Foraging
After the trail with the induction video, the subjects virtually arrive in the forest (Figure 2). In the forest, subjects face multiple interdependent foraging decisions. Each forest consists of up to 4 trials, which are called clearings. Each clearing consists of a foraging phase and an outcome phase. During the foraging phase, the participant is presented with two stimuli; an appetitive stimulus (mushroom icon) and an avoidance stimulus (predator icon). Each clearing has a randomly selected probability of foraging success out of 0.6, 0.45, 0.3 and 0.15.
The chance of foraging success is visualised through the size of the mushroom icon, in order to illustrate the stimulus value through a salient naturalistic attribute. There is also a %-number below the stimulus for clarity. Simultaneous to foraging success, there is an associated randomly selected probability for predator attack as well. The associated probabilities are 0.4, 0.3, 0,2 and 0.1.
Icon size and %-number indicate the attack likelihood for the participant.
During the foraging phase the participant has to make a decision to either forage at the clearing or leave. When a participant decides to leave the clearing
they will move on to the next clearing, independent of the probability values of the stimuli. If the participant decides to forage she will have the respective chance/risk of success and attack. A participant’s success is measured in food points. Foraging success in a clearing is associated with the addition of one food point to the participant’s account. Food points determine the final payoff for the participant. If the participant gets attacked by the predator, she will lose all food points previously collected in the current forest and she will immediately move to the next forest. Food points from past forests are safe.
If a participant chooses to forage and is neither successful nor gets attacked, she will move to the next clearing without any particular reward or punishment.
The participant has 5 seconds to make a decision. If no decision is made, the participant will automatically leave the clearing, and lose one food point. The time remaining at the clearing, as well as the clearing number, are depicted at the top of the screen.
After the foraging phase follows the outcome phase. The purpose of the outcome phase is to communicate the result of the clearing in a neutral way, to minimize the effect on the subject’s affective state. Success is visualised through a “1”, attack through a “-” and all other outcomes through a “0”, since they lead to the same result.
Instruction and Induction Check
The experiment begins with a short introduction that also gives a brief overview of the foraging task. Afterwards, it follows an instruction (Appendix A) outlin- ing the rules and objective of the experiment. To ensure that all participants understand the experiment, they need to answer a set of three comprehension questions. A participant has three attempts to answer the questions correctly, before being eliminated from the study.
After the fourth forest, participants are asked to rate their valence (1 = very negative, 100 = very positive), arousal (1 = very calm, 100 = very excited) and dominance (1 = very submissive, 100 = very dominant) (Mehrabian, 1996) regarding the induction video they saw on the trail on a slider. The rating was counter to common practice conducted not after every video clip, but only after the experiment. The reason for this measurement technique was that the reflection on the own affect would have taken the subjects out of the frame of the experiment. Furthermore, would the conscious contemplation of affect have altered the subjects’ affective state and hence her behaviour. The experiment ends with a goodbye screen that also displays the final payoff.
3.2 Experimental Procedures
Participants were randomly recruited on Prolific (https://prolific.co) and participated in the experiment online. The entire experiment lasted on average approximately 8 minutes. Participants were monetarily incentivised to partici- pate in the experiment. Participation was rewarded with£0.75, with a bonus of£0.15 for every food point in their account, at the end of the experiment. In
Figure 2: Foraging and Outcome Phase. Each forest consists of four clearings.
At each clearing a participant can choose to forage or leave. If a participant chooses to forage at the foraging phase they have a chance of earning a food point (45%
in figure example), but also run the risk of being attacked and getting zero food points for the current forest (20% in figure example). If a participant chooses to leave they move to the next clearing without a chance for food points or attack. In the outcome phase, participants are informed about the result of their foraging. A 1, means foraging success, a - means attack and a 0 means no success. After the outcome phase, participants move to the next clearing or forest depending on the clearing number or result of the current clearing.
total 207 participants were recruited for the study. Of these participants 88 had invalid results because of a technical failure, 4 were excluded for not completing the study and 3 were not able to answer the comprehension questions correctly in the third try. Under the 112 valid participants were 43 females, 68 males and one other. The valid participants had an age distribution of 18 - 30: 92; 31 - 65: 22; 65+: 1. In terms of treatments, 35 participants received the negative treatment, 39 were in the neutral group and 38 in the positive conditions.
The experiment was developed on the basis of the oTree python library (Chen et al., 2016).2 The analysis was conducted in R.3
3.3 Computational Framework
The aim of this experiment is to give a computational account of participants’
behaviour after having been subjected to an affective manipulation. The ex-
2The authors’ implementation of the foraging task can be found here:
https://github.com/tobiball/thesis/tree/master/experiment/otree_thesis.
3All code relevant for conducting the data analysis can be found here:
https://github.com/tobiball/thesis/tree/master/analysis/main.
perimental task by Korn & Bach (2019) has outlined how participants behave under foraging situations with an immediate threat. Their results show that their participants’ behaviour can be best explained by the probability of preda- tor attack DS and the game optimal strategy. The game optimal strategy in the experiment is developed to yield the maximum expected monetary outcome.
It is therefore the optimal strategy for participants who aim to earn the most monetary reward and have no specific risk preferences.
In the framework of this study, the game optimal strategy will therefore be called risk neutral payoff maximisation decision strategy (rnpmDS). This defini- tion is meant to highlight that specifying an optimal strategy always requires a limited time horizon and a limited number of behavioural options. An rnpmDS is hence only computable, because there is a limited number of choice options available to participants (forage and leave) and there is a fixed maximum num- ber of trials. Payoffs of the game will also not significantly alter the total wealth of the subjects. For example risk averseness, rather than maximisation of the expected outcome, would be justified if life changing sums of money would be involved.
The rnpmDS is calculated through a Markov decision process. The im- plementation of the optimisation algorithm for the rnpmDS was developed for the purpose of this experiment and can be found here: https://github.
com/tobiball/thesis/tree/master/analysis/policy_calculations. The rnpmDS optimises over all experimental variables in a forest. Given the lim- ited decision time available to participants, this strategy can be understood as intractable. The rnpmDS strategy takes into account the foraging success and predator attack probabilities, potential losses of food points through preda- tion and all potential future configurations of these variables for the remaining clearings in the forest.
Next to the rnpmDS, the probability of predator DS also approximates par- ticipant behaviour in foraging situations well (Korn & Bach, 2019). These two strategies, as well as the probability of foraging success DS will be the main focus of this study.
To summarise, two DSs are solely based around the probabilistic values of the stimuli (simple DSs), whereas the rnpmDS is a highly complex Markov decision process. These computational models are utilised to investigate the interaction of affective states and DS use. From previous models and empirical results, three experimental hypotheses about the results for this study have been derived.
I Experienced negative affective states lead to less desirable decision strate- gies during small stakes and limited time horizon events.
II Experienced positive affective states lead to more desirable decision strate- gies during small stakes and limited time horizon events.
III Complex affective states explain the use of targeted DSs.
Beyond the key hypotheses, this study aims to utilise the empirical data for an explorative analysis. Due to the hypothesised differences in neural networks
involved, there is reason to believe that these differences will manifest themselves not only in the decisions made, but also in the time taken to compute a decision.
Therefore an open hypothesis for this study is that reaction times differ based on affect and DSs.
4 Results
It follows the analysis of empirical data with the goal of finding evidence for or against the experimental hypotheses of this study. The aim is to show how specifically valence, as a central dimension of affect, may improve or deteriorate the use of beneficial DSs. Additionally, it is hypothesised that complex affect plays a key role in DS selection and behaviour.
Standard errors are displayed in “( )” in all regression tables and in the manuscript, where relevant. Significance levels considered in this study start at p<0.1 (considered significant under reservation) to p<0.001.
4.1 Induction
A key requirement for observing an effect of affective state and DS interactions, is a targeted modulation of affect. Inductive videos are used to achieve this modulation. Before starting the analysis of foraging behaviour, it is therefore important to confirm that the videos had the desired effect on participants’
affect. Linear regressions are conducted for all three dimensions of affect to study the effect of the treatment induction.
Table 1 and Figure 3illustrate the effectiveness of the affect induction. In the following, the induction analysis of the experimental data is outlined. In the analysis, the self reported affective impact of the inductive video is regressed on the treatment variables.
In the text, the difference in valence and arousal ratings between control and treatments from the DEVO (Ack Baraly et al., 2020), will be displayed in
“[ ]”, behind this study’s results (Table 1). The ratings used by the DEVO are converted to match the scale used in this study (1-100). Affect ratings conditional on treatment can be interpreted as follows.
(Valence) (Arousal) (Dominance) (Intercept) 71.0789∗∗∗ 37.0263∗∗∗ 52.3684∗∗∗
(3.1490) (3.9864) (2.8927) Negative Induction −31.8012∗∗∗ 19.7515∗∗∗ −5.4240 (4.5148) (5.7154) (4.1474) Positive Induction 9.6842∗ 1.1842 −10.9211∗∗
(4.4534) (5.6377) (4.0910)
R2 0.4571 0.1202 0.0614
Adj. R2 0.4471 0.1041 0.0441
Num. obs. 112 112 112
∗∗∗p < 0.001;∗∗p < 0.01;∗p < 0.05;‘p < 0.1
Table 1: Affect Induction. Linear models describing the effect of induction on the different affective dimensions.
As expected, the negative induction yields a significantly lower valence rating of -31.801 (4.515; p<0.001 [-27.3]), than the control (i.e. the baseline). The
positive induction is also successful, showing a rating of 9.684 (4.453; p<0.05 [24.1]) more than the control. Valence as the key dimension hence returns the target effects.
a
b
Figure 3: Effectiveness of Induction. Mean values are displayed as yellow dots.
(a) Negative induction led to significantly lower valence ratings than the neutral in- duction. The positive induction has the highest valence ratings (b) The arousal plot suggests a U-shaped relation. Negative and positive induction lead to heightened levels of arousal.
For the arousal dimension the results are only significant for the negative treatment 19.752 (5.715; p<0.001 [36.6]), but not for the positive treatment
1.184 (5.638; p>0.1 [24.8]). As previously discussed, evidence suggests that arousal plays an essential role in the experience of valence (Lindquist et al., 2012). This lack of arousal needs to be accounted for in the later part of the analysis, as it may bias the measured effects of valence or dominance.
The dominance dimension was used exploratively and to give a more com- plete picture of the affective states experienced by the participants. Here the negative treatment is not significant with -5.424 (4.147; p>0.1), whereas the pos- itive induction shows a significantly low dominance rating with -10.921 (4.091;
p<0.01). After confirming the videos were for the most part successful in alter- ing the affective states of the participants, the following parts will be dedicated to the analysis of the DSs.
4.2 Treatment Analysis
The binary dependent variable participant foraging choice, for the regressions (1) - (8), is equal to 1 if the subject chooses to forage. Due to the binary nature of the dependent variable a logit regression was used to investigate the interaction of different DS variables with affect, in regards to the foraging choice. Each trial represents a data point in the regression. The standard errors are clustered by participant for regressions (1) - (8). From all the trials where participants did make an active foraging choice (that is where they did not time out), 15 were removed because their rnpmDS did not prescribe a definite choice. This can occur in certain situations where the expected outcome value of both choices, foraging and leaving, is equal.
Models (1) and (2) show key decision variables, but omit the categorical treatment variables (Table 2). The results of regression (1) show that partici- pants’ DSs use the probability of foraging success P(Success) (p<0.001), as well as the probability of attack P(Predator) (p<0.001), out of the variables that do not require any forecasting. The following strategy variables are insignificant:
food points that were already collected in the current forest (Wealth State), clearing number in the forest (Clearing Nr.) and having been attacked in the previous trial (Attack Prev.).
Their lack of explanatory power is reflected by the difference in quality of fit between regression (1) and (2). Regression (2) shows relatively higher ex- planatory power in the key goodness of fit measures; like the Akaike Informa- tion Criterion (AIC, 1061.9>1056.7) and Bayesian Information Criterion (BIC, 1098.6>1077.7).
The rnpmDS also is significant and has strong explanatory power in regres- sion (1) (p<0.001) and more relevant (2) as well, (p<0.001). This is a very interesting result since the Markov decision process is particularly complex and optimises over many branches (states and probabilities). In fact the rnpmDS has been used in 81.7% of the trials.
Model (3) includes the categorical treatment variables and their interaction effects with the significant DS variables. The treatment on its own shows as ex- pected no significant impact on foraging decisions (Appendix B,Table 6). Most treatment with DS interaction effects do not show any significance either. How-
(1) (2) (3)
(Intercept) −0.1361 −0.2302 −0.2054
(0.3440) (0.2921) (0.2945)
P(Success) 8.9297∗∗∗ 8.6563∗∗∗ 7.6592∗∗∗
(0.8291) (0.7516) (1.5438)
P(Predator) −9.9235∗∗∗ −9.6482∗∗∗ −8.9027∗∗∗
(1.1535) (1.0517) (1.7738)
rnpmDS 0.8431∗∗∗ 0.9550∗∗∗ 1.3732∗∗∗
(0.2523) (0.2205) (0.3600)
Wealth State −0.1226
(0.2118)
Clearing Nr. 0.0080
(0.1030)
Attack Prev. 0.0100
(0.2672)
P(Success)XNegative Induction 1.6416
(1.9120)
P(Success)XPostive Induction 1.1199
(1.9304)
P(Predator)XNegative Induction −1.0861
(2.1838)
P(Predator)XPostive Induction −1.1353
(2.0251)
rnpmDSXNegative Induction −0.8120∗
(0.4760)
rnpmDSXPositive Induction −0.3780
(0.5415)
AIC 1061.9129 1056.7475 1063.1025
BIC 1098.6325 1077.7301 1115.5591
Log Likelihood −523.9565 −524.3738 −521.5513
Deviance 1047.9129 1048.7475 1043.1025
Num. obs. 1402 1402 1402
∗∗∗p < 0.001;∗∗p < 0.01;∗p < 0.05;‘p < 0.1
Table 2: Base DS and Treatment. Logit models describing the effect of different DSs and treatment interaction effects on participant foraging choice. SEs are clustered by participant as implemented in the R package miceadds.
ever, the interaction between rnpmDS and the negative treatment are significant (p<0.05). This finding shows that participants are less likely to approximate the rnpmDS when their affective state was induced negatively (Figure 4). This result provides evidence for HI.
• Experienced negative affective states lead to less desirable decision strate- gies during small stakes and limited time horizon events.
However, regression (3) has lower explanatory power for most measures (BIC, 1115.6; AIC, 1063.1) than regression (1) and (2) and is only better in Log Likelihood (LL, -521.6). This suggests that the treatment variables are not the ideal explanatory variables for participants’ behaviour.
This may be due to the lack of arousal to make the experience of valence more vivid. Another reason may be that affective states are experienced differently, and depend on more complex interactions of various dimensions.
Figure 4: rnpmDS choices by Induction. Negatively induced subjects make the most non-rnpmDS choices and are hence expected to get the lowest payoff. Positively induced subjects on the other hand make the most choices prescribed by the rnpmDS.
4.3 Affect Analysis
One-Dimensional Affect
Regressions (4) - (8) investigate participants’ use of DSs conditional on affective influences (Table 3&Table 4). The scale of the valence and dominance ratings are adjusted for the following analysis. From the self reported values, 50 is de- ducted in order to have negative values for negative valence and low dominance.
The purpose of this transformation is to shift them, to represent that they are opposites to positive valence and high dominance, rather than the lack of those states.
The first affect model that is considered is regression (4)Table 3, which takes into account the interaction effects of only valence with the three key decision variables. All interaction effects are significant. Subjects that are feeling more positively are less likely to forage in high gain situations, than those subjects with more negative feelings (p<0.05). In higher threat situations, however, more positive participants’ are significantly more likely to forage, than the ones reporting to have been negatively induced (p<0.1)
In regards to the rnpmDS, it appears that positively induced participants are more often behaving in a manner that approximates this strategy variable (p<0.1). This finding suggests that in the frame of the game, positive partici- pants are behaving closer to the optimum in terms of their normative outcome.
Evidently this finding lends again support to HI, but also HII.
• Experienced positive affective states lead to more desirable decision strate- gies during small stakes and limited time horizon events.
The quality of the affect interactions model (4) (BIC, 1089.7; AIC, 1053.0;
LL, -519.5) exceeds the quality of the treatment model (3) significantly (∆ BIC, -25.9; ∆ AIC, -10.1; ∆ LL, 2.1). It also improves the affect omitting base model (2) in terms of AIC and LL. The BIC, however, favours the simpler model (2).
Model (5) additionally includes the arousal and dominance dimensions. Its valence interactions are significant at even higher levels (P(Success)XVal, p<0.01;
P(Predator)XVal, p<0.05; rnpmDSXVal, p<0.05). Additionally to these inter- action effects, a negative effect of arousal with success probability (p<0.1), as well as a positive relationship between arousal and the rnpmDS in the arousal dimension (p<0.1), exhibit themselves. In the dominance dimension, there is a significant positive effect on foraging behaviour for higher probabilities of threat (p<0.1). Model (5) has a significantly better AIC (1046.9) and LL (-510.4) than the base regression (2). The BIC, however, is likely due to the large number of model parameters relatively high (1115.1).
(2) (4) (5)
(Intercept) −0.2302 −0.2565 −0.2049
(0.2921) (0.2953) (0.3048) P(Success) 8.6563∗∗∗ 9.3556∗∗∗ 12.3995∗∗∗
(0.7516) (0.8208) (1.5948) P(Predator) −9.6482∗∗∗ −10.2835∗∗∗ −11.9753∗∗∗
(1.0517) (1.1285) (1.6160)
rnpmDS 0.9550∗∗∗ 0.8101∗∗∗ 0.0270
(0.2205) (0.2335) (0.4574)
P(Success)XVal −0.0546∗ −0.0752∗∗
(0.0247) (0.0280)
P(Predator)XVal 0.0520‘ 0.0619∗
(0.0292) (0.0315)
rnpmDSXVal 0.0153‘ 0.0210∗
(0.0080) (0.0085)
P(Success)XAro −0.1155‘
(0.0600)
P(Predator)XAro 0.0595
(0.0606)
rnpmDSXAro 0.0295‘
(0.0164)
P(Success)XDom −0.0236
(0.0471)
P(Predator)XDom 0.0956‘
(0.0526)
rnpmDSXDom −0.0155
(0.0102)
AIC 1056.7475 1052.9794 1046.8942
BIC 1077.7301 1089.6990 1115.0877
Log Likelihood −524.3738 −519.4897 −510.4471
Deviance 1048.7475 1038.9794 1020.8942
Num. obs. 1402 1402 1402
∗∗∗p < 0.001;∗∗p < 0.01;∗p < 0.05;‘p < 0.1
Table 3: One-Dimensional Affect Models. Logit models describing the effect of different one-dimensional affect interaction effects on participant foraging choice. SEs are clustered by participant as implemented in the R package miceadds.
Multi-Dimensional Affect
As discussed previously, a significant body of literature has investigated possible interactions and dependencies between valence and arousal (e.g. Lindquist et al., 2012; Haj-Ali et al., 2020). Regression (6) (Table 4) explains these effects for the participant foraging choices. Significant effects are present for all interactions with the key DS variables (P(Success)XValXAro p<0.05; P(Predator)XValXAro, p<0.05; rnpmDSXValXAro, p<0.1). The directions of the effects are congruent with the effects observed for the sole interaction of valence with the DS variables in regression (4) and (5). Also the quality of model fit parameters for model (6) (BIC, 1088.7; AIC, 1052.0; LL, -519.0) is very similar to the valence interaction effect model (4). This finding also suggests that complex interactions of affect dimensions are relevant for DS selection.
Taking into account all possible 2-way interactions of affective dimensions as in regression (7) does not reveal any additional affective interactions with partic- ipants’ DS variables. The interaction between valence, arousal and probability of predator, however, drops below the significance level (p>0.1). The model shows an improved AIC (1048.7) and LL (-511.3), compared to the valence and arousal only model (6). However, it has a significant handicap in terms of BIC (1116.9).
Next, the focus shifts to possible 3-way interactions between affective dimen- sions and DSs. The relationship of possible interactions between dominance and the other affective dimensions, as well as their effect on different DS variables, is unspecified by previous literature. Given this uncertainty, the direction of the coefficients for these interaction effects are beyond interpretation.
Nevertheless, complex affective interactions in model (8) show a significant effect for two out of three DS variables (P(Success)XValXAroXDom, p<0.01;
P(Predator)XValXAroXDom, p<0.1). Even though they may not be inter- pretable in their effect direction, the evidence strongly suggests that these con- structionist affective states play a crucial role in the way participants behave in the forager world, how they resolve their approach-avoidance conflicts and how they moderate risk through DSs.
This finding is supported by all the model fit measures. Out of all regressions that aim to explain foraging behaviour its AIC (1045.9) is the lowest. Only the BIC of the base model (2) is slightly better than the BIC (1082.6) of the complex affect model (8). Its LL is relatively low as well (-515.9). The significance of the complex affect state model and its relatively strong fit to the experimental data provides experimental evidence for HIII.
• Complex affective states explain the use of targeted DSs.
To ensure that the data is correctly interpreted, the regressors from the rele- vant models are used to estimate logit mixed effects models (Table 5). The mixed effects (ME) model without affective influences (ME2) shows high significance for the three DS variables P(Success), P(Predator) and rnpmDS (p<0.001).
As for model (2), model (ME2) performs the worst of the four models in AIC (1020.5) and LL (-505.2), but performs the best in BIC (1046.7). The model
(2) (6) (7) (8)
(Intercept) −0.2302 −0.2538 −0.2293 −0.2316
(0.2921) (0.2945) (0.3043) (0.2981) P(Success) 8.6563∗∗∗ 9.1112∗∗∗ 9.2781∗∗∗ 8.9817∗∗∗
(0.7516) (0.7312) (0.7561) (0.8005) P(Predator) −9.6482∗∗∗−10.0321∗∗∗−10.2171∗∗∗−10.0923∗∗∗
(1.0517) (1.0558) (1.0989) (1.1292) rnpmDS 0.9550∗∗∗ 0.8886∗∗∗ 0.8445∗∗∗ 0.9238∗∗∗
(0.2205) (0.2233) (0.2278) (0.2269)
P(Success)XValXAro −0.0023∗ −0.0023∗
(0.0010) (0.0011)
P(Predator)XValXAro 0.0021∗ 0.0017
(0.0010) (0.0011)
rnpmDSXValXAro 0.00060 0.0007∗
(0.0003) (0.0003)
P(Success)XValXDom −0.0005
(0.0011)
P(Predator)XValXDom 0.0010
(0.0016)
rnpmDSXValXDom 0.0002
(0.0003)
P(Success)XAroXDom −0.0014
(0.0024)
P(Predator)XAroXDom 0.0030
(0.0026)
rnpmDSXAroXDom −0.0003
(0.0005)
P(Success)XValXAroXDom 0.0001∗∗
(0.0000)
P(Predator)XValXAroXDom −0.00010
(0.0000)
rnpmDSXValXAroXDom 0.0000
(0.0000)
AIC 1056.7475 1052.0271 1048.6800 1045.8757
BIC 1077.7301 1088.7467 1116.8735 1082.5953
Log Likelihood −524.3738 −519.0136 −511.3400 −515.9379
Deviance 1048.7475 1038.0271 1022.6800 1031.8757
Num. obs. 1402 1402 1402 1402
∗∗∗p < 0.001;∗∗p < 0.01;∗p < 0.05;0p < 0.1
Table 4: Multi-Dimensional Affect Models. Logit models describing the effect of different multi-dimensional affect interaction effects on participant foraging choice.
SEs are clustered by participant as implemented in the R package miceadds.
