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.
(ME2) (ME4) (ME6) (ME8)
(Intercept) −0.1629 −0.1743 −0.1641 −0.1716
(0.3035) (0.3045) (0.3037) (0.3036) P(Success) 9.0679∗∗∗ 9.7984∗∗∗ 9.5594∗∗∗ 9.2816∗∗∗
(0.7179) (0.8625) (0.7809) (0.7399) P(Predator) −10.5067∗∗∗−11.1112∗∗∗−10.9149∗∗∗−10.8280∗∗∗
(1.0015) (1.1190) (1.0519) (1.0281)
rnpmDS 1.1300∗∗∗ 0.9306∗∗∗ 1.0284∗∗∗ 1.0998∗∗∗
(0.2021) (0.2267) (0.2114) (0.2074)
P(Success)XVal −0.0538‘
(0.0285)
P(Predator)XVal 0.0477
(0.0294)
rnpmDSXVal 0.0163∗
(0.0073)
P(Success)XValXAro −0.0023∗
(0.0010)
P(Predator)XValXAro 0.0020∗
(0.0009)
rnpmDSXValXAro 0.0006∗
(0.0003)
P(Success)XValXAroXDom 0.0001∗∗
(0.0000)
P(Predator)XValXAroXDom −0.0001‘
(0.0000)
rnpmDSXValXAroXDom 0.0000
(0.0000)
AIC 1020.4599 1019.2081 1018.4409 1015.1770
BIC 1046.6882 1061.1733 1060.4062 1057.1422
Log Likelihood −505.2300 −501.6040 −501.2205 −499.5885
Num. obs. 1402 1402 1402 1402
Num. groups: participant id 112 112 112 112
Var: participant id (Intercept) 0.9047 0.8780 0.8543 0.8169
∗∗∗p < 0.001;∗∗p < 0.01;∗p < 0.05;‘p < 0.1
Table 5: Mixed Effects Affect Models. Logit mixed effects models describing the effect of different affect interaction effects on participant foraging choice. Grouped by participant, as implemented in the R package lme4 with nAGQ = 0, to provide convergence for all models.
including valence interaction effects (ME4) shows higher significance for the rnpmDS interaction (p<0.05) than model (4). This provides further evidence for HI and HII, as it suggests that valence plays a key role in the orientation of DSs. For the P(Predator) interaction the estimate is insignificant (p>0.1).
The valence and arousal interaction model (ME6), shows significance for all valence and arousal DS interactions (p<0.05), as well as having parallel direc-tions to (6) for the effects (Figure 5). This lends support to all three hypotheses, highlighting the role of valence and more generally affect interactions. Lastly the 3-dimensional interactions model (ME8), has the best fits for AIC (1015.2) and LL (-499.6) and the best BIC (1057.1) from all the affect models.
The data hence lends evidence to all three main experimental hypotheses and offers some explanations of the role of affective states in high level decision processes.
Figure 5: Confidence Intervals forTable 5model ME (6). Interaction terms between DSs, valence and arousal. The red bars denote 50% CIs and the pink bars denote 95% CIs.
Reaction Times
To further investigate the interplay of affective states and DSs, the participants’
reaction times for making a foraging choice were recorded. Subsequently an explorative linear mixed effects analysis was conducted. Dependent variable is the reaction time, whereas interactions between all individual affect dimensions and key DSs variables were used as explanatory variables. For the rnpmDS in this model the variable of interest was not which choice would be normative optimal, but if the subject has chosen the rnpmDS.
The mean time taken for all valid measurements is 2.133 (SE, 0.070) seconds.
The most significant interactions interestingly can be observed for DS arousal interactions (P(Success)XAro, p<0.01; P(Predator)XAro, p<0.001; rnpmDS-chosenXAro, p<0.1), while there is no significance for valence interactions (Ap-pendix B,Table 7). In Figure 6a the arousal interaction with the probability of predator attack is visualised. This 3D graph illustrates clearly how the re-action time regression plane rises in subject arousal and predator probability.
This finding suggests that subjects who are aroused will tend to take more time to make a choice when the probability of a threat is higher. Reversely shows Figure 6b that aroused subjects use quicker computations for situations where the probability of a gain is higher.
Exploring the impact of affect and DS on reaction times, hence gives inter-esting results. It suggests that arousal rather than inherent valence determines how fast an individual reacts to salient appetitive and aversive stimuli. How-ever, the variance of reaction times appears to be very high. Before drawing any strong conclusions from this result, this finding would need to be explained and confirmed by a targeted affect and DS reaction time study.
a
b
Figure 6: Reaction Times (RTs) for Simple DSs and Arousal. (a) High probabilities of predator attack paired with high arousal levels lead to increased RTs.
Regression plane rises from the left corner to the right corner (b) High probabilities of foraging success paired with high arousal levels lead to decreased RTs. Regression plane descends from the left corner to the right corner.
5 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.
Specifically, negative valence correlates with less normative optimal (rnpmDS) behaviour (HI), than positive valence (HII). Overall, complex constructionist affective states are a key explanation for human behaviour in naturalistic se-quential decision processes (HIII).
5.1 Key Findings
Valence and Decision Strategies
The model of valence is one of the most established representations of affect across behavioural and cognitive sciences. Perceiving events as good or bad is a human quality that science and the public can readily agree on. Economists develop utility functions and neuroscientists measure the BOLD signal in the vmPFC and VS. Valence is a central axiom of human decision models no matter the discipline.
While the exact motives and mechanisms that drive decision processes be-yond cognitive control may still lay in the dark, approach-avoidance measures can effectively approximate behaviour. This study has discussed previous liter-ature that identifies valence as a characteristic that can not be attributed to a point-like outcome of a function. Previous evidence as well as the results from this study suggest that affect is omnipresent and valence as a key dimension tracks a dynamic state of goodness. This model neatly fits together with the study of metacognitive processes like the use of DS, that may be labelled as heuristics when they are simple to compute. It is one goal of this research to understand how specific DSs that repetitively produce a certain focus in decision making interact with the valence of affective states.
In this empirical study, both positive and negative valence were successfully induced into the affective state of the participants. The aim was to observe the way valence would interact with DSs selection. A previous fMRI imaging study using a similar foraging task has shown that humans tend to favour strategies that are partly aimed at immediate threat avoidance, rather than seeking the highest rewards (Korn & Bach, 2019). This finding is also in line with gen-eral risk averse tendencies in humans in various situations (e.g. Kahneman, 2011). Additionally, there has been converging evidence towards a more posi-tive evaluation of stimuli for more posiposi-tive affecposi-tive states. On the ground of these models, this experiment was developed to show how more negative valence leads to behaviour further diverging from the risk-neutral payoff maximisation decision strategy. Positive valence on the other hand, should lead to a milder threat evaluation and may hence counterbalance a baseline risk averse DS.
This study has demonstrated these phenomena. The negatively inducing
treatment has led participants to act in a way that reduced their expected mon-etary reward. While this result serves as evidence that more negative affective states led to less rnpmDS use, a significant correlation between threat avoid-ance and negative induction could not be established. Treatment appears to be a noisy variable and is not an ideal representation of experienced valence by the participants. The self-reported valence ratings give a clearer picture of affect state and DS interactions. Increased valence leads to a less threat focused DS.
Interestingly, more positive valence also leads to lower focus on gain stimuli.
Ultimately, the valence rating confirms the finding from the treatment anal-ysis, namely that more positive valence leads to closer rnpmDS approximation.
This study, however, argues for an extended dimensional model, where valence only represents certain aspects of an extensive affective state.
Affective States and Decision Strategies
Evolutionary speaking, it does not appear to be good enough to predict the goodness of an outcome of behaviour. Organisms may avoid the occurrence of certain outcomes, even though Bayesian computations may prescribe approach behaviour. The high stakes paired with extreme probabilities in life and death situations appear to necessitate risk averseness that we can not capture through cognitive reasoning.
The brain, as well as the rest of the body, appears to work differently in an aroused rather than a relaxed state, as can be seen through DS selection and reaction times. This makes sense, as the bodily state determines the options available to an organism, when interacting with itself or the environment. Critics of the distinction between arousal and valence may argue that on a certain level arousal is also regulated by the desire to resolve approach-avoidance conflicts.
However, this study has confirmed previous results that perceived valence and arousal are not linearly correlated. Rather does arousal positively correlate with both extremes of valence. Evidently, arousal appears to be involved in the experience of valence. Arousal is positively correlated with the use of the rnpmDS, suggesting that experienced valence benefits the goal of payoff max-imisation. This finding is in line with a prior study, showing that experienced affect positively impacts the professional success of financial specialists (Seo &
Barret, 2007). The need for aroused rather than relaxed states is familiar to most people. A cold shower in the morning is an arousal induction technique, readying the body for the experience of intensive affective states and more vig-orous action.
Analysing the interactions of DS variables with valence and arousal, illus-trates that the directions of the valence effects do not change. Although the DS model quality improvement is only marginal when including arousal effects with valence. The reason this effect is not as pronounced as in previous literature could be due to limitations in the induction method. Overall, the results for considering all dimensions of affect separately are mixed. Depending on the measure of model quality, it may be relatively better or worse in explaining foraging behaviour.
A more explorative finding of the model considering more dimensions, is the higher disregard for threatening stimuli for more dominantly induced subjects.
Intuitively this finding is coherent with our understanding of dominance. Dom-inant affective states suggest control and independence of external influences (Johnson et al., 2012). This should lead to DSs that disregard threats, because of the feeling that the threat is under control. However, this interpretation is only speculative.
The affective model that best explains the data is the model of the three-way interaction between all measured dimensions of affect. Having this result lends strong support to one of the main claims of this study HIII about complex dynamic affective states in the decision process that can be modeled. Evidence for affective state DS interactions can also be found in varying reaction times, conditional on state and stimulus. These complex affective states have a sig-nificant impact on all key foraging DSs. While this is an intriguing finding, it poses a lot of new questions that deserve further exploration.
• How to interpret these DS and complex affective dimension interactions?
• Is there an objective way to measure complex affective states?
• How many separable dimensions are practical to consider when predicting behaviour?
• To what degree are affective states homogeneous across individuals?
• How to model the varying affective state dependent DSs computationally?
Before discussing possible answers to these questions, the author will high-light the limitations and strengths of the study to illustrate the context in which the results were obtained.