Investigations on Anger Experience with Other Basic Emotions Using

Affective Ising Model

Gina Rose N. Tongco-Rosario

, Christie P. Sio

and Jaymar Soriano

Department of Computer Science, University of the Philippines Diliman, Quezon City, Philippines

Department of Psychology, University of the Philippines Diliman, Quezon City, Philippines

Keywords: Anger, Anger Experience, Emotion, Affective Ising Model, Computational Psychology, Personality.

Abstract: Understanding individual differences in anger experiences is pivotal for tailored interventions. This study

explores the variability in individual anger experiences, focusing on fear, happiness, and sadness as

intertwined emotions. A computational approach leveraging the Affective Ising Model (AIM) was performed

to analyze discrete emotion pairs to unravel the complex dynamics of how individuals experience anger. By

applying the AIM to individual-level data collected through Experience Sampling Methodology (ESM), the

study aims to derive parameter estimates that capture the nuanced emotional landscapes of participants. The

investigation seeks to elucidate not only how individuals experience anger but also how it interacts with co-

occurring emotions, shedding light on the uniqueness of emotional responses. This nuanced understanding

can pave the way for personalized interventions. The parameter estimates derived from the AIM will serve as

a basis for tailoring interventions, offering targeted strategies aligned with an individual's emotional

dynamics. Ultimately, this approach holds promise for shaping more effective and personalized interventions

to support emotional well-being.

1 INTRODUCTION

Anger, as a basic emotion, is experienced uniquely by

individuals. While traditional approaches have often

considered emotions as homogenous responses,

recent research demonstrates that people exhibit

substantial diversity in how they experience and

express anger (Loaiza, 2021; Heylen, et al., 2015).

Some individuals might express anger through

assertiveness, while others may exhibit withdrawal or

aggression. Variability in how individuals experience

anger is a complex phenomenon that can significantly

impact mental health and well-being. Thus,

understanding individual differences in the

experience of anger is crucial for developing targeted

and personalized interventions to address these varied

emotional responses (Hamaker, et al., 2015).

Furthermore, emotions rarely exist in isolation.

Fear, happiness, and sadness are closely intertwined

with anger, influencing its expression and experience

(Panksepp, 2017). Exploring how these discrete

emotions interact and co-occur with anger can

https://orcid.org/0000-0001-9647-5999

provide a more comprehensive understanding of an

individual's emotional landscape.

Affective Ising Model (AIM) is a powerful tool

used in computational psychology to model and

understand the dynamics of emotions (Loosens, et al.,

2020). This model not only considers the presence of

discrete emotions but also their interactions,

providing a more nuanced representation of

individual emotional experiences. The AIM enables

the estimation of parameters for each individual,

capturing their unique emotional dynamics. By

applying the AIM to individual records of Experience

Sampling Methodology (ESM) data, researchers can

derive insights into how an individual experiences

and transitions between various emotions. ESM are

generally considered to be the golden standard (Myin‐

Germeys, et al., 2018) to study affect dynamics in an

ecologically valid manner - a participant’s emotional

state is measured repeatedly throughout the day

during several days, giving researchers a window into

their emotional experiences during their daily lives.

The insights gained from the AIM's parameter

estimates can be invaluable in designing interventions

738

Tongco-Rosario, G., Sio, C. and Soriano, J.

Investigations on Anger Experience with Other Basic Emotions Using Affective Ising Model.

DOI: 10.5220/0012470300003657

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2024) - Volume 2, pages 738-745

ISBN: 978-989-758-688-0; ISSN: 2184-4305

that cater to an individual's specific emotional profile.

By understanding how an individual experiences and

transitions between emotions, interventions can be

personalized to address specific triggers, coping

mechanisms, and emotional regulation strategies that

align with their unique emotional patterns.

Investigating the individual experience of anger

using the AIM, within the context of other emotions,

holds the promise of advancing our understanding of

emotions and paving the way for personalized

interventions aimed at improving mental health and

well-being. This approach can revolutionize how we

address emotional concerns by tailoring interventions

to suit the unique emotional fabric of each individual,

thereby fostering more effective and targeted support.

2 AFFECTIVE ISING MODEL

A computational framework for studying the affect

dynamics was developed in 2020 (Loosens et al.) The

framework coined as the Affective Ising Model

(AIM) was inspired by the Ising Model initially used

to represent and explain ferromagnetism in statistical

mechanics. AIM utilizes a similar concept and applies

it to affect states. An individual’s emotional

landscape consists of stochastic binary neurons

grouped into two distinct pools. One pool processes

the positive affect while the other, the negative affect.

Internally, the neurons are self-exciting. Between

pools, mutual excitation or inhibition is present. The

contribution of external stimulus is also accounted for

in the model. These interactions are depicted in

Figure 1.

Figure 1: AIM with two pools of neurons. Neurons in each

pool are self-exciting. Between pool interaction is also

present and each pool may receive an external stimulus.

Define the populations of neurons processing

the positive and negative affective states as PA and

NA, respectively. Each population consist of N

and

stochastic binary neurons. As the neurons change

states over time, the average activations also undergo

temporal variations, resulting in variations in the

affective state. The probability density function (pdf)

is given by:

𝑝(𝑦  𝑒



(



(1)

where 𝐹(𝑦 is the free energy function given by

𝐹(𝑦 

∑

𝑖1



𝜆

𝑖

𝑦

𝑖

𝜃

𝑖

𝑦

𝑖



𝑁

𝑖

𝛽



𝑦

𝑖

𝑙𝑛𝑦

𝑖







1𝑦

𝑖



𝑙𝑛



1𝑦

𝑖

 

𝜆

𝑦

(2)

while Z is the partition function or the normalization

constant of the pdf. The parameter β is associated

with the inverse temperature in statistical mechanics.

Within the AIM framework, the parameter is arbitrary

and is assigned a value of 1 for simplicity. Other

parameters of the free energy equation are

summarized in Table 1.

Table 1: Internal parameters of the AIM.

Parameter Description

strength of self-excitation of PA pool

strength of self-excitation of NA pool

strength of mutual inhibition

activation threshold of PA pool

activation threshold of NA pool

An individual with a more positive affect has,

higher 𝑁



and

𝜆



(than 𝑁



and

𝜆



, respectively)

and lower

𝜃



values (than

𝜃



). A positive value of

𝜆



signifies mutual inhibition between pools while

negative values means that both pools excite each

other.

The dynamics of the affect states are given by

𝑑

𝑦

𝑖

(𝑡  𝛽

𝜕𝐹

𝜕𝑦

𝑑𝑡 

√

2𝑑𝑑𝑊

𝑖

(𝑡

(3)

where

𝑊



(𝑡

are the associated Wiener processes

that are uncorrelated to each other (Verdonck &

Tuerlinckx, 2014).

The movement of affect on the energy

landscape is given by the diffusion parameter 𝐷



(

𝑁

𝑖

𝑁

𝑖



𝛥𝑡

. When

is low, it means that an

individual stays longer in that specific affect state.

3 METHODOLOGY

Inside Out Emotion Tracker is an ESM study that was

participated in by 109 university students from the

Department of Psychology of the University of the

Investigations on Anger Experience with Other Basic Emotions Using Affective Ising Model

739

Philippines Diliman. Students were asked to

complete an experiential measure of anger and other

emotions using their smartphones at multiple random

time points per day, across ten days. Before and after

the experience sampling task, a global measure of

trait anger was administered in a counterbalanced

order together with a Filipino Five-Factor inventory

(Del Pilar, G., et al., 2016). The research study was

approved by the Ethics Review Committee of the

University of the Philippines Diliman Department of

Psychology. We derive the emotion landscape for the

sample. Forty out of 109 satisfy one of the following

conditions: (i)high anger duration, (ii)high

neuroticism or (iii)low agreeableness. Emotional

landscapes from other participants did not have a

good fit based on fitness value and landscape plot.

An example of an ESM-based emotion-pair

impact data is shown in Figure 2. The happiness

impact and anger impact values were calculated based

on the participant’s responses during the experiment.

For each emotion, we determined the emotion impact

by multiplying the normalized emotion intensity with

the emotion duration. The emotion intensity is on a

scale of 1-5 (participants used a five-option scale “not

at all” = coded as 1, “a little” = 2; “moderately” = 3;

“quite a bit” = 4; “extremely” = 5). The emotion

duration is measured for the past hour and is indicated

on a sliding scale, anchored on opposing ends by 0%

(not at all) and 100% (all the time).

Figure 2: An example of an ESM-derived data consisting of

30 records of a participant’s happy-angry emotion impact.

Left plot shows the data in sequence while the right plot

shows the participant’s emotion impact scatter plot from

which the emotion landscape is derived.

We use AIM, with each pool representing discrete

emotions of fear, sadness, happiness, and anger. The

focus is on a basic emotion paired with anger (i.e.

fear-anger, sad-anger, happiness-anger,

fear/sad/happy-anger). To infer the parameters from

data, we used GradientDiffusion (Loosens et al.,

2020), a method developed by Loossens et al. This

method utilizes the maximum likelihood estimation

to derive an individual's affect dynamics in the

absence of an external stimulus i.e. solely on the

internal system. The implementation is carried out

with Julia, a platform known for rapid scientific

computing (Bezanson et al., 2017). In many

instances, multiple local minima exist and a

differential evolution heuristic (Price et al., 2005) is

utilized to find the global optimum.

4 RESULTS AND DISCUSSION

From the estimated parameters, we can plot the

emotion landscapes given by the free energy function

in Equation (1).

4.1 Emotion Landscape and Parameter

Values

Figure 3 shows the emotion landscape of an

individual for three emotion pairs: (a) afraid-angry,

(b) happy-angry, and (c) sad-angry. Each data point

represents an emotion impact pair (e.g. afraid, angry)

which is the product of one’s emotion intensity and

duration for a time point). Each emotion pair

landscape contains data measured across 30 time

points.

Figure 3: Emotion landscapes of an individual for discrete

emotion pairs - (a) afraid-angry, (b) happy-angry and sad-

angry emotion pairs.

Among the four emotions, happy (24%) has the

highest average emotional impact, followed by sad

(21%), angry (13%) and afraid (9%).

Among the

emotions co-occurring with angry, happy has the

lowest activation threshold (θ

). This signifies that

when one’s emotion is coupled with anger, it is

easiest to activate happiness. Fear activation follows

next and then sadness. Once an emotion is activated,

the self-excitation strength (λ

) measures how easy or

difficult it is to keep the emotion in an excited state.

The strength of mutual inhibition (

)

measures the

interaction between emotion pairs. A positive value

indicates that both emotions inhibit each other while

a negative value indicates that the emotions excite

each other.

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740

Table 2: Internal parameters of the emotion pairs of Figure

2. The subscripts refer to emotion 1 - emotion 2.

Emotion Pair

Parameter Values

Afrai

-An

6.062 12.463 0.010 11.697 15.135

Happy-Angry 0.004 8.137 7.493 2.309 8.597

-An

43.885 11.020 0.102 47.903 13.712

Mutual inhibition (

>0)

is evident in the case of

happy-angry. Sad-angry has minimal mutual

inhibition and afraid-angry is almost independent of

each other (

~0)

. The self-excitation strength of

emotion-angry pair is lowest with happy-, followed

by afraid- and then with sad-.

4.2 Co-Occurring Emotions

Co-occurring emotions are emotions that occur

simultaneously, preserving their distinct features such

as valence and impact (Harley et al., 2012). These

emotional states, like anger and disappointment, are

experienced concurrently with one another. In Figure

4 (b1-b3) we can see that happy-angry emotions are

co-occurring for all three individuals. The same is

observed for sad-angry pair in Figure (c1). For the

other emotion pairs, i.e., afraid-angry in Figure 4(a1-

a3) and sad-angry in Figure 4(c2-c3), this

phenomenon is not apparent. We look at the

parameter values for cases in the happy-angry

emotion pair. Compared to the other emotion pairs, θi

is lowest,

is highest, and

is lowest. For sad-angry,

we observe bimodality in Figure 4(c1) and in this case

the

is 0.1 while the rest have

~ 0. This is

somehow consistent with anger and fear being on the

opposite side of the emotional wheel. Co-occurrences

of anger with sadness and happiness have also been

reported (Harley et al., 2012) though small.

4.3 Analysis of Parameter Values

In the succeeding sections we investigate the

parameter relationships with emotion impact. This

time, we consider a sample of forty individuals.

Activation Threshold. Across emotion pairs, higher

anger impact generally means lower anger activation

threshold as shown in Figure 5. Lower activation

threshold allows for easier and magnified anger

experience in an individual. When anger is coupled

with all three emotions (afraid, happy or sad), the

anger activation threshold is lowest with happiness

72% of the time, followed by sadness at 18% and

afraid at 10%. This means that anger is easiest to

activate when someone is happy and hardest when

one is sad.

With the happy-angry pair, the happiness

activation threshold is lower 90% of the time.

Happiness is generally easily activated compared to

anger. In Figure 6a in terms of magnitude, we see that

the activation threshold of happiness is just a fraction

of anger and almost zero for very low values of anger

impact (inset of Figure 6a). This signifies that one

experiences happiness most when anger impact is

low.

Figure 4: Emotion landscape with co-occurring emotions.

Left to right shows the Afraid-Angry, Happy-Angry, Sad-

Angry pairs. Top to bottom plots are for decreasing anger

impact.

Figure 5: Anger activation threshold and anger impact

across emotion pairs.

For the sad-angry emotion pair, the activation

threshold of sadness is lower 70% of the time which

signifies that sadness is easier to experience than

Investigations on Anger Experience with Other Basic Emotions Using Affective Ising Model

741

anger. Generally at lower anger intensity, sadness is

favored (Figure 6b). At higher anger intensity

(>12.86%), anger activation thresholds are low which

means that in this range anger is easier to activate over

sadness. For the Afraid-Angry emotion pair, fear is

easier to activate 75% of the time. We can see that at

high anger intensity (>12.86%), anger is favored over

fear.

(a)

(b)

(c)

Figure 6: Activation Thresholds for (a) Happy-Angry, (b)

Sad-Angry and (c) Afraid-Angry landscapes.

Strength of Mutual Inhibition. The strength of

mutual

inhibition

measures

the

interaction

between

Figure 7: Emotion Impact for fear, happiness, sadness and

anger of participants (indexed based on increasing anger

impact).

Figure 8: Strength of mutual inhibition of afraid-angry,

happy-angry, sad-angry emotion pair.

emotion pairs. A positive value indicates that both

emotions inhibit each other while a negative value

indicates that the emotions excite each other.

Based

on our initial look at the emotion impact magnitude,

it seems to have a relationship with the strength of

mutual inhibition parameters. In Figure 7 we can see

that happiness, sadness and then fear ranks from

highest to lowest in emotional impact. When we look

at the mutual inhibition parameters in Figure 8, we

can see that happy- angry are mutually inhibiting for

most cases with the magnitude of | λ

| >> 1. Sad-

angry follows this trend of mutual inhibition. Afraid-

angry on the other hand is generally independent with

| λ

| ~ 0.

Self-Excitation Strength. Once an emotion is

activated, the self-excitation strength measures how

easy or difficult it is to keep the emotion in an excited

state.

First, we look at the self-excitation strength of

anger when coupled with other emotions (see Figure

9). As the self-excitation strength of anger decreases,

the

anger

impact

increases

across

all

emotions.

For

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Figure 9: Anger self-excitation strength with afraid-, happy-

and sad- anger pairs for increasing anger impact. Inset

shows anger impact from 0%-3%.

anger in this range (anger impact > 10%), we see an

indirect relationship between the self-excitation

strength and emotion impact. Lower

signifies that

the emotion is felt for longer.

It is also evident that

anger self-excitation strength is generally reduced

when coupled with happiness.

In the succeeding subsections we delve deeper for

each emotion pair.

Afraid-Angry Self-Excitation Strength. Figure 10

shows the self-excitation strength with anger impact

for afraid-angry. We consider two cases for this

emotion pair to. One is when

Afraid

Angry

(Figure

11a) and

Afraid

Angry

(Figure 11b).

Figure 10: Self-excitation strength of afraid-angry emotion

pair. Inset shows cases with higher λ

values.

Figure 11a shows 62.5% of the population, where

Afraid

Angry

. We stipulate that for this scenario (case

a), the afraid emotion impact is higher. This is

generally true. However, there are six out of the

twenty

five cases

where

anger

emotion impact is

Figure 11: Self-excitation strengths for (a) Afraid < Angry

and (b) Afraid > Angry landscapes.

higher (Figure 11a inset). For Case b, when anger has

lower self-excitation strength (Figure 11b), afraid

generally has the higher emotion impact. There are

five of the fifteen cases where anger has the higher

emotion impact (Figure 11b-inset). For afraid-angry

emotion pair, the hypothesis that lowers self-

excitation strength leads to higher emotion impact

holds true sixty percent of the time.

Happy-Angry Self-Excitation Strength. Figure 12

shows the self-excitation strength for happy-angry

pair. We test the same hypothesis that lower

means

higher emotion impact for that emotion. For this

scenario, happiness self-excitation strength is lower

so we expect higher happiness impact.

We show the two cases in Figure 13. First, we

check the case when happiness has the lower self-

excitation strength which holds for 85% of our

population. Again, generally, happy impact is higher

than anger impact except for the seven out of the

thirty four cases (Figure 13a inset) where the reverse

is true. When angry has the lower self-excitation

strength, only one out of the six cases disagree with

the hypothesis. For the happy-anger pair, our

hypothesis holds true 67% of the time.

Figure 12: Self-excitation strength of happy-angry pair.

Investigations on Anger Experience with Other Basic Emotions Using Affective Ising Model

743

Figure 13: Self-excitation strengths for (a) Happy < Anger

and (b) Happy > Anger landscapes.

Sad-Angry Self-Excitation Strength. Figure 14

shows the self-excitation strength for the sad-angry

pair. Generally we observe that sadness

has the lower

Again we analyze the two cases and show them in

Figure 15 (a & b). For case a, sad has the lower

for

65% of the sample. Generally, sadness will have the

higher emotion impact for this scenario. We find

however, that twelve of the twenty two samples have

anger impact higher than sad impact (Figure 15 a

inset). For case b, there are six of the fourteen cases

where the reverse of our hypothesis occurs. In the

case of sad-angry pair, our hypothesis is true for only

42.5% of the time.

Across emotion pairs, the self-

excitation strength relationship and contribution to

emotion impact varies.

Figure 14: Self-excitation strengths of sad and angry and

corresponding strength of mutual inhibition.

Figure 15: Self-excitation strengths for (a) Sad < Anger and

(b) Sad > Anger.

Based on our investigations, we find the following

emotion process. An emotion is first activated. Lower

activation threshold allows for easier emotion

activation. Once activated, the interplay between the

pools contribute to the sustained emotional

experience measured by the emotional impact. A

positive value of strength of mutual inhibition

represents two pools mutually inhibiting each other.

The self-excitation strength of an emotion coupled

with the mutual excitation contributes to the emotion

impact.

Across emotion pairs, higher anger impact

generally means lower anger activation threshold.

Lower activation threshold allows for easier and

magnified anger experience in an individual. As the

self-excitation strength of anger decreases, the anger

impact increases across all emotions. For anger in this

range (anger impact > 10%), we see an indirect

relationship between the self-excitation strength and

emotion impact. When we look at the mutual

inhibition parameters, we can see that happiness and

anger are mutually inhibiting for most cases with the

magnitude of | λ

| >> 1. Sadness follows this trend of

mutual inhibition. Fear on the other hand is almost

independent of anger | λ

| ~ 0.

5 CONCLUSIONS

We demonstrated a computational framework of

understanding individual anger experience using

Affective Ising model. By performing maximum

likelihood of discrete emotion-pair landscapes, we

derived insights regarding how an individual

experiences anger differently as it co-occurs with

other basic emotions namely fear, sadness, and

happiness.

While the approach may be promising, the study

is hoped to be validated in consultations with

psychologists and clinicians. The study shall be

extended to include external excitations that are

hypothesized to be events or situations experienced

by individuals that could critically affect their mental

health state and could be the reason for transitioning

to a multimodal emotion landscape. With this

computational approach, it may be possible to reverse

engineer an individual’s mental health state by

providing appropriate interventions. Once fine-tuned

the framework may be utilized to create an anger

software aimed at anger emotion diagnosis and

management.

The study considered a sample size which can be

extended to cover the general population. AIM is a

simplified representation of emotion dynamics and

does not include representation of culturally specific

emotions. Parameter estimation challenges, absence

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744

of biological factors, and limited incorporation of

external influences contribute to its realism

constraints. Despite these limitations, it remains

valuable, and researchers should acknowledge its

constraints while considering complementary

approaches for a more comprehensive understanding

of emotional processes.

ACKNOWLEDGEMENTS

G. Tongco-Rosario would like to acknowledge the

ERDT Program of the DOST-SEI for her scholarship

and other grants.

C. Sio would like to thank the participants in the

Inside Out Emotions Tracker survey, Ms. Grazianne-

Geneve Mendoza for her assistance in the ESM study

and the Philippine Social Science Center for their

support in funding the data collection phase through

the Research Award Program.

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