Longitudinal Data Analysis Based on Triadic Rules to Describe of the

Psychological Reactions During COVID 19 Pandemic

Lincoln A. N. Coutinho, Mark A. J. Song

and Luis E. Zárate

Applied Computational Intelligence Laboratory – LICAP, Computer Science Department,

Pontiﬁcal Catholic University of Minas Gerais, Brazil

Keywords:

Triadic Analysis, Longitudinal Study, Mental Health, COVID-19, Data Mining.

Abstract:

Longitudinal studies are essential to understand the evolution of individuals’ psychological behaviors, espe-

cially in pandemic scenarios. The work proposes the application of the triadic analysis, derived from the

theory of Formal Analysis of Concepts, to describe, through rules, a longitudinal database about the attitudes

and reactions of individuals during COVID 19. As a main result, one can observe how the different factors

considered in the study are related in different scenarios of the pandemic, showing degrees of stress related to

the prevention of the disease.

1 INTRODUCTION

A pandemic has various implications in a global-

ized society (Malta et al., 2020). Mental health is a

highly relevant aspect, especially in an abnormal pe-

riod where there may be a decrease in interpersonal

contact due to imposed health restrictions. This as-

pect should not be downplayed, as it is correlated with

public health issues such as anxiety, depression, dis-

tress, among other psychological problems. There-

fore, studies on the mental health of a social group ex-

posed to extreme situations, if used to identify behav-

ioral patterns, can generate relevant information for

public policies (Prati and Mancini, 2021). In this con-

text, longitudinal studies can be employed to achieve

these objectives. In this work, we present a method

to identify psychological effects during the COVID-

19 pandemic for the proposed longitudinal study in

(O’Brien et al., 2021).

In general, longitudinal studies are used to investi-

gate, for example, activities and behaviors of the same

group of individuals over various periods of time, re-

ferred to as waves. Through periodic updating of

records, it is possible to discover highly relevant pat-

terns and temporal relationships from the available

databases using data mining techniques and machine

learning.

To analyze the longitudinal databases, we propose

https://orcid.org/0000-0001-7315-3874

https://orcid.org/0000-0001-7063-1658

in this work to utilize the foundations of Formal Con-

cept Analysis (FCA) theory (Ganter and Wille, 2012),

a branch of applied mathematics based on the theory

of conceptual lattices. Its main objective is to repre-

sent and extract knowledge from a dataset involving

objects (individuals), attributes (clinical conditions,

symptoms, etc.), and their incidence relations. This

tuple of elements can be represented through a formal

dyadic context, from which it is possible to extract

association rules between the attributes. In summary,

the main purpose of FCA is to summarize items in

a database into information implications, such as the

evidence of an individual symptom in a patient to bet-

ter understand clinical diseases and their representa-

tion in society.

In general, FCA has been used in data analysis and

knowledge representation, where associations and de-

pendencies are identiﬁed from a binary incidence re-

lationship between objects and attributes. Several

works, such as (Carpineto and Romano, 2003), have

discussed the use of extracting dyadic association

rules through FCA.

Since datasets are often expressed by ternary and

more generally n-ary relations, there has been a re-

cent and growing interest in proposing new solu-

tions for the analysis and exploration of these multidi-

mensional data, especially in triadic contexts (Bazin,

2020).

Triadic Concept Analysis (TCA), proposed by

(Lehmann and Wille., 1995), is an extension of FCA

theory that uses triadic formal context. This intro-

Coutinho, L., Song, M. and Zárate, L.

Longitudinal Data Analysis Based on Triadic Rules to Describe of the Psychological Reactions During COVID 19 Pandemic.

DOI: 10.5220/0012314900003657

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 323-329

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

323

duces a third element (to the dyadic context) - a con-

dition determining the incidence relationship between

objects and attributes. In the context of healthcare

area, objects may correspond to patients, attributes to

symptoms, and conditions to different waves of the

longitudinal study. From the triadic context, it is pos-

sible to extract triadic association rules (Biedermann,

1999) that can be used to observe the relationships be-

tween attributes (symptoms) within a given wave or

between waves of the longitudinal study. In this way,

the TCA extends the FCA, showing not only the in-

cidence of a symptom, but its recurrence in different

scenarios (waves).

In (Trabelsi et al., 2012), the authors compared

three algorithms for triadic data: TRICONS, TRIAS,

and DATA-PEELER. In (Ignatov et al., 2015), the au-

thors presented various strategies for discovering op-

timal patterns considering this type of data. In (Sel-

mane et al., 2013), the authors proposed extracting tri-

adic association rules by transforming the triadic con-

text into an equivalent dyadic context. In (Zhuk et al.,

2014), a comparison of algorithms for triadic context

analysis is conducted, and the work by (Missaoui and

Emamirad, 2017) proposes a tool, Lattice-Miner, used

in this work, for extracting triadic association rules.

The articles (Lana et al., 2022) and (Noronha

et al., 2022) are likely the ﬁrst works to explore triadic

analysis in describing longitudinal study databases in

the ﬁeld of health. The ﬁrst article deals with the anal-

ysis of the effectiveness of COVID-19 prevention pro-

cedures, and the second work focuses on pattern dis-

covery related to human aging by observing the tem-

poral evolution of clinical and environmental condi-

tions of individuals. In this work, we propose the ap-

plication of triadic rules to describe the psychological

reactions of individuals to the COVID-19 pandemic

based on a longitudinal study available in (O’Brien

et al., 2021).

This article is divided into the following sections:

in Section 2, the theoretical framework supporting the

work is presented. In Section 3, the methodology

used for discovering psychological patterns during the

pandemic and the description of the dataset used are

presented. Section 4 contains the experiments and

analysis of the results from different scenarios. Fi-

nally, the conclusions and possible future work are

outlined.

2 BACKGROUND

2.1 Formal Concept Analysis and

Triadic Rules

Formal Concept Analysis (FCA) is a branch of ap-

plied mathematics related to the theory of concep-

tual lattices (Ganter and Wille, 2012). This theory is

used to derive implicit relationships between objects

and their attributes from a dataset. This relationship

is formally deﬁned by a tuple K := (G, M, I), which

is called a formal context, where (I ⊆ G × M), with

G representing objects, M representing attributes,

and I representing incidence in the context—meaning

which objects possess certain attributes, or, analo-

gously, which attributes are present in certain objects.

Within FCA, two main operators are deﬁned:

′

:= {m ∈ M|∀g ∈ A : (g, m) ∈ A} (1)

′

:= {g ∈ G|∀m ∈ B : (g, m) ∈ B} (2)

Considering A ⊆ G and B ⊆ M, a formal concept

corresponds to the pair (A, B), where A represents a

subset of objects (extension) and B a subset of at-

tributes (intention) in such a way that A

′

= B, and

′

= A, where A

′

and B

′

are the derivation operators

described by Equations 1 and 2.

Triadic Concept Analysis (TCA) (Wille, 1995) is

deﬁned by a quadruple K := (G, M, I, C), where, in

addition to objects and attributes, the incidence be-

tween them occurs under a condition C. For exam-

ple, considering a longitudinal study with two waves,

the start and end of a clinical treatment. Thus, a tri-

adic concept represented by (I ⊆ G × M ×C) can be

translated as objects that possess a certain subset of at-

tributes under a condition, or similarly, attributes that

are related to a subset of objects under a speciﬁc con-

dition or wave.

From TCA, it is possible to generate two types

of triadic implication rules known as BCAAR (Bie-

dermann Conditional Attribute Association Rule) and

BACAR (Biedermann Attributional Condition Asso-

ciation Rule), which have the following structure

((Biedermann, 1999)):

BACAR: ( C

→ C

) M

[support, con fidence]

BCAAR: ( M

→ M

) C

[support, con fidence]

The ﬁrst rule, BACAR, occurs when C

, C

⊆ C

and M

⊆ M. This means that when the subset of

attributes M

occurs under condition C

, it also oc-

curs under condition C

with a certain support and

conﬁdence. The second rule, BCAAR, occurs when

, M

⊆ M and C

⊆ C. This indicates that in the

HEALTHINF 2024 - 17th International Conference on Health Informatics

324

wave C

, the subset of attributes M

implies M

with

a certain support and conﬁdence. Our goal is to iden-

tify patterns of psychological relationships among in-

dividuals from the longitudinal database using both

types of association rules.

3 METHODOLOGY

As mentioned, for this work, a longitudinal study aim-

ing to assess the psychological conditions of individ-

uals during the COVID-19 pandemic was considered.

The ﬁrst wave was conducted at the beginning of the

pandemic between April 9th and 18th, 2020, and the

second between June 19th and July 11th, 2020, ap-

proximately 2 months after the ﬁrst data collection.

In this database, several socioeconomic questions for

individuals are present, highlighting aspects of isola-

tion, medication, pre-existing conditions, psychologi-

cal tests, working hours, among other issues (O’Brien

et al., 2021).

The database comprises 151 interviewed indi-

viduals and 81 attributes, of which 12 were selected

for a more detailed analysis of the results, totaling

24 for both waves. Tables I, II, and III describe the

sets of questionnaires considered and the conditions

in which they were conducted. It is worth noting

that only the Five Facet Mindfulness Questionnaire

(FFMQ) test, presented in Table I, has derivations,

which is why Table II includes attributes related only

to this speciﬁc scale test.

3.1 Methods

Preprocessing: For representing the longitudinal

database in a triadic context, a discretization process

is required. To achieve this, thresholds (reference

values) had to be deﬁned for marking the incidences

of symptoms for each study wave. The objective is

to describe the negative psychological inﬂuence of

the pandemic, so values equal to or above the refer-

ence, which represent or are associated with a neg-

ative psychological condition, were considered and

marked with ’X’ for incidence, while values below

this threshold did not determine an incidence and re-

mained unmarked. A sample of this discretization is

shown in Table IV.

For the PHQ15 (Patient Health Questionnaire

Somatic Symptom Severity Scale), the literature-

suggested scale was used as the reference threshold:

Minimal (0-4), Low (5-9), Medium (10-14), and High

(15-30). Speciﬁcally, the threshold value of 10, corre-

sponding to the Medium level on the scale, was con-

Table 1: Key Attributes Selected for Triadic Analysis.

Attributes Metric Description

PHQ15_Total

Total Sum of

15 items from

PHQ Scale

Questionnaire

Severity Scale for

Symptoms of the

person in the last

month

FFMQ_Total

Total Sum of

24 items from

FFMQ Scale

Questionnaire

Scale about the

person’s inner

perception in the

last month

GHQ_Total

Total Sum of

12 items from

GHQ Scale

Questtionaire

Scale about the

person’s health in

the last month

PVD_Total

Total Sum of

15 items from

PVD Scale

Questtionaire

Scale about the

person’s

perception of

vulnerability to

diseases

IOUS_Total

Total Sum of

12 items from

IOUS Scale

Questtionaire

Scale about the

person’s

intolerance

to uncertainties

IOES_Total

Total Sum of

22 items from

IOES Scale

Questtionaire

Scale about the

impact of stress on

the person in the

last month

PATS_MEAN

Weighted

Mean of 13

items from

PATS Scale

Questtionaire

Scale about the

preventive actions

of the person

agains diseases

sidered. For the IOES questionnaire, the study by

(Weiss and Marmar, 1997) was used. The threshold

was speciﬁcally set at 33, corresponding to the aver-

age value in the ﬁrst wave of the study (O’Brien et al.,

2021). For other questionnaires, thresholds were de-

termined for extreme situations. To achieve this, an

outlier analysis was performed using a box plot. This

strategy aimed to deﬁne values deviating from the

mean and variance that were associated with negative

psychological conditions.

Subsequently, once the data were represented in

the triadic concept, Lattice Miner ((Missaoui and

Emamirad, 2017)), available on GitHub, was used for

generating triadic rules. Before using the software,

the database was converted to JSON (JavaScript Ob-

ject Notation) format, containing all the relationships

between objects, conditions, and attributes to be in the

appropriate format for the software to generate the tri-

adic rules. Consequently, the BCAARs and BACARs

triadic rules can be generated based on desired conﬁ-

dence and support measures. The ﬁrst, BCAARs can

show the relation between two attributes (clinical con-

ditions) in a certain wave (time) which could imply a

certain dependence on two different symptoms. The

second, BACARs, the recurrence of a attribute (clin-

Longitudinal Data Analysis Based on Triadic Rules to Describe of the Psychological Reactions During COVID 19 Pandemic

325

Table 2: Derived Attributes Selected for Triadic Analysis.

Attributes Metric Description

FFMQ

Observe

Mean

Weighted Mean

of FFMQ Scale

Questionnaire

Items for

Observation

Scale on how easy

it is for the person

to observe

themselves in the

last month

FFMQ

Describe

Mean

Weighted Mean

of FFMQ Scale

Questionnaire

Items for

Description

Scale on how easy

it is for the person

to describe

themselves in the

last month

FFMQ

Aware

Mean

Weighted Mean

of FFMQ Scale

Questionnaire

Items for

Attention

Scale on how easy

it is for a person

to focus

on tasks in the

last month

FFMQ

Nonjudge

Mean

Weighted Mean

of FFMQ Scale

Questionnaire

Items for

Judgment

Scale on the

person’s

self-judgment

in the last month

FFMQ

Nonreact

Mean

Weighted Mean

of FFMQ Scale

Questionnaire

Items for

Reaction

Scale on the

person’s reactions

in the last month

Table 3: Conditions chosen for triadic analysis.

Wave -

Conditions

Date Description

A (before)

April 9th to

18th, 2020

2 to 3 weeks after

the beggining of

the pandemics

in the USA

D (after)

June 19th to

July 11th,

2020

2 to 3 months

after the condition

"A" in the USA

ical condition) in different waves (times), that could

mean a lasting clinical condition.

4 EXPERIMENTS AND RESULTS

For the analysis, four different scenarios were chosen.

The ﬁrst scenario considers the complete database

with employed and unemployed individuals. The re-

maining scenarios were subdivided into employed in-

dividuals and those not in the labor market. Employ-

ment conditions were selected based on the litera-

ture, including references such as (Borsoi, 2007) and

(Hirschle and Gondim, 2020).

Each of the scenarios will be presented below,

along with the most signiﬁcant results observed in

each of them.

Table 4: Transformation for Triadic Concept Analysis.

A - First Wave D - Second Wave

Person ID

PHQ15

TOTAL

IOUS

TOTAL

PHQ15

TOTAL

IOUS

TOTAL

ID 1 X X X

ID 2 X X

ID 3 X

ID 4 X X X

4.1 Scenario 1: Complete Database

In this context, 151 individuals were considered, and

1765 triadic rules were generated. This high number

of rules is due to the fact that the rule explores all

possible association rules within the dataset. In order

to analyze the most signiﬁcant rules, a minimum

support of 30% was chosen for BACARs, and for

BCAARs, a support of 25% was chosen:

BACARs:

R1 - ( A → D ) IOES_Total [support = 36,9%

conﬁdence = 80,9%]

R2 - ( D → A ) IOES_Total [support = 36,9%

conﬁdence = 88,7%]

R3 - ( A → D ) PATS_Mean [support = 30,9%

conﬁdence = 79,3%]

R4 - ( D → A ) PATS_Mean [support = 30,9%

conﬁdence = 68,7%]

BCAARs:

R1 - ( IOES_Total → PATS_Mean ) A [support =

29,5% conﬁdence = 64,7%]

R2 - ( IOES_Total → PATS_Mean ) D [support =

31,5% conﬁdence = 75,8%]

R3 - ( PATS_Mean → IOES_Total ) A [support =

29,5% conﬁdence = 75,9%]

R4 - ( PATS_Mean → IOES_Total ) D [support =

31,5% conﬁdence = 70,1%]

From the complete database, it was observed

through BCAAR rules, R1 and R3, at the begin-

ning of the pandemic, that people (29.5%) who

experienced strong stress symptoms in the last 7

days (IOES_Total) also engaged in preventive actions

against diseases (PATS_Mean) with a conﬁdence of

64.7%. The reverse was also observed (PATS_Mean

→ IOES_Total) in both study waves. This might sug-

gest that concerning a pandemic, stress, which can be

caused by traumatic events, may result in a person

taking more preventive actions to avoid psychologi-

cal conditions. Conversely, individuals accustomed

to taking more preventive measures against diseases

may also experience higher levels of stress.

HEALTHINF 2024 - 17th International Conference on Health Informatics

326

4.2 Scenario 2: Individuals Employed

Before the Pandemic

In this context, 138 individuals who were employed

before the COVID-19 pandemic were analyzed. The

minimum support threshold was set at 30%:

BACARs:

R1 - ( A → D ) IOES_Total [support = 40,4%

conﬁdence = 84,6%]

R2 - ( D → A ) IOES_Total [support = 40,4%

conﬁdence = 90,2%]

R3 - ( A → D ) PATS_Mean [support = 32,4%

conﬁdence = 80,0%]

R4 - ( D → A ) PATS_Mean [support = 32,4%

conﬁdence = 69,8%]

BCAARs:

R1 - ( IOES_Total → PATS_Mean ) A [support =

31,6% conﬁdence = 66,2%]

R2 - ( IOES_Total → PATS_Mean ) D [support =

33,8% conﬁdence = 75,4%]

R3 - ( PATS_Mean → IOES_Total ) A [support =

31,6% conﬁdence = 78,2%]

R4 - ( PATS_Mean → IOES_Total ) D [support =

33,8% conﬁdence = 73,0%]

Analyzing the results for individuals who were

employed before the pandemic, the outcome was very

similar to the complete database (section 4.1). The

only difference is that the support and conﬁdence lev-

els are generally higher, meaning the relationship be-

tween stress and disease prevention worsened even

further in this scenario.

4.3 Scenario 3: Individuals who Were

Working at the Beginning of the

Pandemic

In this scenario, 127 individuals who were working

at the beginning of the COVID-19 pandemic (April

9th to 18th, 2020) were analyzed. BACARs and

BCAARs were analyzed with a minimum support of

30%:

BACARs:

R1 - ( A → D ) IOES_Total [support = 41,6%

conﬁdence = 83,9%]

R2 - ( D → A ) IOES_Total [support = 41,6%

conﬁdence = 92,9%]

R3 - ( A → D ) PATS_Mean [support = 32,8%

conﬁdence = 78,8%]

R4 - ( D → A ) PATS_Mean [support = 32,8%

conﬁdence = 69,5%]

BCAARs:

R1 - ( IOES_Total → PATS_Mean ) A [support =

33,6% conﬁdence = 67,7%]

R2 - ( IOES_Total → PATS_Mean ) D [support =

33,6% conﬁdence = 75,0%]

R3 - ( PATS_Mean → IOES_Total ) A [support =

33,6% conﬁdence = 80,8%]

R4 - ( PATS_Mean → IOES_Total ) D [support =

33,6% conﬁdence = 71,2%]

Analyzing the results for individuals who were

working at the beginning of the pandemic, the out-

come was very similar to the complete database (sec-

tion 4.1) and to individuals who were employed be-

fore the pandemic (section 4.2). However, the support

and conﬁdence levels are mostly even higher, imply-

ing a deterioration in terms of stress, disease preven-

tion, and the relationship between these two factors.

4.4 Scenario 4: Individuals who Were

Not Employed at the Beginning of

the Pandemic

In this scenario, 24 individuals who were not em-

ployed at the beginning of the COVID-19 pandemic

(April 9th to 18th, 2020) were analyzed, and the

BACARs and BCAARs had a minimum support of

25%:

BACARs:

R1 - ( A → D ) FFMQ_NonreactMean [support =

25,0% conﬁdence = 66,7%]

R2 - ( D → A ) FFMQ_NonreactMean [support =

25,0% conﬁdence = 50,0%]

R3 - ( A → D ) PVD_Total [support = 29,2%

conﬁdence = 100,0%]

R4 - ( D → A ) PVD_Total [support = 29,2%

conﬁdence = 87,5%]

BCAARs:

R1 - ( FFMQ_NonreactMean → PATS_Mean ) A

[support = 25,0% conﬁdence = 50,0%]

R2 - ( PATS_Mean → FFMQ_NonreactMean ) A

[support = 25,0% conﬁdence = 75,0%]

Longitudinal Data Analysis Based on Triadic Rules to Describe of the Psychological Reactions During COVID 19 Pandemic

327

Considering the BCAAR rules, R1 and R2, for

individuals who were not employed at the begin-

ning of the pandemic, the rules associate preventive

actions that individuals can take against COVID-19

(PATS_Mean) with attention-related factors such as

non-reactivity (FFMQ_NonreactMean), where non-

reactivity to inner experience is deﬁned in terms of

allowing thoughts and feelings to come and go with-

out being caught up or carried away by them, where

a higher score indicates higher attention (Bohlmeijer

et al., 2011). It can be observed that all individuals

with 75% preventive actions were non-reactive. In

this scenario, it was only highlighted that the major

issues for individuals who were not employed at the

beginning of the pandemic are different compared to

employed individuals analyzed in the previous scenar-

ios.

5 CONCLUSIONS AND FUTURE

WORK

The objective of this study was to demonstrate the

potential of triadic analysis for extracting association

rules within the context of longitudinal studies for

psychological records, focusing on people’s reactions

to stress conditions such as the COVID-19 pandemic.

The rules can contribute to a better understanding of

individuals’ psychological reactions under stressful

conditions.

It is important to emphasize that the approach re-

quires prior deﬁnition of thresholds for discretization

and determining whether an incidence is marked or

not in the triadic context. The difﬁculty in accessing

information about the tests on the applied scale, due

to restricted data, can hinder threshold deﬁnition to

characterize individuals as healthy or not, and to bet-

ter understand the topic being addressed. Although

threshold deﬁnition requires expert knowledge, the

approach allows for the adjustment of various sce-

narios to describe the results of a longitudinal study.

Among the positive aspects, the applicability and ease

of application to various contexts can be highlighted.

As future work, there are several implementations

that can be carried out in the considered longitudinal

study. Implementations can be performed in different

scenarios, and different attributes from the database

can be used in each of these chosen scenarios. Fur-

thermore, with the input of researchers from the ﬁeld

of psychology, the data could be better analyzed to

understand the implications of a pandemic on peo-

ple’s mental health. Our intention was to demonstrate

the potential use of triadic rules to analyze the psy-

chological effects of a pandemic.

ACKNOWLEDGEMENTS

The authors would like to thank: The National

Council for Scientiﬁc and Technological Develop-

ment of Brazil (CNPQ), The Coordination for the Im-

provement of Higher Education Personnel - Brazil

(CAPES) (Grant PROAP 88887.842889/2023-00 –

PUC/MG, Grant PDPG 88887.708960/2022-00 –

PUC/MG - INFORMATICA and Finance Code 001),

Minas Gerais State Research Support Foundation

(FAPEMIG) under grant number APQ-01929-22, and

the Pontiﬁcal Catholic University of Minas Gerais,

Brazil.

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