Observational Study of a Digital Application

to Detect Attachment in Dyads Using Markov Chains

Sebastian Unger and Thomas Ostermann

Department of Psychology and Psychotherapy, Witten/Herdecke University, Witten, Germany

Keywords: Interpersonal Attachment, Digital Application, Observation, Mental Processes, Mental Health Care, Time

Series Analysis.

Abstract: Attachment is a widely used term and basically refers to a strong emotional relationship that one person

develops with another. It is often measured, for example, with the Adult Attachment Interview (AAI), one of

the most popular tools, or the Child Attachment Interview (CAI), an adaption of the former. Even though

these are two excellent tools for measuring attachment, they are labor-intensive and therefore not suitable for

quick use without an adequate training period. Moreover, the mindset towards attachment has changed over

time since the development of these tools, meaning that they can still be applied, but only in specific contexts.

The digital application "IU" is intended to address these two issues by being easy to learn on the one hand

and leaving plenty of freedom for measurement on the other. In this observational study, the interpersonal

attachment of dyads captured by the app is interpreted as three-dimensional time series and analyzed based

on a Markov chains. This approach shows how interpersonal attachment might be determined according to

the homogeneity of the Markov chains, which could probably be improved by capturing other factors such as

the interactions of dyads.

1 INTRODUCTION

In the field of psychology, attachment is a widely

used term that first entered the healthcare system in

the 1950s (Evans, 2004). In its origins, attachment

refers to the strong emotional relationship that an

infant or child develops with a caregiver (Bretherton,

1992). Back then, caregivers were mainly associated

with mothers, so that research also focused on

attachment between mothers and their children. One

of the most popular methods developed through this

mindset is the Adult Attachment Interview (AAI), a

tool for classifying attachment patterns of adults

based on childhood experiences with parents and the

influence of these experiences on personality

development (Main et al., 2008). Another tool is the

Child Attachment Interview (CAI), an adaptation of

the AAI for children (Target et al., 2003). Both AAI

and CAI provide reliable results, as evidenced in

multiple studies (Hesse, 1999; Privizzini, 2017; van

Ijzendoorn et al., 2008). This is why these tools are

very attractive and hard to replace. However, due to

their structural similarity, they have one major

drawback in common: they produce a high workload.

Nowadays, the mindset towards attachment has

considerably changed. One of the main claims is that

attachment is not only related to the child's behavior

but also to the socio-emotional contexts of adulthood

(Fearon et al., 2017). This can be seen in the various

literature in which attachment is addressed, including

studies on social relationships formation (Insel,

1997), on love couples (Brumbaugh et al., 2006), or

even on patient care (Agrawal et al., 2004; Blanco et

al., 2018). Because of this and because of the major

drawback of the AAI and CAI, new and innovative

measurement methods were developed or at least

investigated. The Adult Attachment Projective

(AAP), which uses attachment-related drawings

(George et al., 2004), is one of the few art-based

approaches. Other approaches that focus on

movement patterns are hardly seen in research. A few

examples on this topic are those that combine

conventional attachment methods with the

movements of the eyes, the facial expressions, or the

people themselves (Altmann et al., 2021;

Kammermeier et al., 2020; Uccula et al., 2022).

The approach in this article represents both an art-

based and a movement-based measurement method.

The measurement is performed on a tablet and has

Unger, S. and Ostermann, T.

Observational Study of a Digital Application to Detect Attachment in Dyads Using Markov Chains.

DOI: 10.5220/0012435200003657

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 185-193

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

185

already shown its potential using two-dimensional

time series (Unger et al., 2020). In contrast to the

approach from the previous proof of concept study, a

further meaningful dimension supplements here the

measurement of interpersonal attachment.

The assumption is that the addition of this third

dimension may increase the accuracy of the method,

leading to the research question: “Can interpersonal

attachment of a dyad be captured as three-

dimensional time series with a digital application?”.

To test the question exploratively, the time series are

checked for practical applicability using a Markov

chain approach. It has not yet been examined in this

context, but Markov models are increasingly being

used in clinical psychological research. In addition to

the individual case study by Elbing et al. (2022),

corresponding approaches, e.g., the analysis of

emotions of outpatients with schizophrenia (Strauss

et al. 2019; Strauss et al. 2023), the development of a

clinical decision support system for bipolar disorders

(Valenza et al., 2013), the modelling of emotional

brain states (such as “surprise”, “fear” or “anger”)

among university students (Kragel et al., 2022), or the

investigation of computer-based social interactions

with virtual objects (Dolev et al., 2020; Prasetio et al.,

2020), indicate promising results.

2 METHODS

2.1 Participants

Participants were recruited via the internal bulletin

board, social media, and verbal communication.

Eligible participants were between 18-65 years old,

were able to operate a tablet independently, had no

acute disorders that could interfere with the use of a

tablet, and were not pregnant due to unknown effects

on stress levels. In addition, an informed consent

form had to be signed by all participants before the

examination could start.

With this inclusion criteria, a total of 60 people

(43 females and 17 males) were motivated to

voluntarily participate, a lot of whom registered

directly with a familiar partner. The age of the

participants ranged between 19 and 37 years

age

= 23.78 years).

2.2 Examination Set-up

In a first step, the participants were organized into

dyads, as the examination could only be conducted in

a dyadic constellation. Participants registered with a

partner were automatically assigned to each other.

Otherwise, they were randomly assigned to a partner.

After 30 dyads were formed, the dyads were asked to

arrive in a specially prepared laboratory room. The

equipment included a table on which two tablets as

well as two styli were positioned and two chairs for

the participants to sit on. On site, there was also a

person in charge who informed the participants about

the procedure, checked their suitability, and had them

sign the informed consent form.

Next, the participants had to place themselves

opposite their partner. Once they were seated, the

person in charge handed each of them one of the two

tablets, which were already running an app called

“IU”. Participants were now asked to enter an

assigned identification number (ID) as well was their

age and gender in the text fields provided by the app.

Figure 1: State diagram of the participants’ measurable

thoughts, showing the two first level states and the two

second level states.

In the last step, the person in charge handed the

participants a pen for digital drawing (stylus). The

task for the participants was to seek eye contact for

three minutes, while transferring their thoughts to the

tablet with the stylus. The thoughts that are attempted

to be captured are mapped on the basis of four mental

states, consisting of two first level states and two

second level states, as show in Figure 1. The two first

level states express if the participants are thinking

about themselves or about their partner, who is sitting

opposite to them. Therefore, the former state is called

“I”-state, named after the personal pronoun “I”,

whereas the latter state is called “U”-state, named

after the sound of the personal pronoun “You”. Both

states can each reach one of the two second level

states to express if the thought has a positive or

negative orientation. On the tablet, the combinations

of the four states are displayed by dividing the bottom

(“I”-state) from the top (“U”-state) half of the screen

and by dividing the left (negative orientation) from

the right (positive orientation) side of the screen.

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From this it follows that participants who are thinking

about themselves move the stylus to the bottom half

and participants who are thinking about the partner

move the stylus to the top half. At the same time,

participants have to consider the positive or negative

orientation of their thought by moving the stylus

either to the left (negative) or right (positive) side.

The stylus is then meant to remain in the

corresponding location of the screen as long as the

thoughts do not change. If there is a change, the stylus

is moved accordingly, which is likely be expected

during this examination.

2.3 Output Measures

While the participants look at each other and transfer

their thoughts to the tablet by moving the stylus back

and forth for 3 minutes, a tracking process runs in the

background of the app. With this tracking, the pixel

coordinates touched by the stylus (x

, y

) and the time

of this touch (t

) are saved for each participant

(k = A, B) of the dyad j continuously, creating a

time series (x

, y

, t

)

. Such three-dimensional time

series describes the course of the thoughts of a

participant, whereby the x-coordinate, the y-

coordinate, and the time each correspond to one

dimension. To enable the individual time points of a

time series to be assigned to the four mental states in

retrospect, the vertical and horizontal screen divisions

are additionally saved.

2.4 Statistical Analysis

The analysis of the thoughts is based on Markov

chains, which aim to provide transition probabilities

from a long and uninterrupted observation

(Billingsley, 1961), as this method has repeatedly

demonstrated its usefulness in medical contexts.

However, since the raw values of the corresponding

three-dimensional time series are not of interest, a

reconversion into mental states must be conducted in

advance. This can be done using the pixel coordinates

, y

) contained in the time series (x

, y

, t

)

. The

chronologically correct order of these states is

determined using the time dimension (t

According to the four mental states, the resulting

Markov chain also has four states. To assign this, the

horizontal screen division is considered first. If a y-

coordinate is above this screen division, it is

interpreted as “U”-state, and if the y-coordinate is on

or below the screen division, it is interpreted as “I”-

state. Afterwards, the vertical screen division is

considered. If the corresponding x-coordinate is to the

left of this screen division, the state is given a

negative orientation, and if the x-coordinate is on or

to the right of this screen division, the state is given a

positive orientation. This leads to the mental state

constellations: thinking positive about the other (+U),

thinking negative about the other (-U), thinking

positive about oneself (+I), and thinking negative

about oneself (-I).

After determining the Markov chains, the Markov

property is subsequently tested. For this, the R

package “markovchain” (Spedicato et al., 2016;

version 0.9.1) is used. The method is based on a Chi-

Square Test: if the corresponding p-value of the Chi-

Square Test is above the level of significance of

α = 0.05, the Markov property is satisfied. The

purpose of testing this property is to ensure that a

future state depends only on the current state and not

on any other past states (Asmussen, 2003), which is

the necessary condition for a Markov chain. The

Markov chains of a dyad j are furthermore tested

against homogeneity. If, on the one hand, the Markov

property is present and there is homogeneity between

them, it is assumed that the time series of a dyad are

similar. If, on the other hand, there is heterogeneity

despite the Markov property, it is assumed that the

time series are different. Since the optimal interval

length between the mental states is unknown, the

procedure is repeated for different intervals, a

technique based on a study in which heatmaps

through different grid sizes were created to examine

the movement entropy of people (Unger et al., 2021).

Starting with a 100 ms interval predefined by the app,

the interval is repeatedly increased by 100 ms until

the maximum of 10,000 ms is reached.

3 RESULTS

To begin with, the data was checked for completeness

and applicability to the planned statistical procedures.

It was noticed that the time series of two participants

had too large gaps to apply the different interval

lengths to the three-minute measurement time. The

data of these participants had to be removed. In

addition, the data of their associated partners were

removed, because the time series of this dyad cannot

be tested for homogeneity. For the analysis, 28 dyads

with the corresponding 56 time series remained.

Table 1 shows the dyadic constellations that have

been formed. In most Dyads, the participants were

friends or colleagues. Only a few couples and a few

dyads of strangers were formed. From Table 1, it can

also be taken that the mean time since the dyads have

known each other is neither particularly low, i.e., a

few days or weeks (except for the strangers), nor

Observational Study of a Digital Application to Detect Attachment in Dyads Using Markov Chains

187

particularly high, i.e., more than 5 years, which

provides a good and stable basis for the data.

Table 1: Amount of dyadic constellations with an indication

of their self-reported form of interpersonal attachment and

the mean time of knowing each other.

Interpersonal

Attachment Form

Amount of

ads

Known since

(in Years)

Colleagues 9

1 ¾

[¼, 3]

Love Couples 2

3 ¼

[1 ½, 5]

Friends 14

1 ¼

[¼, 3 ½]

Strangers 3

Looking at the results of the Markov property test,

it appears that most of the time series follow a Markov

chain. In Figure 2, the amount of time series that

satisfy the property is compared with the amount of

time series that do not satisfy the property. It is easy

to see that the Markov property increases with

increasing interval length. Nevertheless, even at the

smallest interval length of 100 ms, the proportion of

satisfied Markov properties (40 ≙ about 71 %) is

more than twice as high as the proportion of

unsatisfied Markov properties (16 ≙ about 29 %).

Figure 2: Overview of testing the time series with regard to

the Markov property. The amount is shown on the y-axis

and the interval (in ms) used for testing is shown on the x-

axis.

After the Markov property has been tested, the

homogeneity of the time series per dyad can be tested

next. However, the only dyads suitable for the test are

those in which both time series satisfy the Markov

property, as these time series can be interpreted as

Markov chains. Dyads can therefore have

homogeneous, heterogeneous, or not comparable

time series.

Figure 3 shows the results by comparing the

amount of the three cases. As expected from the

previous test, there are only a few dyads with

homogeneous time series when using the small

intervals. It must be noted that, unfortunately, the

time series that did not satisfy the Markov property

often belonged to different dyads, so that there are

many not comparable dyads, which could not be

tested in the first place. But as soon as the intervals

become larger and more time series satisfy the

Markov property, the time series of the dyads become

increasingly homogeneous. This can particularly be

seen around the maximum interval length.

Figure 3: Overview of testing the time series of dyads

against homogeneity. The amount is shown on the y-axis

and the interval (in ms) used for testing is shown on the x-

axis.

Figure 4 illustrates how both time series of a

randomly picked dyad change with increasing

interval lengths. The similarities that are consistently

revealed despite the change can be found in the

movements of both styli to mainly positive mental

states. In particular, the state of thinking positively

about the partner (+U) is predominant the greater the

interval becomes.

Starting with the preset default interval of 100 ms,

partner B shows noticeably more activity than partner

A. The states of the two corresponding time series

have a high probability of circling around themselves

and therefore a minimal probability of changing to

another state. The Markov property was not achieved

for either time series with this interval length, so that

homogeneity was not tested either, i.e., this dyad is

not comparable.

With 1,000 ms, partner B is still the more active

one, but the similarity that both think positively about

their partner (+U) becomes more visible. Now, the

probability of one state changing into another

increases slightly as the points in the time series

decrease. This time, the Markov property is satisfied

for both time series. However, homogeneity can still

not be achieved for this dyad, which is consistent with

the different drawings.

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Figure 4: Time series of a dyad as Markov chains for the intervals 100 ms, 1,000 ms, and 10,000 ms. Above the Markov

chains, the corresponding drawings of the participants are shown. The mental states are emphasized by the vertical and

horizontal division lines within the drawings and match the positions of states in the Markov chains.

Observational Study of a Digital Application to Detect Attachment in Dyads Using Markov Chains

189

With last interval length of 10,000 ms, there are

much clearer effects due to the change in the time

series. The dyad has now much more harmonious

drawings and the state of thinking negatively about

oneself (-I) can no longer be detected, as it rarely

occurred in the beginning. The consequence is that

the Markov chains are simplified, so that both the

Markov property and homogeneity are now satisfied

for this dyad. The homogeneity is furthermore

consistent with the similar drawings.

4 DISCUSSION

4.1 Key Results

The first analysis shows that the participants' thoughts

generally can be modelled using a Markov chain

approach. This becomes particularly clear when the

lengths of the intervals between individual thoughts

are increased. One reason for this could be that fewer

states are included, as it can be seen in Figure 4 at an

interval of 10,000 ms. Thus, it seems that this interval

is no longer suitable for the analysis, even if all four

states were still present in some cases. In contrast,

when small interval lengths are applied, many of the

participants' thoughts lose the Markov property and

the probabilities that the states remain predominantly

in their state are very high. It could indicate that either

maintaining a mental state over a long period of time

cannot be determined as Markov chain or that the

screen area was too large to capture the states

accurately over time by this measurement method.

Whether thoughts can be accurately determined as

Markov chains remains unclear. Although Markov

chains have already been used as models, e.g., for the

development of caries in periodontology (Lu, 1966)

or for predicting the success of therapy, as in

outpatient departments for epileptics (Kriedel, 1979)

or in chronic cardiovascular diseases dependent on

therapy variants (Grimm et al., 1988), these

approaches never succeeded in gaining a global

acceptance in the field of medical research

methodology, which could be the reason for the lack

of relevant literature.

Based on the analysis of the homogeneity within

dyads, similarities can be drawn to the analysis on the

Markov property. For example, the strong trend

towards more homogeneous thinking dyads with

increasing interval lengths could be due to the

reduced states in thoughts, which most likely distorts

reality. Therefore, high intervals also seem rather

unsuitable here. In the smaller interval lengths, the

homogeneous and heterogeneous thinking dyads are

relatively evenly distributed, i.e., there are dyads that

are attached and dyads that are not attached. With

respect to the former study (Unger et al., 2020), from

which it appears that interpersonal attachment is

higher among couples and friends than among

colleagues and strangers, the approximately equally

distribution of constellations seem to explain the

equally distribution of interpersonal attachment in

this study. It is in accordance with studies that

investigated the interactions of dyads (Benjamin,

1979; Bollenrücher et al., 2023). It might indicate that

this novel approach is able to measure interpersonal

attachment with specific intervals, which at the same

would support the former results on this app. By

combining the two approaches, i.e., measuring

thoughts and interactions of dyads simultaneously, an

even more meaningful result could be provided. At

least, it is worth investigating.

In terms of Markov chain models, they seem very

useful for this type of stochastic research. As

highlighted in a recent opinion paper on research

methodologies for studying affect dynamics, Markov

chain models are powerful tools for analyzing the

underlying dynamics in the change of emotional

states and may provide substantial insights into the

dynamics of emotional responses and changes over

time (Cipresso et al. 2023). In combination with

machine learning approaches, Markov chains open

further opportunities, as they can be used not only to

analyze but also to predict emotional states (Sükei et

al. 2021) or students’ performance in a laboratory

environment (Paxinou et al. 2021).

4.2 Limitations

The innovative measurement method presented here

depends on continuous data collection and large gaps

in the data could lead to incorrect predictions, which

is one of the main limitations of this approach. Even

small gaps in the data may occur, as it was not

intended to entirely monitor the input. However, by

increasing the time intervals for the analysis, these

gaps can be covered.

Furthermore, the choice of interval lengths may

represent a limitation. At the time of the examination,

there was no literature on the optimal interval lengths

for analyzing thoughts. Only studies from other areas

that provide a solution to this issue could be found

(Sugimoto et al., 2021; Unger et al., 2021).

Nevertheless, the intervals could already be too wide

at 100 ms and it may possible that the optimum

interval was not covered by this incremental increase.

Nevertheless, the total of 100 different intervals

should provide a good basis for future research.

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Another limitation is the division of the screen

into four areas to represent the mental state. On the

one hand, the pixels of the vertical and horizontal

screen divisions relate to a specific state. The

corresponding counter-state is thereby reduced by a

few pixels. On the other hand, movements within a

state are always assigned to this state, even if the

thoughts were about the partner. While the former can

be neglected, the latter shows that states could be

missed. As this is the same for every participant, this

error compensates for itself. An alternative

measurement method would be to consider the

direction of the movement. Here, the predefined path

length of the movement should be calculated and

tested against a minimum distance to compensate for

the human tremor.

In terms of participants, the total amount is too

small to draw a final conclusion of this study. In

addition, only participants in a certain age range have

registered. Other age groups could possibly change

the result, as there could be cohort effects (Lindström

et al., 2002). And lastly, it is unclear whether the

participants understood their task immediately. As the

study was conducted on the basis of the movements

to be analyzed identically, the localization of the

states to which the stylus had to be moved was

predetermined. To achieve better results, it might be

advisable to consider personal movement preferences

or to include a familiarization phase in the future so

that the participants develop a feeling for the way to

move the stylus accordingly.

5 CONCLUSION

In this observational study, interpersonal attachment

in dyads was measured with a digital application.

During the measurement, the participants had to

transfer their thoughts to the app. The thoughts are

tracked as three-dimensional time series and analyzed

as Markov chains. Overall, the results showed that the

thoughts were mainly present as Markov chain. When

analyzing these thoughts of the dyads for

homogeneity, there were both heterogeneous as well

as homogeneous thinking dyads. Despite the

limitations, this study demonstrates from a

methodological point of view how time series data

captured by a tablet app as interpersonal attachment

can be analyzed using stochastic process models

outside the conventional methods of clinical studies.

In contrast, the limitations also lead to the need to

validate the results in further studies. Such studies

should incorporate other factors in the measurement.

In particular, the simultaneous examination of

thoughts and interactions of the dyads appears to be a

promising research project. Even an examination with

the addition of conventional tools, e.g., AAI or CAI,

would be an interesting project for the future.

ETHICAL VOTE

This study, which was conducted at Witten/Herdecke

University between 2021 and 2023, was approved by

the Ethics Committee of the Witten/Herdecke

University (Reference S-185/2021).

ACKNOWLEDGEMENTS

We would like to thank Theresa Frische and Fidan

Brand for their support in recruiting participants and

conducting the examination.

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