=Paper=
{{Paper
|id=Vol-433/paper-12
|storemode=property
|title=Application of the Formal Concept Analysis in Evaluation of Results of ANEWS Questionnaire and Physical Activity of the Czech Regional Centers
|pdfUrl=https://ceur-ws.org/Vol-433/paper8.pdf
|volume=Vol-433
}}
==Application of the Formal Concept Analysis in Evaluation of Results of ANEWS Questionnaire and Physical Activity of the Czech Regional Centers==
https://ceur-ws.org/Vol-433/paper8.pdf
Application of the Formal Concept Analysis in
Evaluation of Results of ANEWS Questionnaire
and Physical Activity of the Czech Regional
Centers?
Jiřı́ Zacpal1 , Erik Sigmund1 , Josef Mitáš2 , Vladimı́r Sklenář2
1
Dept. Computer Science, Palacky University, Olomouc
Tomkova 40, CZ-779 00 Olomouc, Czech Republic
{vladimir.sklenar,jiri.zacpal}@upol.cz
2
Centre for Kinanthropology Research, Palacky University, Olomouc
tr. Miru 115, CZ-771 11 Olomouc, Czech Republic
{erik.sigmund,josef.mitas}@upol.cz
Abstract. Formal concept analysis is a method of exploratory data
analysis that aims at the extraction of natural clusters from object-
attribute data tables. The clusters, called formal concepts, can be similar
to human-perceived concepts in a traditional sense and can be partially
ordered by a subconcept-superconcept hierarchy. The hierarchical struc-
ture of formal concepts (so-called concept lattice) represents structured
information obtained automatically from the input data table. The goal
of this paper is to describe a method of evaluation of ANEWS question-
naire by Formal concept analysis. We describe a method adjustment of
questionnaire by scaling to classical formal context. After that we sepa-
rate some attributes to groups and make so-called ”aggregate atributes”.
This way we make modified formal context and calculate formal concept
lattice. We define term ”characteristic function” for every concept. This
is function, which for given extent or intent return a real number, which
characterized this concept and is important for evaluation. Our method is
illustrated on ANEWS questionnaire and measured steps in randomized
sample of 15-65 years-old inhabitants of the Czech regional centers.
1 Introduction and problem setting
Questionnaires are being used in many areas of human activities. The aim is
to reveal patterns of behavior and various kinds of dependencies among vari-
ables being surveyed. Descriptive statistics and statistical hypotheses testing are
among the tools traditionally used for evaluation of questionnaires. A practical
disadvantage of the traditional statistical approaches is the need to formulate
?
Supported by grant No. 1ET101370417 of GA AV ČR, by grant No. 201/05/0079
of the Czech Science Foundation, by institutional support, research plan MSM
6198959214, and by grant No. 6198959221 ’Physical activity and inactivity of in-
habitants of the Czech Republic in the context of behavioral changes’ of the MSM.
c Radim Belohlavek, Sergei O. Kuznetsov (Eds.): CLA 2008, pp. 97–108,
ISBN 978–80–244–2111–7, Palacký University, Olomouc, 2008.
98 Jiřı́ Zacpal, Erik Sigmund, Josef Mitáš, Vladimı́r Sklenář
hypotheses to be tested. Without any prior structured view on the data con-
tained in the questionnaires, formulation of relevant hypotheses is a difficult
task. Another disadvantage of traditional statistical approaches is the limitation
regarding what statistics can tell about data and how statistical summaries can
be understood by experts in the field of inquiry who are not experts in statistics.
This paper presents results on evaluation of ANEWS questionnaire and phys-
ical activity of the czech regional centers. The paper is a continuation of previous
studies regarding the IPAQ questionnaire, see [5]. At the beginning of our study,
there was a need for an alternative means of evaluation of questionnaires for-
mulated by experts (domain experts) from the Faculty of Physical Culture of
the Palacky University, Olomouc, who are involved in a world-wide project of
monitoring physical activities in today’s population. The experts struggled with
classical statistical techniques and were looking for alternative methods of eval-
uation of the questionnaires. It turned out that basic methods of formal concept
analysis (FCA) [10] are quite useful for the domain experts. Putting briefly, a
concept lattice and its parts provide the experts with an easy-to-understand
hierarchical view on the data.
In terms of FCA, the basic idea is the following. The objects are the indi-
viduals (or their groups) being surveyed in the questionnaires, the attributes
correspond to the variables being monitored by the questionnaires. The corre-
sponding concept lattice or its parts reveals to the domain expert the groups
in dependence on the attributes and the expert can see various dependencies
between attributes, how large the groups are etc. Therefore, the concept lattice
provides the expert with a first insight into the data. Such an insight is crucial.
Very often, this insight is what the expert needs to see. Furthermore, based on
this insight, the expert can pursue more detailed inquiries including those based
on classical statistical techniques.
Recent study focuses on considering groups of individuals as objects. The
present study is based on the idea that some questions are closely related. It’s
useful to group those attributes which resulted from scaling of the questions
into one attribute. Thus we would obtain a more comprehensive view of the
questionnaire. This idea made us create so-called ”aggregate attributes”.
The advantage of taking groups and the relative frequencies instead of indi-
viduals and original attributes is conciseness of the description provided by the
resulting concept lattice which is what the experts asked for. The disadvantage,
as with any other method which involves aggregation and summarization, is loss
of information. We present our method, experimental results, as well as a brief
description of the software tool we used.
2 Questionnaire adjustment
Each questionnaire consists of questions to which the respondents choose an
answer from a multiple choice. From the perspective of FCA the group of re-
spondents can be understood as a set of objects and individual questions as
attributes. The respondents answers then create binary relation between the
Application of the Formal Concept Analysis in Evaluation of Results of 99
ANEWS Questionnaire and Physical Activity of the Czech Regional Centers
set of objects and the attributes. The answers do not have to be necessarily
bi-valent (yes-no). Multiple-value type of answers (age, number of steps,) can
appear here. Due to this, a suitable scale needs to be applied to transfer the
multiple-value type of answers into bivalent forms. The result of this process is
a context hX, Y, Ii, where X is the set of objects – respondents, Y is the set of
attributes – adjusted answers from the questionnaire and I is the binary relation
between X and Y , where (x, y) ∈ I means that respondent x answered yes to
question y.
Another adjustment of the questionnaire is based on the idea that some ques-
tions are closely related. For example question: ”The streets in my neighborhood
do not have many cul-de-sacs (dead-end streets)” is closely related with question:
”The distance between intersections in my neighborhood is usually short (100
yards or less; the length of a football field or less)”, because the questions are
related to conditions for walking. Was it not more useful than to group those at-
tributes which resulted from scaling of the questions into one attribute? Thus we
would obtain a more comprehensive view of the questionnaire. This idea made
us create so-called ”aggregate attributes”.
Firstly, an expert needs to decide which questions can be grouped into an
”aggregate attributes”. Then, we replace all the attributes which were formed
through scaling with ”aggregate attributes” using the following procedure. We
calculate the weighted mean of individual attributes and we scale this mean.
Formally: There is number n of questions in the questionnaire which we want
to
Pn cluster into the ”aggregate attributes”. Through scaling of these questions
i=1 m i of attributes was created, where mi is the number of attributes which
was formed through scaling of i-question. The weighted mean for the object x,
is calculated according to the formula:
n
X mi
X
v(x) = σi ωij I(x, aij )
i=1 j=1
where
σi is weight of question i
ωij is weight of attribute j which was formed through scaling of question i
aij is attribute which was formed through scaling of question i, j ∈ mi
I is binary relation between X and Y1 , which is the original set of attributes
from which we remove all the attributes which we have grouped into aggregate
attributes and then we add the aggregate attributes into it.
Value v(x) ∈ h0, 1i. We create 5 aggregate attributes according to these rules:
hx,NAME-very lowi ∈ I1 iff v(x) ∈ h0, 0.2i
hx,NAME-lowi ∈ I1 iff v(x) ∈ (0.2, 0.4i
hx,NAME-moderatei ∈ I1 iff v(x) ∈ (0.4, 0.6i
hx,NAME-highi ∈ I1 iff v(x) ∈ (0.6, 0.8i
hx,NAME-very highi ∈ I1 iff v(x) ∈ (0.8, 1i,
where NAME is the name of the group of attributes which we grouped. Using
these aggregate attributes, we replace all the grouped attributes. This way a
100 Jiřı́ Zacpal, Erik Sigmund, Josef Mitáš, Vladimı́r Sklenář
formal context hX, Y1 , I1 i is created, where Y1 is the original set of attributes
from which we remove all the attributes which we have grouped into aggregate
attributes and then we add the aggregate attributes into it. hx, yi ∈ I1 if y is not
aggregate attribute and for aggregate attributes the above rules are applied.
Example 1. For better understanding we provide an example. There are ques-
tions (G1-G3) in the questionnaire which concern Streets in my neighborhood.
The expert states the values in individual weights: σG1 = 0.4, σG2 = 0.4 and
σG3 = 0.2 To all questions, the respondents could choose these answers: 1
- strongly disagree, 2 - somewhat disagree, 3 - somewhat agree, 4 - strongly
agree. The value of weights is stated in Tab. 1. They created 5 ”aggregate at-
tributes”: Street-very low, Street-low, Street-moderate, Street-high, Street-very
high (the classification of streets depending on their suitability for walking). If
respondent x answers the questions this way: G1 - 3, G2 - 1, G3 - 2, will be
v(x) = 0.4 · 0.75 + 0.4 · 0.5 + 0.2 · 0, 5 = 0.6 and then hx,Street-moderatei ∈ I1 .
Table 1. Weights ωij from example 1.
questions answers
1 2 3 4
G1 - absence of cul-de-sac (dead-end streets) 0.25 0.5 0.75 1
G2 - short distance between intersections 0.25 0.5 0.75 1
G3 - alternative routes for getting from place to place 0.25 0.5 0.75 1
Typically, such a formal context contains many objects and a manageable
number of attributes. The corresponding concept lattice is too large for an expert
to comprehend. In addition, the expert might not be interested in the formal
concepts from this concept lattice. Rather, the expert might want to consider
aggregates of the individual respondents as objects in the formal context with the
aggregates defined by having the same attributes on a set S of attributes specified
by an expert, such as those regarding age, sex, etc., with S being a subset of the
set Y of all attributes. Attributes from S will be called characteristic attributes.
The aggregates we consider are equivalence classes of individual respondents.
For respondents x1 , x2 ∈ X, put
x1 ≡S x2 if and only if {x1 }↑ ∩ S = {x2 }↑ ∩ S.
Clearly, ≡S is an equivalence relation on X and x1 ≡S x2 means that x1 and x2
have the same attributes from S, i.e. are indistinguishable by the attributes from
S. We call the classes [x]≡S of ≡S aggregate objects and denote, furthermore,
– by X1 the set of all classes of ≡S , i.e. X1 = X/ ≡S , by Y2 the set of those
attributes from Y1 not included in S, i.e. Y2 = Y1 − S.
Application of the Formal Concept Analysis in Evaluation of Results of 101
ANEWS Questionnaire and Physical Activity of the Czech Regional Centers
Now, for each class [x]≡S from X1 and each attribute y ∈ Y2 , we consider the
relative frequency of objects in having attribute y and denote it by I2 ([x]≡S , y)
or simply by I2 (x, y). That is, we put
|{x1 ∈ [x]≡S : x1 has y}|
I2 (x, y) =
|[x]≡S |
We can consider I2 a fuzzy relation which will indeed be the case in this study.
Namely, we will consider a particular concept lattice associated to hX1 , Y2 , I2 i,
called a lattice of crisply generated fuzzy concepts. For technical reasons, we
round the degrees assigned by I1 to those from the scale {0, 0.01, . . . , 0.99, 1}.
More details on this method are described in the article [5].
3 Characteristic concept function
With Formal Concept Analysis we can find concepts whose intent include at-
tributes interesting for our way of evaluation. Extents of these concepts contain
some number of respondents. Often we are not interesting in attributes of indi-
vidual respondent. Only values that characterize all respondents in the concept
extent as a whole are interesting for concept evaluation. Arithmetic mean of the
value with more than two-valued attribute is possible example of such value. We
will use the term ”characteristic function” for function that returns such value
for given extent.
4 Questionnaire analysis
The ANEWS questionnaire (Neighborhood Environment Walkability Scale - Ab-
breviated) includes 54 questions in total. They were answered by 662 respon-
dents. Using the method described above, we created 8 aggregate attributes, from
which we created 40 attributes using scaling (8x5). Next to these attributes, the
context involves other attributes of demographic data: gender (2 attributes),
BMI (4), age (5), smoking (2), driver (2), orgPA (4), Steps5bigger2 (2) - at-
tribute indicated, whether the respondents shows more steps during week than
at weekend, Steps (4) - see Tab. 2.
Table 2. Scale for value Steps
attribute steps per week
Steps-low less then 5 999
Steps-moderate 6 000-9 999
Steps-high 10 000-13 999
Steps-very high more than 14 000
Thus we obtained a formal context which includes 662 objects and 65 at-
tributes. For another adjustment of formal context, aggregate objects are ap-
102 Jiřı́ Zacpal, Erik Sigmund, Josef Mitáš, Vladimı́r Sklenář
plied. We used Sex-male, Sex-female and steps (Steps-low, Steps-moderate, Steps-
high a Steps-very high) as characteristic attributes. The obtained formal fuzzy
context includes 8 objects and 59 attributes. Using it, we created corresponding
fuzzy conceptual lattice. When studying the lattice, we tried to examine what
influence the environment (characterized by aggregate attributes) has on the
number of steps in respondents. We studied males and females separately. The
Tab. 3 shows the corresponding concepts for male and Tab. 4 for female. We
state only the aggregate attributes in the levels of very high (VH) and high (H).
It is possible to compare also the other levels (moderate, low a very low), but
we were interested mainly in the positive influence of the environment on steps.
Table 3. Degree of some attributes in concepts, which extents consist of aggregate
objects SexMale an Steps-low, Steps-moderate, Steps-high, Steps-very high. Aggregate
objects: L - Steps-low, M - Steps-moderate, H - Steps-high, VH - Steps-very high.
attribute extent
L,M,H,VH VH L
BuildingsFlat-very high 0 0.01 0
BuildingsFlat-high 0.18 0.18 0.23
BuildingsHouse-very high 0 0.06 0
BuildingsHouse-high 0.34 0.42 0.46
Distance-very high 0.01 0.01 0.08
Distance-high 0.15 0.26 0.15
Neighbourhood-very high 0.08 0.14 0.08
Neighbourhood-high 0.23 0.28 0.23
Safety-very high 0.38 0.53 0.53
Safety-high 0.39 0.39 0.46
Service-very high 0.38 0.53 0.38
Servie-high 0.35 0.39 0.46
Street-very high 0.38 0.57 0.38
Street-high 0.26 0.26 0.46
Walking-very high 0.15 0.24 0.15
Walking-high 0.43 0.45 0.76
The levels of correspondence express minimal number of respondents in per-
centage, which show the given attribute. Based on the comparison of the con-
cepts, we can see that great difference between respondents who show high num-
ber of steps (VH) and low number of steps (L) on a day, are apparent mainly
in the Street-very high attribute. It is apparent that the type of street is closely
associated with the number of steps. Due to this we focused on the aggregate
attribute Street. We formed a formal context of attributes which were parts
of the aggregate attribute Street. These attributes are formed from questions
ClosedStreet (The streets in my neighborhood do not have many cul-de-sacs
(dead-end streets)), ShortDistance (The distance between intersections in my
neighborhood is usually short (100 yards or less; the length of a football field or
Application of the Formal Concept Analysis in Evaluation of Results of 103
ANEWS Questionnaire and Physical Activity of the Czech Regional Centers
Table 4. Degree of some attributes in concepts, which extents consist of aggregate ob-
jects SexFemale an Steps-low, Steps-moderate, Steps-high, Steps-very high. Aggregate
objects: L - Steps-low, M - Steps-moderate, H - Steps-high, VH - Steps-very high.
attribute extent
L,M,H,VH VH L
BuildingsFlat-very high 0 0 0
BuildingsFlat-high 0.10 0.19 0.10
BuildingsHouse-very high 0 0.05 0
BuildingsHouse-high 0.34 0.34 0.52
Distance-very high 0.03 0.03 0.10
Distance-high 0.21 0.26 0.21
Neighbourhood-very high 0.05 0.09 0.05
Neighbourhood-high 0.10 0.33 0.10
Safety-very high 0.44 0.47 0.52
Safety-high 0.34 0.45 0.36
Service-very high 0.47 0.57 0.47
Servie-high 0.30 0.30 0.42
Street-very high 0.34 0.48 0.36
Street-high 0.33 0.35 0.42
Walking-very high 0.21 0.21 0.26
Walking-high 0.41 0.56 0.57
less) and MoreWays (There are many alternative routes for getting to one place
in my neighborhood. (I don’t have to go the same way every time). Each ques-
tion can be answered in values 1 to 4. Using scaling we obtained a context which
was formed by 662 objects (respondents) and 36 (25 - demographic attributes,
12 - attributes of environment) attributes. We used the method of aggregate
objects. As characteristic attributes, we used gender (Sex-male, Sex-female) and
steps (Steps-low, Steps-moderate, Steps-high a Steps-very high). A formal fuzzy
context was thus created which included 6 objects and 33 attributes. We formed
a corresponding fuzzy conceptual lattice. Examining the lattice we were trying
to identify whether any question from the aggregate attribute Street has greater
influence on the number of steps in respondents. We studied males (Tab. 5) and
females (Tab. 6) separately.
The levels of correspondence express minimal number of respondents in per-
centage, which show the given attribute. Based on the comparison of the con-
cepts, we can see that great difference between respondents who show high num-
ber of steps (VH) and low number of steps (L) on a day, are apparent mainly in
the MoreWays attribute (here we are interested primarily in the value 4 of the
answer – strongly agree). It is apparent that the variety of walking routes, when
I do not have to take just a one way, are attractive and motivating for walking
and cycling.
Another possibility of the questionnaire analysis is using so-called charac-
teristic function of the concept. In this case, we define it as arithmetic mean of
number of steps for respondents – objects, for 7 days in the extent of the concept.
104 Jiřı́ Zacpal, Erik Sigmund, Josef Mitáš, Vladimı́r Sklenář
Table 5. Degree of some attributes in concepts, which extents consist of aggregate
objects SexMale an Steps-low, Steps-moderate, Steps-high, Steps-very high. Aggregate
objects: L - Steps-low, M - Steps-moderate, H - Steps-high, VH - Steps-very high.
attribute extent
L,M,H,VH VH L
ClosedStreets-1 0.03 0.06 0.08
ClosedStreets-2 0.10 0.10 0.15
ClosedStreets-3 0.28 0.28 0.46
ClosedStreets-4 0.31 0.54 0.31
MoreWays-1 0 0.03 0
MoreWays-2 0.09 0.09 0.15
MoreWays-3 0.38 0.38 0.62
MoreWays-4 0.23 0.49 0.23
ShortCross-1 0.09 0.10 0.08
ShortCross-2 0.21 0.22 0.23
ShortCross-3 0.35 0.40 0.54
ShortCross-4 0.15 0.27 0.15
Table 6. Degree of some attributes in concepts, which extents consist of aggregate
objects SexMale an Steps-low, Steps-moderate, Steps-high, Steps-very high. Aggregate
objects: L - Steps-low, M - Steps-moderate, H - Steps-high, VH - Steps-very high
attribute extent
L,M,H,VH VH L
ClosedStreets-1 0.05 0.09 0.11
ClosedStreets-2 0.13 0.15 0.21
ClosedStreets-3 0.27 0.29 0.32
ClosedStreets-4 0.37 0.47 0.37
MoreWays-1 0.03 0.03 0.05
MoreWays-2 0.10 0.10 0.21
MoreWays-3 0.42 0.40 0.42
MoreWays-4 0.32 0.46 0.32
ShortCross-1 0.10 0.13 0.11
ShortCross-2 0.16 0.18 0.16
ShortCross-3 0.33 0.40 0.37
ShortCross-4 0.23 0.27 0.37
Application of the Formal Concept Analysis in Evaluation of Results of 105
ANEWS Questionnaire and Physical Activity of the Czech Regional Centers
We used a formal context with aggregate attributes. We wanted to examine what
influence service availability has on the value of characteristic function (aggre-
gated attribute Service-very high, Service-high, Service-moderate, Service-low
and Service-very low). The values of the characteristic function for individual
concepts are shown in Tab. 7.
Table 7. Value of characteristic concept function
intent avarage of steps number of objects
Sex-male 12198 278
Sex-male, Distance-very high 8934 8
Sex-male, Distance-high 13226 60
Sex-male, Distance-moderate 12193 138
Sex-male, Distance-low 11707 69
Sex-male, Distance-very low 11871 3
Sex-female 11907 384
Sex-female, Distance-very high 10574 21
Sex-female, Distance-high 12019 110
Sex-female, Distance-moderate 12318 180
Sex-female, Distance-low 11095 69
Sex-female, Distance-very low 11408 4
Using this type of analysis, we can replace the classification of steps ac-
cording to clear limits set in advance (Tab. 2) with one more concrete value.
Along with the value of the arithmetic mean, we have to consider the number of
objects to which the arithmetic mean is related (Tab. 5). Tab. 5 shows that in
groups of men, it is apparent that longer distance to services (Distance-moderate,
Distance-high and Distance-very high) is closely associated with higher number
of steps per day. In women, the difference is not so apparent. Services (shops,
restaurants, offices, banks, etc.) are an important part of everyday life, therefore
further distance from the place of living does not impede women and men in
accessing them.
5 Software tool
We used a software tool which is developed in the Department of Computer
Science at Palacky University, Olomouc, to create the fuzzy contexts and to
browse the corresponding fuzzy concept lattice. This software tool supports the
whole process of the processing and evaluation of IPAQ questionnaire. The basic
overview of functions that are supported and their succession is shown in Fig.
1.
The processing of the questionnaire consists of the following steps.
– Reading data. IPAQ questionnaire is recorded in the form of an MS Ex-
cel file. The columns of this file contain respondents’ answers to individual
106 Jiřı́ Zacpal, Erik Sigmund, Josef Mitáš, Vladimı́r Sklenář
Fig. 1. Base screen of application
questions. The software tool allows to specify which columns are included in
the processing.
– Scaling. The answers to some questions may be in the form of many-valued
attributes. For example, the values in the column Age may be in the interval
from 18 to 69. Due to this fact it is necessary to transform the original file
to the form in which each column contains only 0 or 1. This process is called
conceptual scaling [10]. Our software tool allows one to specify the bivalent
attributes and the scale for each column in data source file.
– Creation of aggregate objects. The tool allows to interactively specify the
set of characteristic attributes. The user also chooses parameters regarding
the structure of truth degrees.
A fuzzy context is created after these steps. A user can then explore the
associated fuzzy concept lattice and its concepts. Our software tool does not
create the whole concept lattice. Instead, it supports an interactive navigation
in the concept lattice. It shows the information related to the current concept
and its direct neighbors. A user selects next steps by choosing an ancestor or
successor of the current concept. He/she can move from a more general concept
to a more special concept and vice versa. He/she can also specify the content of
the extent or the intent and move to the appropriate concept. We can see the
user’s screen in Fig. 2.
The navigation in the concept lattice needs the calculation of the current
concept and its neighbors only. This calculation is relatively fast and does not
depend on the size of the whole concept lattice. Due to this fact the navigation
proceeds on-line and the user can modify the course of navigation interactively,
based on information gained. The user can also specify additional constraints to
be satisfied by formal concepts which are to be presented to him/her.
Application of the Formal Concept Analysis in Evaluation of Results of 107
ANEWS Questionnaire and Physical Activity of the Czech Regional Centers
Fig. 2. Navigation in fuzzy concept lattice
6 Conclusions
Our paper described a method of analysis of a questionnaire which comprises
number of questions which can be grouped based on their relation in meaning.
Such an approach allows for a more global assessment of the data. We have
applied this method to the ANEWS questionnaire. We can conclude that envi-
ronment which is physical activity friendly and stimulating in Czech cities can be
on the basis of the data and number of steps per day characterized by availability
of services in short distances, walking friendly streets (walkability and cleanness
of streets, no cul-de-sacs) and by nice environment in residential areas.
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