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Working Paper 11-36

Statistics and Econometrics Series 28

November 2011

Departamento de Estadística

Universidad Carlos III de Madrid

Calle Madrid, 126

28903 Getafe (Spain)

Fax (34) 91 624-98-49

PROFILE IDENTIFICATION VIA WEIGHTED RELATED METRIC SCALING:

AN APPLICATION TO DEPENDENT SPANISH CHILDREN

Irene Albarrán(1), Pablo Alonso(2) and Aurea Grané(1)

Abstract:

Disability and dependency (lack of autonomy in performing common everyday actions)

affect health status and quality of life, therefore they are significant public health issues.

The main purpose of this study is to establish the existing relationship among different

variables (continuous, categorical and binary) referred to children between 3 and 6 years old

and their functional dependence in basic activities of daily living. We combine different

types of information via weighted related metric scaling to obtain homogeneous profiles for

dependent Spanish children. The redundant information between groups of variables is

modeled with an interaction parameter that can be optimized according to several criteria.

In this paper, the goal is to obtain maximum explained variability in an Euclidean

configuration. Data comes from the Survey about Disabilities, Personal Autonomy and

Dependence Situations, EDAD 2008, (Spanish National Institute of Statistics, 2008).

Keywords: ADL, Disability, Mixed-type Data, Public Health, Related Metric Scaling.

AMS subject classification: 62-07, 62-09, 62H20, 62H99, 62P05.

Authors’ address: (1) Statistics Department, Universidad Carlos III de Madrid, C/ Madrid

126, 28903 Getafe (Madrid), Spain. (2) Statistics Department, Universidad de Alcalá, Pza.

San Diego, s/n - 28801 Alcalá de Henares (Madrid).

E-mail: A. Grané, aurea.grane@uc3m.es (Corresponding author), I. Albarrán,

irene.albarran@uc3m.es, P. Alonso, pablo.alonso@uah.es .

This work has been partially supported by Spanish grant MTM2010-17323 (Spanish

Ministry of Science and Innovation).

Proﬁle identiﬁcation via weighted related metric scaling:

An application to dependent Spanish children

Irene Albarr´an(1) Pablo Alonso(2) Aurea Gran´e(1)

(1) Statistics Department. Universidad Carlos III de Madrid.

(2) Statistics Department. Universidad de Alcal´a.

Abstract

Disability and dependency (lack of autonomy in performing common everyday

actions) aﬀect health status and quality of life, therefore they are signiﬁcant

public health issues. The main purpose of this study is to establish the exist-

ing relationship among diﬀerent variables (continuous, categorical and binary)

referred to children between 3 and 6 years old and their functional dependence

in basic activities of daily living. We combine diﬀerent types of information via

weighted related metric scaling to obtain homogeneous proﬁles for dependent

Spanish children. The redundant information between groups of variables is

modelled with an interaction parameter that can be optimized according to sev-

eral criteria. In this paper, the goal is to obtain maximum explained variability

in an Euclidean conﬁguration. Data comes from the Survey about Disabilities,

Personal Autonomy and Dependence Situations, EDAD 2008, (Spanish National

Institute of Statistics, 2008).

Keywords: ADL, Disability, Mixed-type Data, Public Health, Related Metric Scaling

AMS Subject Classiﬁcation: 62-07, 62-09, 62H20, 62H99, 62P05.

1 Introduction

Living is not always an easy task, specially if the physical or mental conditions are

not in their fullness. This is the case when people are not able to carry out certain

activities that are common in our daily life because they suﬀer some disabilities. This

situation refers to the negative aspects of the interaction between the individual and

the environment, i.e., deﬁcits, limitations in the activity and restrictions in his/her

social participation (WHO 2001b). This set of obstacles turns into a tougher situation

when a third person is required to do these activities, which is the case of depen-

dency. Disability has traditionally been a marginalized concern of public health and

has usually been viewed as a failure of primary prevention. However, disparities in

Financial support from research project MTM2010-17323 by the Spanish Ministry of Science and

Innovation.

Authors’ address: (1) Statistics Department, Universidad Carlos III de Madrid, C/ Madrid 126,

28903 Getafe, Spain. (2) Statistics Department, Universidad de Alcal´a, Plaza de la Victoria

2, 28802 Alcal´a de Henares, Spain. E–mails: I. Albarr´an, irene.albarran@uc3m.es, P. Alonso,

pablo.alonsog@uah.es, A. Gran´e, aurea.grane@uc3m.es

Corresponding author: A. Gran´e; Date: December 1, 2011.

1

health behaviours, health access, and health status between people with and without

disabilities suggest that opportunities exist for public health to engage people with

disabilities to improve their overall health (Crews and Lollar 2008). Disability is a

large public health problem in the main developed countries. It has been analysed in

the US (Pope and Tarlov 1991) and in the Western European countries (Haveman and

Wolfe 2000). The International Classiﬁcation of Functioning, Disability and Health

(ICF)(WHO 2001b) tries to establish a consensus in its understanding, by establish-

ing a diﬀerence between the basic activities of the daily life and the instrumental

activities of the daily life. The ﬁrst ones are deﬁned as those essential activities for

an independent life. There are many ways to deﬁne what dependency is. One of the

most accepted is that included in Resolution R(98) of the Council of Europe that

deﬁnes it as “such state in which people, whom for reason connected to the lack or

loss of physical, mental or intellectual autonomy, require assistance and/or extensive

help in order to carry out common everyday actions”.

This general deﬁnition has been translated to national legislations in an heterogeneous

way (Kamette 2011). In fact, it may happen that a man/woman can be considered

dependant in a country but not in another. For instance, a 58 year-old dependent

man in Spain or in Germany will not be considered dependant in France because in

the French system it is required to be over 60 years old. Or, in a another way, the

intensity of the legally recognized dependence may change amongst countries (see

Albarr´an, Alonso, and Bolanc´e 2009). If we consider the Spanish case, the deﬁnition

of dependency is that included in article 2 of Act 39/2006, of 14th December, on

the Promotion, Personal Autonomy and care for Dependent persons. It is deﬁned

as a “permanent state in which persons that for reasons derived from age, illness or

disability and linked to the lack or loss of physical, mental, intellectual or sensorial

autonomy require the care of another person/other people or signiﬁcant help in or-

der to perform basic activities of daily living or, in the case of people with mental

disabilities or illness, other support for personal autonomy”.

Another key element is the assessment of dependency. This question is usually solved

using speciﬁc scales that take into account the disabilities suﬀered by the person

jointly with their intensity. It is not easy to measure this last matter, being one of

the most extended solutions to evaluate the time dedicated by a third person to help

him/her to do certain activities, such as dressing or eating by him/herself. This is

how it is assessed in several national systems such as those currently in force in Spain

or in Germany. The evaluation of dependency in Spain is ruled by the Royal Decree

504/2007, of 20th April, that passes the scale for assessment of the situations of de-

pendency set by Act 39/2006. According to it, the scale goes from 0 to 100 points

and at least 25 points are needed to acknow the entitlement to the beneﬁts of the

System. In Table 1 we show the dependency graduation following Spanish legislation.

According to the scale value reached by an individual, Act 39/2006 establishes a min-

imum level of protection, which is deﬁned and ﬁnancially guaranteed by the General

State Administration. Dependent persons shall be entitled to access under equal con-

ditions to the beneﬁts and services foreseen in this Act, according to the terms laid

down in it. For instance, regarding dependent children, some family beneﬁts, social

service beneﬁts in re-education and rehabilitation can be obtained. This scale is used

in all cases when individuals are over 3 years old. Nevertheless, when the individuals

are under 6, the International Classiﬁcation of Functioning (ICF) mentioned before

2

Table 1: Dependency graduation following Spanish legislation

Dependency Degree Level Scale values Dependency Degree Level Scale values

Non dependant - - [0,25) Severe II 1 [50,65)

II 2 [65,75)

Moderate I 1 [25,40) Major III 1 [75,90)

I 2 [40,50) III 2 [90,100]

Moderate dependency The person needs help in order to perform various basic ADL(1)

at least once a day or the person needs intermittent or limited

support for his/her personal autonomy.

Severe dependency The person needs help in order to perform various basic ADL

two or three times a day, but he/she does not want the

permanent support of a carer or he/she needs extensive support

for his/her personal autonomy.

Major dependency The person needs help in order to perform various basic ADL

several times a day or he/she needs the indispensable and

continuous support of another person or he/she needs

generalised support for his/her personal autonomy.

(1) ADL stands for Activities of Daily Living.

is replaced by its version for children and youth (ICF-CY) (WHO 2001a). This ver-

sion is based on the same model as ICF with added content adapted to these groups

of people. ICF is meant to provide a common language to professionals and other

stakeholders involved in facilitating functioning for persons with body impairments

and activity limitations. Besides, in this case the term limitation is used instead of

disability. However, the federal Maternal and Child Health Bureau (MCHB) deﬁnes

children with special health care needs as those for a chronic physical, developmental,

behavioral, or emotional condition and who also require health and related services

of a type or amount beyond that required by children generally (see USDHHS 2004).

Dependence is the main impact factor on health and quality of life (Mill´an-Calenti

2006). There are many studies about dependence when people is over 65 (see Gram-

menos 2003, Lafortune and Balestat 2007, Giannakouris 2009). However, concerning

children, there is a lack of research using internationally accepted measurements. Be-

navente and Pfeiﬀer (2002) pointed out that children with disabilities is a large area

to be covered. In particular, our contribution is to study those children with speciﬁc

disabilities linked to some limitations (see Annex I) who are considered dependant ac-

cording to the Spanish legislation. Becoming dependant during the ﬁrst stages of life

implies that the individual is going to need special cares during the rest of his/her

life (Claeson and Waldman 2000 and Hauser-Cram, Warﬁeld, and Shonkoﬀ 2001).

Nowadays, thanks to the combined eﬀorts of medicine, public health and policy, chil-

dren with chronic conditions or disability live to adulthood, often with a life span

similar to the general population (Cannell, Brumback, Bouldin, Hess, Wood, Sloyer,

Reiss, and Andresen 2011). For this reason, it seems quite necessary to know as best

as possible how the Spanish child population is living in these circumstances, that is,

we are interested in establishing homogeneous proﬁles. Each of these groups will have

diﬀerent necessities (for instance, medical, psychological or social cares) with diﬀer-

ent economic consequences. The aim of this paper is to classify into diﬀerent groups

3

the dependent Spanish population between 3 and 6 years old. These groups will be

created depending on certain inherent characteristics such as sex, suﬀered limitation

and its severity or weekly hours of personal assistance. The statistical information

comes from the Survey about Disabilities, Personal Autonomy and Dependence Sit-

uations, 2008 (EDAD 2008, according to its Spanish acronym). This question, which

is crucial in actuarial science, has been usually solved by classical segmentation tech-

niques, such as k-means (see, for instance, Anderberg 1973 and Morgan and Ray

1995). Applications to class rating deﬁnitions may be found in Loimaranta, Jacobs-

son, and Lonka (1980), Campbell (1986), Boj, Claramunt, and Fortiana (2001) and

Boj, Claramunt, and Fortiana (2004). However, technical relevant problems arise be-

cause of (i) the sampling design and (ii) the nature of the variables observed. Indeed,

in EDAD 2008 a two-stage sampling was conducted by INE, leading to individuals

that represent population groups of diﬀerent sizes. We refer to this situation as a

weighted context, in contrast to the classical iid sampling. Regarding the nature of

the variables, data collected through questionnaires are often of mixed-type obtained

as measures of variables at diﬀerent levels, e.g. quantitative, multi-scale categorical

and binary variables. The repertory of statistical techniques suitable for this mixed-

type data is scarce. Among them, multidimensional scaling appears to be one of the

most ﬂexible techniques dealing with mixed-type data. Bearing in mind the setting

of homogeneous proﬁles, it becomes crucial the deﬁnition of a proper distance (or dis-

similarity) function among individuals. The well-known Gower’s general similarity

coeﬃcient (see Gower 1971, Cox and Cox 2000) considers mixtures of quantitative,

multi-scale categorical and binary variables. Nevertheless, the additive treatment of

the variables of Gower’s based similarity coeﬃcients results in a lack of considera-

tion of the association between variables. Gran´e and Romera (2009) proposed to

construct a joint metric via related metric scaling (Cuadras and Fortiana 1998) from

three diﬀerent distance matrices computed on quantitative, multi-scale categorical

and binary variables, respectively. Through a case study these authors show the po-

tential of this technique, which overperforms the classical Gower’s metric, and study

the sensitivity and robustness of their proposal through crossvalidation procedures.

This paper extends their proposal in two directions. Firstly, we consider related met-

ric scaling in the weighted context, in the sense that each individual can represent

a group of individuals, and secondly we model the redundant information between

groups of variables through an interaction parameter, that can be optimized accord-

ing to several criteria (see also Esteve 2003). For example, in the case study of data

coming from EDAD 2008, since we are interested in obtaining homogeneous proﬁles

for dependent Spanish children, the interaction parameter is achieved by imposing

maximum explained variability in the Euclidean conﬁguration.

Searching for proﬁles of homogeneous dependent Spanish children we ﬁnd out that the

Spanish scale is not suﬃcient in order to measure properly the severity of the situation

of dependency, since the time devoted to care dependent children and the intensity

of the dependency is not directly related. This is quite relevant, since the scale value

reached by an individual allows him/her to access to the beneﬁts entitled by the

Spanish Act 39/2006. Finally, we have observed that the deﬁnition and classiﬁcation

that the International Classiﬁcation of Functioning for children and youth (WHO

2001a) establishes can be reﬁned and complemented according to USDHHS (2004).

The rest of the paper is organised as follows: the Spanish database is described in

4

Section 2. Section 3 is devoted to multidimensional scaling methodology for mixed-

type data in the weighted context, where the new proposal of weighted related metric

scaling is introduced. An application of this new methodology can be found in Section

4, where we obtain diﬀerent homogenous proﬁles for dependent Spanish children using

data coming from EDAD 2008. Finally, we conclude in Section 5.

2 Database used in the analysis

Three surveys about disability have been undertaken by INE (Spanish National In-

stitute of Statistics) during the last 25 years in Spain. The ﬁrst one, elaborated in

1986, was the Survey about Disabilities, Impairments and Handicaps (EDDM 1986,

according its Spanish acronym). The next one, the Survey about Disabilities, Im-

pairments and Health Status (EDDES 1999, according its Spanish acronym), was

prepared using data of 1999. Finally, the last one was the Survey about Disabilities,

Personal Autonomy and Dependence Situations (EDAD 2008, according its Spanish

acronym). Although all of them talk about disabilities, it is impossible to track this

phenomenon in a homogeneous way along the years because the deﬁnition of that

concept has been changing through the years depending on the classiﬁcation used to

prepare the survey.

2.1 Recent disability survey in Spain: EDAD 2008

In order to provide reliable estimates at the national level, the survey was performed

around the country using sampling. In particular, a two-stage sampling was per-

formed, stratiﬁed and proportional to the size of the Spanish autonomous regions

(with stratiﬁed sampling distribution proportional to population size in stratum,

within each Spanish province). See INE (2010) for more details on the sampling

methodology.

EDAD 2008 gives information about people with disabilities that were living either

in a particular home or in institutions. In the ﬁrst case, the survey was prepared

interviewing 260,000 people who were living in 96,000 diﬀerent houses whereas for

institutionalized people, 11,000 people in 800 centers were asked about their situation.

This survey is based on the concept of self perceived disability, in accordance with

the recommendations of the World Health Organization. So, the target people is

identiﬁed through a set of questions about the possible diﬃculties they can ﬁnd

in doing some speciﬁc activities. Despite its drawbacks, the main advantage of this

strategy is that it is focused in the daily activities of the individuals and the problems

they may have while doing them, with no consideration of medical matters. That is,

it puts the attention of both interviewer and interviewed in functional aﬀairs since

they are key aspects when talking about disability (Jim´enez and Huete 2010).

According to EDAD 2008, there are more than 4.1 million Spanish people suﬀering

at least one kind of disability, 3.85 million out of them living with their relatives or

in their own homes, whereas the remaining 0.27 millions are in specialized centers.

Although the global prevalence rate is 9.1%, in the case of people living at home, this

rate is lower than that for people living in institutions (8.5% and 17.7%, respectively).

Disability is mainly related to two main variables: sex and age. Until 45 years old, the

male prevalence is greater than the female one. After that age, the relative incidence

5

is greater for women. In general terms, more than 50% people with this problem are

at least 65 years old, being most of them women. Figures about people aﬀected that

are living at home can be seen in Table 2.

Table 2: People with disability living at home: number and prevalence rate

Number (000) Prevalence rate (%)

Ages (years) Total Men Women Total Men Women

Under 6 60.4 36.4 24.0 2.2% 2.5% 1.8%

Between 6 and 44 608.1 345.1 263.0 2.5% 2.8% 2.3%

Between 45 and 64 951.8 409.0 542.8 8.7% 7.6% 9.8%

65 or more 2,227.5 756.7 1,470.8 30.3% 24.1% 34.9%

Total 3,847.8 1,547.2 2,300.6 8.5% 6.9% 10.1%

Source: own elaboration using EDAD 2008

Despite the fact that the survey includes the term “dependence” into its denomina-

tion, the questionnaire does not consider questions on this topic. In fact, if we looked

for the number of dependants reﬂected in the survey, we would not be able to know

how many individuals would be in this situation. So, the only way to answer this

question is trying to apply as best as possible both the deﬁnition incorporated in ar-

ticle 2 of Act 39/2006 and the assessment scale regulated by Royal Decree 504/2007.

Hence, the result is an estimation.

Besides this problem, there is another aspect that makes the study of this contin-

gency in children even more diﬃcult. It must be considered that the analysis of this

phenomenon for population until 6 years old has to be done using the ICF-CY Clas-

siﬁcation, where the concept of disability is replaced by that of limitation, because

children are dependant by themselves. For instance, it has no sense to talk about

self care in children. Moreover, there are other limitations that can only be seen

during the growth of a child, i.e., some diﬃculties in speaking. Therefore, it is no

surprising that the proportion of children with limitations increases with age (Grupo

de Atenci´on Temprana 2000). In addition, children in the earlier ages (0-2 years old)

are assessed with an special scale whose concepts are not reﬂected in EDAD 2008.

This is the reason why this paper is focused on children between 3 and 6 years old.

In a strict sense, the considered ages are those between 36 and 71 months old.

2.2 Description of the data set

After having ﬁltered the information with the deﬁnition of dependency included in

Act 39/2006, the number of records to be analysed is 84. Taking into account the

sampling methodology, the Spanish National Institute of Statistics estimates that

the number of dependent Spanish children with possibilities of receiving public aid is

13,296. Their number and prevalence rate by age and gender are shown in Table 3.

In Table 4 we brieﬂy describe the twenty-four mixed-type variables considered in the

analysis. They consist of three continuous variables such as the age of the child (in

months), the scale value reached by the child and weekly hours of attention, three

multi-state categorical variables such as some information about the respondent,

the type of received aids and the severity of limitations to perform activities of daily

6

Table 3: Dependent children: number and prevalence rate by age and gender

Number Prevalence rate (%)

Ages (months) Total Boys Girls Total Boys Girls

Between 36 and 47 2,751 1,702 1,049 0.6% 0.7% 0.5%

Between 48 and 59 5,621 3,473 2,148 1.2% 1.5% 0.9%

Between 60 and 71 4,923 3,272 1,652 1.1% 1.4% 0.8%

Source: own elaboration using EDAD 2008

living (ADL) and, ﬁnally, eighteen binary variables such as sex and several limitations

described in the Annex.

Table 4: Variables included in the analysis with its possible values

Values/categories Values/categories

Type Description (% frequency distribution) Type Description (% frequency distribution)

B(1) sex male(66.6%), female (33.3%) B lim 15 yes (7.9%), no(92.1%)

B lim 1(2) yes (13.1%), no(86.9%) B lim 16 yes (70.1%), no(29.9%)

B lim 2 yes (21.5%), no(78.5%) B lim 17 yes (76.5%), no(25.5%)

B lim 3 yes (26.6%), no(73.4%) B lim 18 yes (79.3%), no(20.7%)

B lim 5 yes (7.6%), no(92.4%) C age (months) from 36 to 71

B lim 6 yes (2.0%), no(98.0%) C scale from 0 to 100

B lim 7 yes (14.4%), no(85.6%) C hours-week from 0 to 168

B lim 8 yes (24.5%), no(75.5%) CT inf-relac parents (92.8%), tutor (2.4%),

B lim 9 yes (36.1%), no(63.9%) (respondent) grandparents (4.8%)

B lim 10 yes (17.1%), no(82.9%) CT B-2 only personal assistance (67.1%),

B lim 11 yes (80.9%), no(19.1%) (received aids) personal assistance and aids (32.9%),

B lim 12 yes (7.6%), no(92.4%) only technical aids (0.0%)

B lim 13 yes (33.4%), no(66.6%) CT B-5 (severity moderate(69.9%), severe (19.2%),

B lim 14 yes (30.2%), no(69.8%) of limitations cannot perform ADL(3) (10.9%)

to perform ADL)

(1) B=binary, C=continuos, CT=categorical. (2) See Annex I for the deﬁnition of limitations lim 1 to lim 18.

(3) ADL stands for Activities of Daily Living.

3 Weighted Multidimensional Scaling

for mixed-type data

Multidimensional Scaling (MDS) is a multivariate technique closely related to Prin-

cipal Component Analysis (PCA) and Correspondence Analysis (CA), well-known

techniques and widely used by applied researchers. The objective of these techniques

is the description and the pictorial representation of a data set. The information

provided by the data set may be a matrix of observations corresponding to a set of

continuous variables, which is the case of PCA, a contingency table obtained from the

classiﬁcation of a set of objects according to categorical variables, which is the case

of CA, and for the MDS the data set is a square matrix of dissimilarities between a

set of objects. The main advantage of MDS is that it is able to cope with variables of

any type (binary, categorical, numerical, functional, . . .) or even a mixture of them,

since using a proper “distance” function one can obtain the matrix of dissimilarities

7

between the set of objects (see Ramsay 1980). In particular, the purpose of MDS

is to construct a set of points in a Euclidean space whose interdistances are either

equal (metric or classical MDS) or approximately equal (nonmetric MDS) to those

in a given matrix of dissimilarities, in such a way that the interpoint distances ap-

proximate the interobject dissimilarities as closely as possible. That is, given a n×n

matrix ∆, containing the squares of dissimilarities between nobjects, the goal is

to obtain a n-point conﬁguration onto orthogonal axes (called Euclidean conﬁgura-

tion/map or MDS conﬁguration), so that the L2–distances between the coordinates

of these npoints coincide with the corresponding entries in ∆. These coordinates are

called a metric scaling representation of ∆. Various possible measures of approxi-

mation between interpoint distances and interobject dissimilarities can be used, each

resulting in a diﬀerent MDS conﬁguration. In this work, these coordinates are ob-

tained via spectral decomposition. General context references are Borg and Groenen

(2005), Cox and Cox (2000) and Krzanowski and Marriott (1994) as well as Gower

and Hand (1996).

In the following we review the extension of classical MDS concepts to the weighted

context, derived by Boj, Claramunt, and Fortiana (2001). Recall that in the weighted

context each individual can represent a population group of diﬀerent size.

Given n p-dimensional vectors {zi,1≤i≤n}containing the information of the n

diﬀerent individuals we compute a squared distances matrix ∆, with entries δ2(zi,zj),

for 1 ≤i, j ≤n. Since this information can be either of qualitative or quantitative

nature, or both, it is crucial the adequacy of the dissimilarity function used in the

computation of ∆. Additionally, we have w= (w1,...,wn)′a vector of weights, such

that wi>0, for i= 1,...,n, and 1′w= 1, where 1is the n×1 vector of ones.

Suppose that we are interested in obtaining a metric scaling representation of ∆,

provided that ∆satisﬁes the Euclidean requirement. Given w, deﬁne Dw=diag(w),

an×ndiagonal matrix whose diagonal is the vector of weights, and Kw=1w′, then

Jw=I−Kwis the w-centering matrix, which is an orthogonal projector with respect

to Dw, idempotent and self-adjoint with respect to Dw. Then, the doubly w-centered

inner-product matrix is

Gw=−1

2Jw∆ Jw

and

Fw=D1/2

wGwD1/2

w(1)

is the standardized inner-product matrix. The Euclidean requirement is equivalent

to the positive semi-deﬁniteness of Gw, hence to the existence of an Xwsuch that

Gw=XwX′

w, called in the weighted context a w-centered Euclidean representation

of ∆, meaning that w′Xw=0and that the squared Euclidean interdistances between

the rows of Xwcoincide with the corresponding entries in ∆.1

This matrix Xwis the w-weighted metric scaling representation of ∆, which is ob-

tained through the spectral decomposition of (1) as

Xw=D−1/2

wU Λ,(2)

1If some of the eigenvalues of Gware negative, then ∆does not admit an Euclidean conﬁguration,

which means that some of the axes in the representation are imaginary. In this case, a possible

solution (still valid in the weighted context, since wis an eigenvector of Gwof 0 eigenvalue) is to

consider the transformation ˜

∆=∆+c(1n1′

n−In), where c≥2|λ|and λis the negative eigenvalue

of maximum module, which assures an Euclidean conﬁguration for ˜

∆.

8

where Λ2is a diagonal matrix containing the eigenvalues of Fw, ordered in decreasing

order, and Uis the matrix whose columns are the corresponding eigenvectors. The

rows of Xwcontain the principal coordinates of the nindividuals and its columns

are the principal axes of this representation.

In the following we describe two ways of obtaining a w-weighted metric scaling rep-

resentation of ∆from pcontinuous and categorical variables measured on a set of

nindividuals with a weight vector w. The ﬁrst one is the classical approach and

proceeds by computing Gower’s general similarity coeﬃcient in the weighted con-

text, whereas the second one is called weighted related metric scaling and extends

the proposal of Cuadras and Fortiana (1998) to the weighted context.

3.1 Classical approach: Gower’s general similarity coeﬃcient

After a review of the specialized literature, we found that the most popular similarity

measure in the context of mixed-type data is the well-known Gower’s general simi-

larity coeﬃcient (see Gower 1971), which for two p-dimensional vectors ziand zjis

equal to

sij =Pp1

h=1 (1 − |zih −zjh|/Rh) + a+α

p1+ (p2−d) + p3

,(3)

where p=p1+p2+p3,p1is the number of continuous variables, aand dare the

number of positive and negative matches, respectively, for the p2binary variables, α

is the number of matches for the p3multi-state categorical variables, and Rhis the

range of the h-th continuous variable. The entries of matrix ∆are computed as

δ2(zi,zj)=1−sij.(4)

Gower (1971) proved that (4) satisﬁes the Euclidean requirement.

3.2 Weighted Related Metric Scaling

Like all distance functions satisfying additivity with respect to variables, the distance

based on Gower’s general similarity coeﬃcient implicitly ignores any association (e.g.

correlation) between variables (Gower 1992, Krzanowski 1994). Alternative metrics

have been proposed in the literature to overcome that problem, among them, we de-

cided to extend Related Metric Scaling (Cuadras and Fortiana 1998) to the weighted

context. Related metric scaling is a multivariate technique that allows to obtain

a unique representation of a set of individuals from several distance matrices com-

puted on the same set of individuals. The method is based on the construction of a

joint metric that satisﬁes several axioms related to the property of identifying and

discarding redundant or repeated information.

Given a set of m≥2 matrices of squared distances measured on the same group of

nindividuals, {∆α}α=1,...,m, and a vector of weights w, the ﬁrst requirement in the

construction of the w-joint metric is that all matrices ∆αhave the same geometric

variability. This concept was introduced by Cuadras and Fortiana (1995) as a variant

of Rao’s diversity coeﬃcient (Rao 1982a, Rao 1982b) and, given a squared distances

matrix ∆α=δ2(zi,zj){1≤i,j≤n}, its sample version in the weighted context is:

Vw,α(δ) = 1

2w′∆αw=tr(Fw,α),(5)

9

where Fw,α is the corresponding standardized inner-product matrix.

For each squared distances matrix {∆α}α=1,...,m, we consider its doubly w-centered

inner-product matrix Gw,α and its standardized inner-product matrix

Fw,α =D1/2

wGw,α D1/2

w,for α= 1,...,m,

and obtain the w-joint metric as that whose standardized inner-product matrix is:

Fw=

m

X

α=1

Fw,α −λX

α6=β

F1/2

w,α F1/2

w,β,(6)

where λis an interaction parameter that can be optimized according to several cri-

teria. For example, in this work, we are interested in obtaining maximum explained

variability in an Euclidean conﬁguration, and in Section 4 we call optimum weighted

related metric scaling to the Euclidean conﬁguration obtained by this procedure. See

Esteve (2003) for a wide and rigorous study on the construction of metrics.

The second summand of formula (6) is the key tool for eliminating redundant infor-

mation coming from diﬀerent sources (diﬀerent variable types, in our case). Roughly

speaking, this second term makes the diﬀerence with Gower’s metric and provides

the desired ﬂexibility when dealing with mixed-type data. Formula (6) extends for-

mula (8) of Cuadras (1998) to the weighted context, where the interaction parameter

was ﬁxed to λ= 1/m and inner-product matrices were used instead of standardized

inner-product matrices. Formula (6) is obtained so that the following properties are

fulﬁlled when λ= 1/m. We explicit them for m= 2:

1. If ∆1=0then Fw=Fw,2,

2. If ∆1=∆2then Fw=Fw,1=Fw,2,

3. If the Euclidean conﬁgurations associated to ∆1and ∆2generate orthogonal

subspaces on Rn, then Fw=Fw,1+Fw,2,

4. Fw≥0.

Principal coordinates are computed directly from matrix Fwof (6), but in case it is

necessary, we can recover matrix ∆with the following formula:

∆=gw1′+1 g′

w−2Gw,(7)

where Gw=D−1/2

wFwD−1/2

wand gw=diag(Gw).

4 A case study

In this Section we apply the two techniques described above to the data matrix Z,

whose rows are 84 records representing 13,296 dependent children with possibilities of

receiving public aid (see Section 2.2 for the data set description). Hereafter, we call

Gower’s metric to the distance matrix derived using formula (4) and w-joint metric

to the distance matrix obtained from formula (7).

In this study, the w-joint metric is constructed from m= 3 diﬀerent squared distances

matrices measured on the same set of n= 84 individuals. We call them ∆1,∆2and

10

∆3. The vector of weights, w, is estimated by INE from the survey and taking into

account the sampling design.

Matrix ∆1contains the information related to the three numerical variables consid-

ered in the study, that were the age of the child, the scale value reached by the child

and weekly hours of attention. In particular, we compute ∆1matrix using a robust

version of Mahalanobis’ distance

δ2(zi,zj) = (zi−zj)′S∗−1(zi−zj),

that consists of estimating the entries in the covariance matrix S∗in a robust way.

The variance of the j-th continuous variable is estimated from a 5%-trimmed sam-

ple, as suggested by Tuckey (1960). A robust estimator for the covariance between

variables Zjand Zkis obtained from

s∗

jk =1

4(ˆσ∗2

+−ˆσ∗2

−),

where ˆσ∗2

+and ˆσ∗2

−are robust estimators of the variances of Zj+Zkand Zj−Zk,

respectively (see Gnanadesikan 1997).

Matrix ∆2contains the information concerning three multi-state categorical vari-

ables, that is, information about the respondent, the type of received aids and the

severity of limitations to perform ADL. In this case, we start by computing a sim-

ilarity matrix S2, that contains Sokal-Michener’s pairwise similarities, and obtain

∆2= 2 (1 1′− S2).

Matrix ∆3contains the information of eighteen binary variables (sex and the lim-

itations described in the Annex). In this case, we compute a similarity matrix S3,

whose entries are the Jaccard’s pairwise similarities, and obtain ∆3= 2 (1 1′− S3).

Finally, from formula (6) we construct the w-joint metric and obtain the Euclidean

conﬁgurations shown in Figures 1–4. In this study, the interaction parameter λis

optimized so that these conﬁgurations have maximum explained variability.

4.1 Euclidean conﬁgurations

In Figure 1 we depict three-dimensional principal coordinate representations of the

data set obtained via the classical approach (panels (a1) and (a2)) and through

weighted related metric scaling technique (panels (b1) and (b2)). We give two diﬀer-

ent views of each representation for better comparison.

Two main advantages can be observed while using the new proposal based on the

w-joint metric. Firstly, there is an increase in the percentage of explained variability

and, secondly, the group of non-dependent children is quite well identiﬁed. A possible

explanation may be that the information contained in the continuous variables is

better incorporated with the w-joint metric than with the classical approach. Hence,

hereafter, and with the aim of deﬁning homogeneous proﬁles of dependent children,

we focus our attention in the w-joint metric representation.

4.2 Looking for inﬂuent variables

Next, we are interested in capturing the underlying structure of the groups obtained

in a natural way through weighted related metric scaling. To determine which vari-

ables are more powerful in explaining the homogeneity within groups we compute the

11

Figure 1: Euclidean maps obtained via (a) classical MDS and (b) Optimum weighted

related metric scaling

Classical approach, 37.17% of explained variability.

(a1) Gower’s metric. View 1. (a2) Gower’s metric. View 2.

00.2 −0.4

−0 2

00.2

−

−

−0.2

−0.1

0

0.1

0.2

0.3

x2

x1

x3

No dependency

Degree II level 1

DegreeII level 2

Degree III level 1

Degree III level 2

4

0

0.2

−0.4

−0 2 00.2

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

x1

x2

x3

No dependency

Degree II level 1

Degree II level 2

Degree III level 1

Degree III level 2

Weighted related metric scaling, 47.08% of explained variability.

(b1) Optimum w-joint metric. View 1. (b2) Optimum w-joint metric. View 2.

00.5 11.5 −1 01

−0 5

0

0 5

1

1 5

x2

x1

x3

No dependecy

Degree II level 1

Degree II level 2

Degree III level 1

Degree III level 2

5

0

0 5

1

1.5

−1 01

−1.5

−1

−0.5

0

0.5

1

1.5

x1

x2

x3

No dependecy

Degree II level 1

Degree II level 2

Degree III level 1

Degree III level 2

the correlation coeﬃcients between the original variables and the ﬁrst three principal

axes, shown in Table 5. We consider Pearson’s correlation coeﬃcient for continu-

ous variables, whereas Spearman’s correlation coeﬃcient is computed for categorical

variables.

Form Table 5 it can be seen that continuous variables, such as age, scale or hours-

week, are more correlated with the principal axes obtained from the w-joint metric

than with those obtained via Gower’s metric. Moreover, categorical variable B5 and

binary variables lim2, lim3, lim9 and lim11 also have inﬂuence on the principal axes.

For instance, when using the w-joint metric, the ﬁrst principal coordinate is mostly

determined by variables lim 2, lim 3, lim 9, lim 11, B5, scale and hours-week, whereas

age and hours-week are inﬂuent variables for the second principal axis. Finally,

lim11, age and scale have great inﬂuence on the third principal coordinate. Such an

information will be valuable in the deﬁnition of homogeneous proﬁles. Bearing this

12

Table 5: Correlation coeﬃcients (Pearson for continuous variables and Spearman for

categorical ones) between the principal coordinates and the considered variables.

Gower’s metric Optimum w-joint metric

1st P.C. 2nd P.C. 3rd P.C. 1st P.C. 2nd P.C. 3rd P.C.

(x1) (x2) (x3) (x1) (x2) (x3)

sex 0.3187 0.3291 0.2791 -0.0844 0.1614 0.0771

lim 1 -0.5261 -0.0153 0.1754 0.3529 -0.2787 -0.3602

lim 2 -0.6452 0.0450 0.1500 0.5226 -0.2826 -0.2988

lim 3 -0.7548 -0.0622 0.0908 0.5269 -0.2890 -0.4046

lim 5 -0.3040 0.0550 0.1006 0.2376 -0.0197 -0.0322

lim 6 -0.0507 -0.0784 0.3159 -0.0438 -0.0922 -0.0715

lim 7 0.0409 0.0288 0.1031 -0.0667 0.0152 0.1167

lim 8 -0.5914 -0.2052 -0.0842 0.3816 -0.1556 -0.2870

lim 9 -0.7910 -0.1824 -0.0318 0.5082 -0.2490 -0.4591

lim 10 -0.3183 0.3550 -0.2097 0.3781 -0.0794 -0.0156

lim 11 -0.5475 0.4665 -0.0522 0.5745 0.1485 -0.6378

lim 12 -0.1840 0.1405 -0.4131 0.2392 -0.2743 0.0468

lim 13 -0.1332 0.6302 -0.4703 0.2756 0.0154 -0.0133

lim 14 -0.2475 0.6663 -0.1949 0.4333 -0.0048 0.0070

lim 15 -0.1164 0.2514 0.0755 0.0471 -0.2443 -0.3135

lim 16 0.0854 0.7082 0.4083 0.1135 0.2739 -0.0187

lim 17 0.1268 0.4842 0.5499 0.0427 0.2801 -0.0749

lim 18 -0.2546 0.3283 -0.2625 0.3271 0.0232 -0.0244

age 0.2712 0.0286 0.0448 0.2062 0.6345 0.7274

scale -0.6824 0.5046 -0.0776 0.7425 0.1188 -0.6761

hours-week -0.5723 0.1520 -0.4066 0.6839 -0.5928 0.0779

inf-relac -0.1459 -0.1216 -0.1411 0.1557 0.0309 0.1409

B2 -0.3906 -0.3593 0.5739 0.1021 -0.1416 -0.2125

B5 -0.4657 0.4320 -0.1206 0.5812 -0.2005 -0.1699

Notes: Bold numbers reﬂect coeﬃcients greater than 0.5 in absolute value.

Source: Own elaboration.

objective in mind, in Figures 2–3 we plot several projections (in dimension two) of

the principal coordinate representations shown in panels (b1) and (b2) of Figure 1,

using the information of those variables more correlated with the principal axes (lim

2, lim 3, lim 9, lim 11, B5, age, scale, hours-week) to color the individuals. In this

way, groups of homogeneous individuals will become apparent.

After analysing all possible projections, we decided to include only the most represen-

tative ones. For this reason, Figure 2 contains the principal coordinate representation

(3rd P.C. versus 1st P.C.) obtained from the w-joint metric. Looking at panel (f),

and comparing it with panel (a), we can see that lim 11 (the child can hardly do the

things that other children do at the same age) is crucial in splitting the individuals

in two groups: dependants and non-dependants. In fact, when a child is declared as

dependant, almost always lim 11 is present (95.1% and 90.8% in Degree II level 1

and 2, respectively, and 100% in Degree III). The remaining variables with correla-

tion coeﬃcients greater than 0.50 in absolute value (lim 2, lim 3, lim 9, age, scale,

hours-week and B5) are quite useful for constructing dependency proﬁles. That is,

children not aﬀected by dependency show a moderate severity in limitations linked to

ADL. Besides, they neither suﬀer those limitations associated to vertical movements

(lim 2, lim 3 and lim 9) nor lim 11. Their scale value is fully identiﬁed using the 1st

and 3rd principal corrdinates and, in most cases, their ages are between 48 and 71

months old.

13

Figure 2: Principal coordinate representations obtained via optimum weighted related

metric scaling. Projections of Figure 1 (panels (b1) and (b2)) conﬁgurations onto 1st

and 3rd P.C.

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x1

x3

No dependency

Degree II level 1

Degree II level 2

Degree III level 1

Degree III level 2

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x1

x3

mod. difficulty

severe difficulty

cannot perform ADL

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x1

x3

no

yes

(a) scale (b) B5 (c) limitation 2

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x1

x3

no

yes

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x1

x3

no

yes

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x1

x3

no

yes

(d) limitation 3 (e) limitation 9 (f) limitation 11

The most important features in dependent children can be summarized as follows:

none of them is under 50 points in the dependency scale; all exhibit moderate severity,

at least; lim 2, lim 3 and lim 9 are not suﬀered by those with a scale value between

50 and 75 and they are hardly manifested in children with Degree III (37.9% and

5.2% in level 1 and 2, respectively). That is, these three limitations are associated to

severe dependency cases. Summing up, we can establish the following proﬁles:

[Pr1] Non-dependent children (19%): Moderate diﬃculty to perform ADL, none of

limitations 2, 3, 9, 11 are suﬀered, less than 56 weekly hours of attention are

needed by 79% of them.

[Pr2] Severe dependent children (40.6%): Composed by 100% of children in Degree

II (level 1,2). None of limitations 2, 3, 9 are suﬀered, almost all (93%) suﬀer

limitation 11 and 59% of them need less than 56 weekly hours of attention.

[Pr3] Major dependent children (25.4%): Composed by 75% of children in Degree III

level 1. All of them suﬀer limitations 9, 11 and 53% of them need more than

56 weekly hours of attention.

[Pr4] Utmost dependent children (15%): Composed by 100% of children in Degree III

level 2 and 25% of children in Degree III level 1. Severe diﬃculties to perform

14

ADL or cannot perform them. All of them suﬀer limitation 11 and almost all

(95%) suﬀer limitations 2, 3, 9, 82% of them need more than 56 weekly hours

of attention, 88% of whom need more than 155 weekly hours of attention.

Proﬁles [Pr1] and [Pr4] clearly describe opposite situations, whereas proﬁles [Pr2]

and [Pr3] consider diﬀerent realities under the same Degree of dependency. In fact,

it is possible to ﬁnd individuals with the same scale value but with huge diﬀerences

in diﬃculties to perform ADL, age and necessity of attention.

If we focus the attention on the relationship between the intensity of severities (B5)

and the scale value reached by each child, we see that both variables are directly

related. In fact, children in Degree II level 1 show a moderate severity and 78.8%

of those in Degree III level 2 cannot perform ADL. On the other hand, looking at

Figure 2 it seems that it is diﬃcult to distinguish between severe diﬃculty to perform

ADL and cannot perform ADL (there are groups of individuals with same values for

limitations 2, 3, 9, 11, but not for B5). This may lead us to conclude that it would

be better to join those categories in only one.

Figure 3 contains several projections of the principal coordinate representation ob-

tained from the w-joint metric. Panels (a1)–(c1) depict 2nd P.C. versus 1st P.C.,

panels (a2)-(c2) show 3rd P.C. versus 1st P.C. and, ﬁnally, panels (a3)–(c3) contain

3rd P.C. versus 2nd P.C. We prefer to include again variable scale (panels (a1)–(a3)),

for better comparison. For example, we can see the usefulness of variable age in panel

(b3). A special case is that of variable hours-week, which seems to be contradictory

with the groups deﬁned by variable scale.

Despite the Spanish Act establishes a direct link between the amount of time devoted

to care dependent people and the intensity of the dependency, one of the most sur-

prising results is that there is a no direct relationship between the number of weekly

hours for care and the level of dependency. In fact, there are individuals that need

more than 155 hours per week in opposite situations (61% of children in Degree III

level 2 versus 21.2% that are non dependent). See Figure 4 and also panels (a3) and

(c3) of Figure 3. This same eﬀect was noticed by Albarr´an and Alonso (2006) and

Gispert Magarolas, Clot-Razquin, Rivero Fern´andez, Freitas Ram´ırez, Ru´ız-Ramos,

Ru´ız Luque, Busquets Bou, and Argim´on Pall`as (2008). Similar results were found

in Bihan and Martin (2006) when studying some European systems of assistance to

dependent people. This fact reﬂects that the Spanish scale is not properly measuring

the severity of the situation of dependency, which is quite worrying, since the scale

value reached by an individual allows him/her to access to the beneﬁts entitled by

the Spanish Act 39/2006.

5 Concluding remarks

Disability is a large public health problem even in developed countries. Dependence

is the main impact factor on health and quality of life. Suﬀering dependency when

people is over 65 is the most common situation. For this reason, some authors

join both states, dependency and ageing (see Casado and L´opez 2001, Moragas and

Cristofol 2003, and L´opez(Dir.), Comas, Monteverde, Casado, Caso, and Ibem 2005).

However, it is not true that all people over a certain age would be included in the

group of population aﬀected by this contingency. It would be possible to prevent

15

Figure 3: Principal coordinate representations obtained via optimum weighted related

metric scaling. Projections of Figure 1 (panels (b1) and (b2)) conﬁgurations onto two

principal axes.

2nd P.C. vs. 1st P.C. 3rd P.C. vs. 1st P.C. 3rd P.C. vs. 2nd P.C.

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

x1

x2

No dependency

Degree II level 1

Degree II level 2

Degree III level 1

Degree III level 2

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x1

x3

No dependency

Degree II level 1

Degree II level 2

Degree III level 1

Degree III level 2

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x2

x3

No dependency

Degree II level 1

Degree II level 2

Degree III level 1

Degree III level 2

(a1) scale (a2) scale (a3) scale

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

x1

x2

[36,48)

[48,60)

[60,72]

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x1

x3

[36,48)

[48,60)

[60,72]

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x2

x3

[36,48)

[48,60)

[60,72]

(b1) age (in months) (b2) age (in months) (b3) age (in months)

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

x1

x2

[0,14)

[14,56)

[56,156)

≥ 156

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x1

x3

[0,14)

[14,56)

[56,156)

≥ 156

−1.5 −1 −0.5 0 0.5 1 1.5

−1.5

−1

−0.5

0

0.5

1

1.5

2

x2

x3

[0,14)

[14,56)

[56,156)

≥ 156

(c1) hours-week (c2) hours-week (c3) hours-week

this situation if people followed a healthy way of life, the health care system was

more eﬃcient than today is and if we were able to have an early diagnosis of the

chronical illness (Zunzunegui 1998). Although the former is true, it must be said

that it is possible to ﬁnd people in dependency at any age during the lifetime, even

in the childhood. There are many studies about dependence when people is over 65,

however, concerning children, there is a lack of research. This study contributes in

this line. Our main purpose is to establish the existing relationship among diﬀerent

16

Figure 4: Principal coordinate representations obtained via Optimum Weighted Re-

lated Metric Scaling. Individuals identiﬁed by (a) scale and (b) hours-week.

−1

0

1

−1

−1

0

1

x1

x2

x3

No dependecy

Degree II level 1

Degree II level 2

Degree III level 1

Degree III level 2

−1

0

1

−1

−1

0

1

x1

x2

x3

[0,14)

[14,56)

[56,156)

≥ 156

(a) scale (b) hours-week

variables (numerical, categorical and binary) referred to Spanish children between 3

and 6 years old and their functional dependence in basic activities of daily living.

Data comes from the Survey about Disabilities, Personal Autonomy and Dependence

Situations, EDAD 2008, (Spanish National Institute of Statistics, 2008), where each

individual represents a number of similar individuals. The number of multivariate

techniques than can cope with mixed-type and weighted data is quite scarce. In this

paper we propose a multivariate methodology for mixed-type data to search for ho-

mogeneous proﬁles. In particular, we extend the work of Gran´e and Romera (2009) to

the weighted context. Moreover, we include an interaction parameter which provides

more ﬂexibility when dealing with mixed-type data. The main ﬁndings are: Firstly,

this new technique overperfoms the classical one based on Gower’s metric, in the sense

that homogeneous groups are better separated. This may be due to the possibility

of constructing an ad-hoc metric with the property of discarding redundant informa-

tion. Secondly, the things that a child can hardly do compared with other children

at the same age (limitation 11) seems to be crucial in splitting the individuals into

dependants and non-dependants. This ﬁnding goes in the line of USDHHS (2004)

and complements the universal deﬁnition and classiﬁcation established by the Inter-

national Classiﬁcation of Functioning for children and youth (WHO 2001a). Thirdly,

the time devoted to care dependent children and the intensity of the dependency is

not directly related. This was also found by Albarr´an and Alonso (2006), among

others, and reinforces the ﬁnding that the Spanish scale is not properly measuring

the severity of the situation of dependency. This is quite relevant, since the scale

value reached by an individual allows him/her to access to the beneﬁts entitled by

the Spanish Act 39/2006.

17

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Annex I

Deﬁnition of limitations

lim 1 For children over 9 months old: the child has troubles to stay

sitting down without help

lim 2 For children over 9 months old: the child has troubles to stay

standing up without help

lim 3 For children over 9 months old: the child has troubles to walk

by his/her own

lim 5 The child can hardly see

lim 6 The child is fully deaf

lim 7 It seems that the child can hardly hear

lim 8 The child has troubles to move his/her arms

lim 9 The child has any weakness or stiﬀness in the legs

lim 10 The child sometimes has convulsions, goes rigid or lose consciousness

lim 11 The child can hardly do the things that other children do

at the same age

lim 12 The child is frequently sad or depressed

lim 13 The child can hardly mix with other children,

as the children at the same age do

lim 14 For children over 2 years old: the child can hardly understand

simple instructions

lim 15 For children between 2-3 years old: the child can hardly

recognize and name objects

lim 16 For children between 3-5years old: the child can hardly speak

lim 17 The child is into any specialized education system for stimulation

lim 18 The child has been diagnosed by a doctor or a psychologist of any

illness that last more than one year

Source: ICF-CY Classiﬁcation

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