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Business Research Unit (UNIDE-IUL) / Instituto Universitário de Lisboa
Ed. ISCTE-IUL, Av. Forças Armadas
1649-026 Lisbon – Portugal
Phone: 210 464 019
E-mail: [email protected]
Internet: http://www.bru-unide.iscte.pt/We acknowledge financial support from
FCT – Fundação para a Ciência e a Tecnologia
FCT Strategic Project UI 315
PEst-OE/EGE/UI03152
A Grade of Membership A Grade of Membership A Grade of Membership A Grade of Membership
Representation of Representation of Representation of Representation of
REFLEX Project DataREFLEX Project DataREFLEX Project DataREFLEX Project Data
Abdul Suleman, ISCTE-IUL, BRU, Portugal
Fátima Suleman, ISCTE-IUL, DINAMIA-CET, Portugal
DEHEMS Second International Conference,
Slovenia, Ljubljana, 27 & 28 of September, 2012
FCT Strategic Project UI 315
PEst-OE/EGE/UI03153
Motivation
— One of the goals of REFLEX Project is to examine whether higher
education institutions in Europe are up to the task of equipping
graduates with the competencies needed to meet the demands the
modern knowledge society places on higher education graduates
(Allen and von der Velden, 2011);
— Graduates from 15 European countries as well as from Japan
were asked to rate their own level of competence in different
dimensions of competencies.
FCT Strategic Project UI 315
PEst-OE/EGE/UI03154
Our Objective
— Quantification of the overall competence of individuals, based
on a list of 19 items of competence used in self-assessment
(dimension H of the REFLEX Questionnaire);
— Given that, how competencies are, on average, distributed
among different countries that have participated in the project?
FCT Strategic Project UI 315
PEst-OE/EGE/UI03155
The Data
— Dimension H of the master questionnaire referred to as
Competencies;
— Focus on the skills acquired at higher education institutions from
individuals’ own perspective;
— List of 19 dimensions of competencies (from a to s), measured in
a 7 points Likert scale: 1: very low; 7: very high (intermediate values
are not labelled);
FCT Strategic Project UI 315
PEst-OE/EGE/UI03156
REFLEX Master Questionnaire: H - Competencies
Item Description
a Mastery of your own field or discipline
b Knowledge of other fields or disciplines
c Analytical thinking
d Ability to rapidly acquire new knowledge
e Ability to negotiate effectively
.... ..........
s Ability to write and speak in a foreign language
FCT Strategic Project UI 315
PEst-OE/EGE/UI03157
Data Details
— 16 countries participated in the project; we received data from
14 countries only (Sweden and Switzerland data were not included
in the database provided to us);
— Initial sample size: 34,347;
— Missing data and the data from the graduates who answered to
have not even spent one hour a week studying were omitted from
the analysis (5,002 cases in the total);
— Final sample size: 29,345;
— The question is: how to analyse these data?
FCT Strategic Project UI 315
PEst-OE/EGE/UI03158
Statistical Methodology
— Data reduction due to correlation among variables (items);
— PCA is the common method but it is designed for real-valued
data;
— REFLEX data are categorical;
— Discrete version of PCA: GoM – Grade of Membership analysis to
identify competence related groups or fuzzy clusters;
—What is then a fuzzy clustering?
FCT Strategic Project UI 315
PEst-OE/EGE/UI03159
Fuzzy Clustering
FCT Strategic Project UI 315
PEst-OE/EGE/UI031510
Example of a Fuzzy Clustering (2 clusters)
FCT Strategic Project UI 315
PEst-OE/EGE/UI031511
Quantification
— Suppose the woman overall competence is worth 100 and the
one of the fish is worth 10. What is then the overall competence of
a mermaid? It depends on its grades of membership.
— (0.1; 0.9) -> 100 x 0.1 + 10 x 0.9 = 10 + 9 = 19;
— (0.5; 0.5) -> 100 x 0.5 + 10 x 0.5 = 50 + 5 = 55;
— (0.8; 0.2) -> 100 x 0.8 + 10 x 0.2 = 80 + 2 = 82.
— The key issue is to quantify each fuzzy cluster.
FCT Strategic Project UI 315
PEst-OE/EGE/UI031512
Example of a Fuzzy Clustering (3 clusters)
A1 (Red)
A2 (Green)A3 (Blue)
Examples:
= (1, 0, 0)
= (0, 1, 0)
= (0.5, 0.5, 0)
= (0.4, 0, 0.6)
= (1/3, 1/3, 1/3)
= (1/2, 1/4, 1/4)
= (1/5, 2/5, 2/5)
FCT Strategic Project UI 315
PEst-OE/EGE/UI031513
Application to REFLEX Data
— GoM model devised by Woodbury and Clive (1974);
— Allows the estimation of two kind of parameters:
—How likely a particular outcome is in each fuzzy cluster;
—For each individual: the vector of grades of membership
accounting for the degree of belongingness in fuzzy clusters.
— The number of fuzzy cluster was determined by a likelihood ratio
test which leads to 4 fuzzy clusters.
FCT Strategic Project UI 315
PEst-OE/EGE/UI031514
Empirical Findings
ItemCluster 1
(Low)
Cluster 2
(Medium)
Cluster 3
(High)
Cluster 4
(Very high)
a = 1 3.64 4.80 5.80 6.63
b = 2 2.97 4.12 5.03 5.69
c = 3 3.49 4.74 5.85 6.86
d = 4 3.85 5.17 6.00 7.00
e = 5 2.78 4.33 5.63 6.58
.... .... .... .... ....
s =19 2.26 4.04 4.75 5.91
FCT Strategic Project UI 315
PEst-OE/EGE/UI031515
Average Competencies in Fuzzy Clusters
Cluster 1
(Low)
Cluster 2
(Medium)
Cluster 3
(High)
Cluster 4
(Very high)
Average 3.28 4.74 5.78 6.74
Normalisation 0.38 0.62 0.80 0.96
FCT Strategic Project UI 315
PEst-OE/EGE/UI031516
Distribution of Individual Overall Competence
FCT Strategic Project UI 315
PEst-OE/EGE/UI031517
Comparing Countries by Competence
FCT Strategic Project UI 315
PEst-OE/EGE/UI031518
Duncan Post-hoc Analysis
Country N Group for α = 0.10
1 2 3 4 5 6 7 8 9
Japan 2148 .5448
France 1410
.6510
Finland 2313
.6727
Norway 1943
.6822
Estonia 815
.6853
Belgium 1201
.6880
Spain 3455
.6891 .6891
Netherlands 3003
.6958
Italy 2201
.7037
UK 1428
.7121
Czech 5896
.7137
Portugal 574
.7373
Germany 1453
.7419
Austria 1505
.7657
THANK YOU
Business Research Unit (UNIDE-IUL) / Instituto Universitário de Lisboa
Ed. ISCTE-IUL, Av. Forças Armadas
1649-026 Lisbon – Portugal
Phone: 210 464 019
E-mail: [email protected]
Internet: http://www.bru-unide.iscte.pt/