AD ALTA
JOURNAL OF INTERDISCIPLINARY RESEARCH
We selected 15 restaurants for our research. The selection was
made based on local inhabitant recommendations and according
to TripAdvisor rating.
For the evaluation of the results, Statistica 13 EN Program was
used. Further, we used the analysis method (also
Correspondence analysis - CA), mathematical, and statistical
methods. Using the graphic tools of this CA, it is possible to
describe an association of nominal or ordinal variables and to
obtain a graphic representation of a relationship in
multidimensional space – for the readers; it is easier to
understand. The analysis provides further evidence that
dependencies exist between variables. Correspondence analysis
(CA) is a multivariate statistical technique. It is conceptually
similar to principal component analysis but applies to
categorical rather than continuous data. In a similar manner to
principal component analysis, it provides a means of displaying
or summarizing a set of data in a two-dimensional graphical
form (Zámková & Prokop, 2014).
All data should be non-negative and on the same scale for CA
to be applicable, and the method treats rows and columns
equivalently. It is traditionally applied to contingency tables -
CA decomposes the chi-squared statistic associated with this
table into orthogonal factors. The distance between single
points is defined as a chi-squared distance. The distance
between the i-th and i’-th row is given by the formula
()
(
)
∑
=
−
=
c
j
j
j
i
ij
c
r
r
i
i
D
1
2
´
´
,
(1)
where r
ij
are the elements of row profiles matrix R and weights
c
j
correspond to the elements of column loadings vector c
T
,
which is equal to the mean column profile (centroid) of the
column profiles in multidimensional space. The distance
between columns j and j‘ is defined similarly, weights
correspond to the elements of the row loadings vector r and
sum over all rows. In correspondence analysis we observe the
relation between single categories of two categorical variables.
The result of this analysis is the correspondence map
introducing the axes of the reduced coordinates system, where
single categories of both variables are displayed in graphic
form. The aim of this analysis is to reduce the multidimensional
space of row and column profiles and to save as far as possible
original data information. Each row and column of the
correspondence table can be displayed in c-dimensional (r-
dimensional respectively) space with coordinates equal to the
values of the corresponding profiles. The row and column
coordinates on each axis are scaled to have inertias equal to the
principal inertia along that axis: these are the principal row and
column coordinates (Hebák et al., 2007).
For the correspondence analysis model, the degree of
dispersion of points is defined, i.e., row and column categories,
the so-called total inertia. The term inertia comes from
mechanics, where it is defined as the sum of the product of
mass and square distances from the centroid of all the object’s
particles. Geometrically, inertia expresses the degree of
dispersion of points in multidimensional space and it can be
understood as an analogy to the dispersion known from
statistical modeling. In the correspondence analysis, the total
inertia (I) is equal to the weighted average (with weights
)
chi-square of the distance of the row profiles from their
average/mean (vector )
(2)
the same as the weighted average (with weights
) chi-
square of the distance of the column profiles from their average
(vector )
(3)
A significant part of the total inertia of the original table is
usually explained by the first several axes. That is why it is
generally sufficient for the result of the correspondence analysis
to be represented in the space of the first two or three ordinal
axes. Total inertia equals the sum of all eigenvalues of the
matrix. Therefore, it is possible to specify how many ordinal
axes it is reasonable to interpret. This can be decided in either
of two ways: (1) we set the threshold value (e.g., 80%) and
determine how many axes have the cumulative inertia higher
than the set threshold value, (2) we interpret the ordinal axes
whose eigenvalue is above-average, i.e., higher than the
average of all eigenvalues.
The contributions of the row points to the inertia in the
corresponding dimension are defined by the quotient
(4)
where
corresponds with the elements of the matrix (the
score of the -th row category in the -th dimension),
elements of the row loadings vector and
is inertia
expressed by the -th dimension (an eigenvalue of the matrix).
A contribution of the row points to inertia expresses the relative
degree of the effect of the given category on the final
orientation of the main axes. In a similar fashion, the
contributions of column points to inertia are expressed in the
corresponding dimension
(5)
For each row category, we can calculate the total row inertia,
defined as
(6)
Similarly, for column categories, the total column inertia is
defined as
(7)
The values of inertia for individual columns and rows give us
an indication of the significance of the various categories on the
resulting ordination.
4 Results and Discussion
Portugal is a country located mostly on the Iberian Peninsula in
southwestern Europe. The border on the west and south is the
Atlantic Ocean, on the north and east Spain.
The direct contribution of Travel & Tourism to GDP in 2017
was EUR 13.2bn (6.8% of GDP). It primarily reflects the
economic activity generated by industries such as hotels, travel
agents, airlines and other passenger transportation. The direct
contribution of Travel & Tourism to GDP is expected to grow
by 2.6% pa to EUR 18.0bn (8.2% of GDP) by 2028 (WTTC,
2019).
Travel & Tourism generated 401,500 jobs directly in 2017
(8.5% of total employment). It also includes, for example, the
activities of the restaurant and leisure industries directly
supported by tourists. By 2028, Travel & Tourism will account
for 493,000 jobs directly, an increase of 1,6% pa over the next
ten years (WTTC, 2019).
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