Chapter 8
Multivariate Analysis
Pranvera Lazo, Flora Qarri, Shaniko Allajbeu, Sonila Kane, Lirim Bekteshi,
Marina Frontasyeva, and Trajce Stafilov
The environment is a multidimensional system characterized by multiple chemical, physical and biological parameters which display very complex relationships
between them. A complex study in environmental researches that produce big data
matrixes with a large number of sampling sites and several investigated parameters
is not easy to give a solution to the raised environmental hypothesis, to discover the
structure and the properties of the data and to explain the factors affecting to the
structure of these data. Multivariate analysis is a strong tool widely used in environmental research for the exploration of the multidimensional data. The main goal of
multivariate analysis is determine the most important factors that affect to the state
of natural ecosystems. Correlation analysis of parametric (Pearson linear correlation) or non-parametric (Spearman rank correlation) datasets are useful statistical
tools to identify the relationship between pollutants, that leads to the identification
of the factors affecting the association of the chemical parameters and to understand the most probable phenomena and the sources of these parameters. In addition, factor analysis (FA) is used to explore the hidden multivariate structures of the
data (Reimann et al. 2002; Astel et al. 2008) and to clarify the link between the
elements with similar origins or similar associations on the data matrix. Each factor
was explained on the basis of the associations of the elements extracted from the
correlation matrix.
The correlation analysis (Spearman Rho and Pearson correlation, shown in the
Appendix, Tables A.1 and A.2) carried out to the concentration data of the elements,
could give an insight on the strength of the association between the variables
(elements). Similar values of Spearman Rho and Pearson correlations were found
to the pairs of elements which showed strong and significant Pearson correlation
coefficients (r2 > 0.4, P < 0.001). The differences founded to the weak correlation
coefficients did not affect the factor Analysis (FA) that was carried out to the original
concentration data since such weak correlations are neglected on FA process. The
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
P. Lazo et al., The Evaluation of Air Quality in Albania by Moss Biomonitoring and Metals
Atmospheric Deposition, SpringerBriefs in Environmental Science,
https://doi.org/10.1007/978-3-030-62355-5_8
89
Multivariate Analysis
Pranvera Lazo, Flora Qarri, Shaniko Allajbeu, Sonila Kane, Lirim Bekteshi,
Marina Frontasyeva, and Trajce Stafilov
The environment is a multidimensional system characterized by multiple chemical, physical and biological parameters which display very complex relationships
between them. A complex study in environmental researches that produce big data
matrixes with a large number of sampling sites and several investigated parameters
is not easy to give a solution to the raised environmental hypothesis, to discover the
structure and the properties of the data and to explain the factors affecting to the
structure of these data. Multivariate analysis is a strong tool widely used in environmental research for the exploration of the multidimensional data. The main goal of
multivariate analysis is determine the most important factors that affect to the state
of natural ecosystems. Correlation analysis of parametric (Pearson linear correlation) or non-parametric (Spearman rank correlation) datasets are useful statistical
tools to identify the relationship between pollutants, that leads to the identification
of the factors affecting the association of the chemical parameters and to understand the most probable phenomena and the sources of these parameters. In addition, factor analysis (FA) is used to explore the hidden multivariate structures of the
data (Reimann et al. 2002; Astel et al. 2008) and to clarify the link between the
elements with similar origins or similar associations on the data matrix. Each factor
was explained on the basis of the associations of the elements extracted from the
correlation matrix.
The correlation analysis (Spearman Rho and Pearson correlation, shown in the
Appendix, Tables A.1 and A.2) carried out to the concentration data of the elements,
could give an insight on the strength of the association between the variables
(elements). Similar values of Spearman Rho and Pearson correlations were found
to the pairs of elements which showed strong and significant Pearson correlation
coefficients (r2 > 0.4, P < 0.001). The differences founded to the weak correlation
coefficients did not affect the factor Analysis (FA) that was carried out to the original
concentration data since such weak correlations are neglected on FA process. The
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
P. Lazo et al., The Evaluation of Air Quality in Albania by Moss Biomonitoring and Metals
Atmospheric Deposition, SpringerBriefs in Environmental Science,
https://doi.org/10.1007/978-3-030-62355-5_8
89