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G. M. Oliveira et al.
Some variables’ raw data are already standardised in their database formats, as
is the case of variables expressed as “rate” such as “Infant mortality rate (2 IMR)”
or “Dropout rate (13 DR)”. For these situations, no standardization procedure was
applied. Descriptive statistics of all individual indicators I i,j in the period of observation are presented in Table 8 (Appendix).
2.2 WeGIx Model Construction and Validation
The normalization method adopted for WeGIx (Eq. 3) is of the type “Distance to a reference”. For each year of analysis, the reference value for every standardised variable
I i,j is the correspondent national mean value AV jP listed in Table 8 (Appendix).
Normalization by “Distance to a reference” method was used for all indicators:
NI i,j =
I i,j
AV j,P
; i ∈ [1, 308]; j ∈ [1, 42]
(3)
where:
I i,j
is the value of the standard individual indicator I j for the municipality i in a
certain year
AV jP is the value of the indicator I j for Portugal (mean value for the country) for a
determined year
NI i,j is the normalized value of the indicator I j for the municipality i.
With this normalisation procedure, for each of the forty-two individual indicators
NI Portugal,j = 1. For every municipality i, each NI i,j indicator is a relative value to the
national reference that is always one for each year of analysis.
Interaction between all the individual indicators NI i,j was statistically tested and
analysed, in order to build up a coherent composite model integrating just the necessary dimensions. Spearman correlation test was applied to verify the statistic dependence among normalised NI i,j indicators. For all comparative analyses, a confidence
level of 95% or 99% (α = 0.05; α = 0.01) was used. Data distribution was analysed
by Kolmogorov-Simirnov test but normality in data distribution was not verified.
Some of the indicators (such as 21 DEC) showed skewness distributions. Nevertheless, parametric tests were still applied, because the condition N > 30 was verified
for each group in analysis. Spearman correlation test reveals strong, moderate and
weak associations between the indicators. Correlations above 0.9 and significant at
0.01 level are presented in Table 2. Table 9 (Appendix) lists only the correlations
that can be consider moderate (> 0.5) and strong, all weak correlations were erased
for easier reading. WeGIx indicators without at least one moderate correlation were
also removed from Table 9.
The set of forty-two indicators chosen for the WeGIx model was tested using a
factor analysis of exploratory type. Wellbeing is a very complex issue; thus, this analysis had the purpose of knowing data structure and interaction. Kaiser Meyer-Olkin
G. M. Oliveira et al.
Some variables’ raw data are already standardised in their database formats, as
is the case of variables expressed as “rate” such as “Infant mortality rate (2 IMR)”
or “Dropout rate (13 DR)”. For these situations, no standardization procedure was
applied. Descriptive statistics of all individual indicators I i,j in the period of observation are presented in Table 8 (Appendix).
2.2 WeGIx Model Construction and Validation
The normalization method adopted for WeGIx (Eq. 3) is of the type “Distance to a reference”. For each year of analysis, the reference value for every standardised variable
I i,j is the correspondent national mean value AV jP listed in Table 8 (Appendix).
Normalization by “Distance to a reference” method was used for all indicators:
NI i,j =
I i,j
AV j,P
; i ∈ [1, 308]; j ∈ [1, 42]
(3)
where:
I i,j
is the value of the standard individual indicator I j for the municipality i in a
certain year
AV jP is the value of the indicator I j for Portugal (mean value for the country) for a
determined year
NI i,j is the normalized value of the indicator I j for the municipality i.
With this normalisation procedure, for each of the forty-two individual indicators
NI Portugal,j = 1. For every municipality i, each NI i,j indicator is a relative value to the
national reference that is always one for each year of analysis.
Interaction between all the individual indicators NI i,j was statistically tested and
analysed, in order to build up a coherent composite model integrating just the necessary dimensions. Spearman correlation test was applied to verify the statistic dependence among normalised NI i,j indicators. For all comparative analyses, a confidence
level of 95% or 99% (α = 0.05; α = 0.01) was used. Data distribution was analysed
by Kolmogorov-Simirnov test but normality in data distribution was not verified.
Some of the indicators (such as 21 DEC) showed skewness distributions. Nevertheless, parametric tests were still applied, because the condition N > 30 was verified
for each group in analysis. Spearman correlation test reveals strong, moderate and
weak associations between the indicators. Correlations above 0.9 and significant at
0.01 level are presented in Table 2. Table 9 (Appendix) lists only the correlations
that can be consider moderate (> 0.5) and strong, all weak correlations were erased
for easier reading. WeGIx indicators without at least one moderate correlation were
also removed from Table 9.
The set of forty-two indicators chosen for the WeGIx model was tested using a
factor analysis of exploratory type. Wellbeing is a very complex issue; thus, this analysis had the purpose of knowing data structure and interaction. Kaiser Meyer-Olkin