Transitioning Regional Economies



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107.E.3 Principal component analysis results

108.Single PCA approach


Table E.8 displays PCA results under the single PCA approach. The correlations between indicators and principal components are presented in the table, as well as the cumulative proportions of total variance captured by the principal components, and eigenvalues. These results were used to determine the number of principal components to retain, according to the criteria set out in section E.1. Retained components are presented in bold font within the tables.

Five principal components were retained according to two main criteria: the cumulative proportion of variance explained being greater than 0.7, and interpretability. Under the eigenvalueone criterion, seven principal components would have been retained, but the extra two principal components only explained an additional 6 per cent of the total variation, and did not have a strong interpretation.

The five retained principal components do not exactly correspond to the five types of capital in the literature. Many principal components are correlated with factors from multiple capital groupings.

The first principal component (which captures 27 per cent of the total variation) is most strongly correlated with factors relating to socioeconomic status, health and infrastructure.

The second principal component is correlated with factors relating to remoteness, Indigenous population, wealth and community strengths.

The third principal component is correlated with employment, agriculture, volunteering and industry concentration.

The fourth principal component is correlated with skills and providing support.

The fifth principal component is correlated with national parks and nature reserves.

Some individual principal components have strong correlations with indicators in the opposite direction to that expected for adaptive capacity. For example, although the first principal component is positively correlated with factors such as skills and education, it is negatively correlated with agriculture, which is also proposed to be a positive influence on adaptive capacity. The fourth principal component is negatively correlated with mining, which might be interpreted as capturing the challenges faced by regions with high mining employment when there is a disruption to the mining sector.

As described in section E.1, the index was created through a weighted sum of the retained principal components. Therefore, an individual indicator’s total contribution to the index depends on its weight across each retained principal component, and the relative amount of variance explained by each retained principal component. The weights of each indicator to the final index are presented in table E.9. The indicators with the largest weights are largely factors associated with socioeconomic status and have the expected signs. Although the sign of the weights on a few indicators (such as mining) are in the opposite direction to expected, they have smaller contributions to the overall index. Nevertheless, this may have a large impact on those regions that have high employment in mining.



The weights on each indicator were aggregated by capital type to provide an indication of the contribution of a type of capital to the adaptive capacity index (table E.10). Human capital indicators represent over half of the index, which partly reflects the large number of human capital variables included. Social and financial capital variables make the second largest contributions, followed by physical, natural and other variables.


Table E.8 Single PCA — PCA correlationsa,b,c




PC1

PC2

PC3

PC4

PC5

PC6

Correlations



















yr12plus

0.90

0.34

0.01

0.05

0.02

0.04

youtheng

0.48

0.79

0.20

0.02

0.15

0.10

skill1to3

0.59

0.26

0.12

0.59

0.16

0.01

emptolf

0.32

0.43

0.65

0.02

0.05

0.14

participation

0.64

0.17

0.59

0.29

0.17

0.12

ltnewstart

0.79

0.28

0.41

0.06

0.15

0.06

wkage

0.60

0.70

0.11

0.05

0.14

0.08

indig

0.33

0.83

0.11

0.03

0.06

0.03

patents

0.48

0.54

0.12

0.09

0.03

0.01

trademarks

0.56

0.63

0.13

0.07

0.12

0.14

bsnsentryrate

0.71

0.34

0.45

0.00

0.02

0.10

bsnsexitrate

0.74

0.26

0.29

0.32

0.03

0.15

dsp

0.77

0.23

0.41

0.06

0.11

0.27

selfhealth

0.65

0.11

0.26

0.42

0.16

0.18

psychdistress

0.27

0.31

0.17

0.22

0.38

0.41

comprisk

0.71

0.25

0.15

0.05

0.33

0.07

highinc

0.73

0.59

0.23

0.00

0.05

0.08

invinc

0.18

0.67

0.36

0.29

0.27

0.30

govtpyts

0.75

0.41

0.42

0.01

0.12

0.10

propprice

0.71

0.19

0.49

0.15

0.16

0.09

ownhome

0.26

0.88

0.01

0.04

0.08

0.04

housingstress

0.07

0.71

0.57

0.23

0.05

0.18

remoteness

0.31

0.81

0.32

0.04

0.05

0.05

internet

0.86

0.37

0.01

0.19

0.03

0.03

buildappvalpp

0.61

0.51

0.04

0.12

0.06

0.14

accesstransport

0.00

0.63

0.06

0.18

0.45

0.17

agind

0.66

0.11

0.63

0.16

0.04

0.11

miningind

0.02

0.37

0.26

0.62

0.08

0.33

nature

0.20

0.22

0.07

0.05

0.77

0.03

volunt

0.40

0.48

0.68

0.15

0.04

0.10

getsupport

0.03

0.23

0.44

0.10

0.45

0.37

providesupport

0.20

0.25

0.17

0.66

0.08

0.13

safeatnight

0.18

0.68

0.33

0.08

0.09

0.31

discriminated

0.01

0.76

0.23

0.10

0.33

0.34

culturalacceptance

0.59

0.13

0.30

0.35

0.00

0.42

homeless

0.05

0.86

0.29

0.24

0.02

0.07

herfinneg

0.16

0.39

0.69

0.12

0.07

0.04

wkagechange

0.57

0.32

0.40

0.15

0.04

0.24

interflows

0.01

0.19

0.31

0.37

0.36

0.32

Cumulative proportion

0.27

0.52

0.64

0.70

0.75

0.79

Eigenvalues

10.49

9.73

4.86

2.30

1.84

1.42




a Bold font indicates the principal components (PCs) that were retained and the indicators with the highest correlations with these components. b For brevity, only the first six PCs are displayed. c The signs of retained PCs were reversed where appropriate so that a higher value indicates greater adaptive capacity.

Source: Productivity Commission estimates.









Table E.9 Single PCA — weights of indicators in index

Ordered from largest to smallest in absolute value

Indicator

Weight in index




Indicator

Weight in index

invinc

0.116




propprice

0.047

selfhealth

0.089




remoteness

0.046

indig

0.088




wkagechange

0.043

emptolf

0.086




miningind

0.041

youtheng

0.085




govtpyts

0.041

ltnewstart

0.082




culturalacceptance

0.034

yr12plus

0.079




accesstransport

0.027

getsupport

0.078




highinc

0.021

skill1to3

0.078




agind

0.013

nature

0.070




herfinneg

0.013

patents

0.067




wkage

0.012

trademarks

0.066




interflows

0.008

internet

0.065




discriminated

0.007

safeatnight

0.064




bsnsexitrate

0.007

comprisk

0.064




bsnsentryrate

0.003

volunt

0.062




buildappvalpp

0.003

homeless

0.061




psychdistress

0.002

participation

0.060




housingstress

0.002

dsp

0.051




providesupport

0.002

ownhome

0.048













Source: Productivity Commission estimates.









Table E.10 Single PCA — contributions of each capital domain

Ordered from largest to smallest contribution

Capital domain

Contribution to index (%)

Human

50.30

Social

16.83

Financial

14.98

Physical

7.69

Natural

6.73

Other

3.47




Source: Productivity Commission estimates.






For the presentation of results, regions were grouped into four categories according to their index value. Regions in the most adaptive category (10 regions) and the least adaptive category (13 regions) had index values greater than one standard deviation away from the mean. The remaining regions were classed into above average (27 regions) and below average (27 regions) categories. A map of regions by their adaptive capacity category is presented in figure E.4. The results are discussed in section E.5.


Figure E.4 Single PCA — relative adaptive capacity of FERs, 2016

this figure shows a map of the adaptive capacity of australia’s regions, as per the commission’s index using the single pca approach. regions are coloured according to their adaptive capacity category. further information can be found in the text surrounding the figure.



Source: Productivity Commission estimates.





109.Nested PCA approach


As described in section E.1, under the nested PCA approach, separate PCAs for human, financial, physical, natural and social capital indicators were first conducted. Indicators were then removed if they had a correlation of less than 50 per cent with the first principal component within their capital domain. This led to the removal of a total of nine indicators, representing the workingage population, Indigenous population, psychological distress, investment incomes, property prices, building approvals, mining, providing support and cultural acceptance.
PCA was performed again for each capital domain with the reduced set of indicators, with the results presented in tables E.11 to E.15. Across the capital domains, cumulative proportions of variance explained by the first principal components range from 47 per cent (for human capital) to 71 per cent (for financial capital). Although only the first financial capital component meets the 70 per cent threshold of variance explained, the indicators in each PCA all have correlations greater than 50 per cent with their respective first principal components. The first principal component from each PCA was retained, and can be interpreted as representing indexes of each capital type. (For example, the first principal component in the human capital PCA can be interpreted as a human capital index.)

It is noted that the removal of some indicators under this approach means that some factors that are thought to be important, have large weights in the single PCA approach or are highly correlated with the second principal component in the initial capital domain PCAs (such as investment incomes, property prices and mining) are not captured in the index.




Table E.11 Nested PCA — human capital PCA correlationsa,b,c




PC1

PC2

PC3

PC4

PC5

Correlations
















yr12plus

0.93

0.03

0.23

0.03

0.07

youtheng

0.67

0.64

0.21

0.01

0.07

skill1to3

0.55

0.48

0.17

0.52

0.22

emptolf

0.56

0.62

0.32

0.06

0.27

participation

0.78

0.30

0.39

0.28

0.09

ltnewstart

0.89

0.21

0.16

0.14

0.08

patents

0.58

0.23

0.53

0.38

0.16

trademarks

0.66

0.33

0.50

0.08

0.00

bsnsentryrate

0.50

0.68

0.35

0.20

0.08

bsnsexitrate

0.57

0.53

0.28

0.46

0.02

dsp

0.76

0.24

0.42

0.14

0.27

selfhealth

0.67

0.25

0.31

0.49

0.25

comprisk

0.66

0.49

0.10

0.00

0.39

Cumulative proportion

0.47

0.66

0.77

0.85

0.88

Eigenvalue

6.13

2.42

1.43

1.03

0.47




a Bold font indicates the principal components (PCs) that were retained and the indicators with the highest correlations with these components. b For brevity, only the first five PCs are displayed. c The signs of retained PCs were reversed where appropriate so that a higher value indicates greater adaptive capacity.

Source: Productivity Commission estimates.









Table E.12 Nested PCA — financial capital PCA correlationsa,b




PC1

PC2

PC3

PC4

Correlations













highinc

0.94

0.30

0.02

0.17

govtpyts

0.89

0.38

0.21

0.15

ownhome

0.83

0.21

0.52

0.05

housingstress

0.71

0.63

0.31

0.01

Cumulative proportion

0.71

0.88

0.99

1.00

Eigenvalue

2.86

0.68

0.41

0.05




a Bold font indicates the principal components (PCs) that were retained and the indicators with the highest correlations with these components. b The signs of retained PCs were reversed where appropriate so that a higher value indicates greater adaptive capacity.

Source: Productivity Commission estimates.









Table E.13 Nested PCA — physical capital PCA correlationsa,b




PC1

PC2

PC3

Correlations










remoteness

0.88

0.05

0.47

internet

0.77

0.55

0.31

accesstransport

0.73

0.65

0.23

Cumulative proportion

0.63

0.88

1.00

Eigenvalue

1.90

0.73

0.37




a Bold font indicates the principal components (PCs) that were retained and the indicators with the highest correlations with these components. b The signs of retained PCs were reversed where appropriate so that a higher value indicates greater adaptive capacity.

Source: Productivity Commission estimates.









Table E.14 Nested PCA — natural capital PCA correlationsa,b




PC1

PC2

Correlations







agind

0.76

0.65

nature

0.76

0.65

Cumulative proportion

0.57

1.00

Eigenvalue

1.14

0.86




a Bold font indicates the principal components (PCs) that were retained and the indicators with the highest correlations with these components. b The signs of retained PCs were reversed where appropriate so that a higher value indicates greater adaptive capacity.

Source: Productivity Commission estimates.









Table E.15 Nested PCA — social capital PCA correlationsa,b,c




PC1

PC2

PC3

PC4

Correlations













volunt

0.72

0.45

0.42

0.31

getsupport

0.55

0.58

0.60

0.01

safeatnight

0.88

0.02

0.13

0.40

discriminated

0.63

0.66

0.28

0.24

homeless

0.88

0.24

0.11

0.02

Cumulative proportion

0.55

0.76

0.89

0.95

Eigenvalue

2.76

1.03

0.65

0.31




a Bold font indicates the principal components (PCs) that were retained and the indicators with the highest correlations with these components. b For brevity, only the first four PCs are displayed. c The signs of retained PCs were reversed where appropriate so that a higher value indicates greater adaptive capacity.

Source: Productivity Commission estimates.






Each capital domain index and the ‘other’ domain were combined through an equally weighted sum to form the index of adaptive capacity. The weights of each individual indicator to the nested PCA index are presented in table E.16. As expected from this method, capital domains that have few indicators get disproportionately large weights in the index. The natural capital indicators (the domain with the fewest indicators) have the largest weights in the index, while the human capital indicators (the domain with the most indicators) have the smallest weights.


Table E.16 Nested PCA — weights of indicators in index

Ordered from largest to smallest in absolute value

Indicator

Weight in index




Indicator

Weight in index

agind

0.110




discriminated

0.038

nature

0.110




getsupport

0.033

remoteness

0.077




yr12plus

0.025

internet

0.068




ltnewstart

0.024

accesstransport

0.064




participation

0.021

herfinneg

0.056




dsp

0.021

wkagechange

0.056




youtheng

0.018

interflows

0.056




selfhealth

0.018

highinc

0.055




trademarks

0.018

safeatnight

0.053




comprisk

0.018

homeless

0.053




patents

0.016

govtpyts

0.052




bsnsexitrate

0.016

ownhome

0.048




emptolf

0.015

volunt

0.043




skill1to3

0.015

housingstress

0.042




bsnsentryrate

0.014




Source: Productivity Commission estimates.






The total contribution of human capital in the nested PCA index is much lower than in the single PCA index (17 per cent compared with 50 per cent). The total contribution of social and financial capital are about the same, while the contributions of all other capital domains are larger due to the equal weighting of domains with few indicators.

Like the index formed from the single PCA, regions were grouped into four categories according to their index value — most adaptive (11 regions), above average (31), below average (21) and least adaptive (14). A map of regions by their adaptive capacity category under the nested PCA approach can be found in figure E.5.




Figure E.5 Nested PCA — relative adaptive capacity of FERs, 2016

this figure shows a map of the adaptive capacity of australia’s regions, as per the commission’s index using the nested pca approach. regions are coloured according to their adaptive capacity category. further information can be found in the text surrounding the figure.



Source: Productivity Commission estimates.







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