Transitioning Regional Economies

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 correlations^a,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

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 correlations^a,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 correlations^a,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 correlations^a,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 correlations^a,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 correlations^a,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

Source: Productivity Commission estimates.