Abstract
This study quantifies and analyses quality of life in the Gauteng City-Region of South Africa. First we adapt and extend a method used in research on market regulations to construct composite indices to the field of quality of life. In the adapted method we employ categorical principal components analysis suitable for the analysis of categorical data typically used in quality of life research. The newly constructed index is a comprehensive quality of life index, which includes objective and subjective as well as economic and non-economic indicators. This is the first composite index of its kind in South Africa. Second, this index is used to compare the quality of life of different demographic and socio-economic groups in the region. The quality of life scores of Africans, low income, female, older and urban informal dwellers are relatively low. Third, the explained variance of the dimensions of quality of life is compared across groups. The dimensions ‘housing and infrastructure’ and ‘social relationships’ explained the most variance for groups with lower and higher quality of life scores respectively. The results shed light on quality of life in this region, including the great unevenness of well-being. The study provides a basis for the measurement and analysis of quality of life in other regions and countries.
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Notes
The narrow unemployment rate of the GCR (OECD 2011).
See OECD (2008) for a discussion of different weighting methods.
See Tabachnick and Fidell (2007) for a comprehensive explanation of PCA.
Using CATPCA, categorical indicators are transformed by assigning optimal scale values to the categories, thus transforming categorical indicators to numeric-valued indicators referred to as category quantifications. CATPCA, given the number of extracted components, finds optimal category quantifications, implying that the overall variance accounted for in the transformed indicators are maximised (Linting et al 2007). The category quantifications for an indicator together form that indicator’s transformation. In the optimal scaling process, the initial information provided by the categorical data is retained in the category quantifications. However the degree to which the original data is retained depends on the optimal scaling level (nominal, ordinal or numeric) selected for each indicator (Linting et al. 2007). The transformed indicators have metric properties which allow the researcher to use all standard methods normally applied to continuous indicators.
In mathematical terms the aggregation of the intermediate composite indices to derive at the composite index of quality of life (CIQoL) is as follows: \({\text{CIQoL}}_{\text{i}} = \left( {\sum\nolimits_{i = 1}^{n} {(ICI_{i} w_{i} )} } \right) \times 100\) where CIQoL is the composite index of quality of life, ICI i = Intermediate Composite Index (i = 1 … n), and w i is the weight of the ith ICI determined by the explained variance of the intermediate composite index (extracted component) in the dataset.
We derived the percentage by dividing the life satisfaction score of each respondent by the maximum life satisfaction score (5) and multiplying by 100.
To calculate eta squared when using ANOVA we used the formula
\(Eta\;squared = \frac{sum\;of\;squares\;between\;groups}{Total\;sum\;of\;squares}\), and when using t tests we used the formula
\(Eta\;squared = \frac{{t^{2} }}{{t^{2 + (N1 + N2 - 2)} }}\) (for more information on the calculation of effect sizes see Pallant 2007).
The Kish grid is commonly used in selecting cases at random when more than one case is eligible for inclusion when the interviewer calls at a sampled address or household.
No information is available in the dataset as to whether respondents were in the originally selected households or in substituted households.
Due to a field sampling error, some municipalities were over-sampled and a few were under-sampled. Therefore the data was weighted in accordance to the Census 2001 (Stats SA 2002) population data.
The income figure includes salaries, grants, pensions and any other source of income. Household income was used in the analysis as neither individual income nor a continuous income indicator were available in the survey. An individual income measure was calculated, converting bracket midpoints to a per capita measure. This was found to be highly correlated with the household income measure. The estimated per capita measure was also used in the analysis as a robustness check, and the results were highly consistent with those from the household measure, which was preferred. R1 is approximately US$0.9 (March 2014).
Amount of variance in the indicator explained by the component.
Seven was the total number of dimensions of quality of life used to guide the selection of the indicators (see the list of dimensions in Sect. 4).
The Kaiser rule, known as the Kaiser’s criterion or the eigenvalue rule is related to the eigenvalue of each principal component. The eigenvalue (variance) for each principal component indicates the percentage of variation explained in the data. Using this rule, components with an eigenvalue of 1.0 or more are extracted.
32 % was derived by dividing 19.43 % of the variance explained by the first extracted component by 60 %, which is the sum of the variances of each of the five extracted components (19.43 + 13.13 + 10.01 + 9.81 + 7.48) (see Table 3).
For reasons of space, Table 5 only shows racial groups. For the other group categories, similar tables are not shown, but relevant results are noted in the text; the additional tables are available from the authors on request.
Employed is defined as a person who has worked in the last seven days before the interview.
See Table 1.
The tolerance value of all the variables were >0.1 and the Variance Inflation Factor (VIF) of all the variables were <2. On inspection of the correlation matrix no signs of multicollinearity were found.
Results from the SAARF development index (2011) also noted the importance of the ‘socio-economic status’ dimension in improving South Africans’ well-being and highlighted the need for higher levels of employment.
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Acknowledgments
We thank the Gauteng City-Region Observatory (GCRO) for access to the GCRO Quality of Life Survey data set and financial support. We also thank Economic Research Southern Africa (ERSA) for their financial support.
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Appendices
Appendix 1: Recoding of Nominal Indicators
The recoding of the nominal indicators was based on the guidelines provided in the Reconstruction and Development Programme (1996). This policy was developed by the first democratic government to address South Africa’s development challenges. It set out guideline standards for service delivery, which are used here (See Tables 7, 8).
Appendix 2
See Table 9.
Appendix 3
See Table 10.
Appendix 4
Comparison of the newly created Quality of Life Score, the Life satisfaction Index and the Quality of Life Score (Equal weighting) and the Quality of Life Sumscore. Source: Authors’ calculations using GCRO data (GCRO 2009). Note: (1) Scores are shown as a percentage, with 100 % the maximum possible score. (2) Asians are excluded from the analysis due to their small number in the dataset, in order to ensure statistical robustness of the analysis
Appendix 5: Regression Results
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Greyling, T., Tregenna, F. Construction and Analysis of a Composite Quality of Life Index for a Region of South Africa. Soc Indic Res 131, 887–930 (2017). https://doi.org/10.1007/s11205-016-1294-5
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DOI: https://doi.org/10.1007/s11205-016-1294-5