5. Compound indexes

The construction of composite indicators involves selection of various methods at different stages of development process [94]. Development of composite indicators is considered to be a unique approach for evaluating sustainable development. Composite indices can be constructed with or without weights depending on its application. Indices are very useful in focusing attention and often simplify the problem [95]. The selection of the appropriate methods depends on the data and the scope of the study. After aggregation of indicators, an index requires to be checked for robustness and sensitivity.

There is a critical need to develop indicators to assess the relative degree of sustainability of the production systems, especially those throughout the rural sector of the developing world [62]. This is important for the Natural Resource Management Systems (NRMS) in the peasant context, because despite being highly resilient, diverse and based on the use of renewable local natural resources, have been undervalued on the basis of criteria that focus on short-term economic benefits. Its complexity has been alluding to the tight interactions among the different activities related to natural resource management and their repercussion in the satisfaction of a multiplicity of economic, environmental, and social objectives [96, 97].

For constructing a composite index, policy goal has to be clearly defined [93]. When empirical analysis is used for selection, bivariate and multivariate statistical techniques can be employed. Bivariate analysis measures the correlation between all pairs of variables using correlation matrices, while multivariate analysis assesses the strength of any set of variables to measure any other variable, using discriminant, principal component, and factor analyses. The objective of these techniques is to determine the number of key variables that influence the composite index [98].

For performing the scaling for composite indexing purposes, Booysen [93] defined that the use of standard scores (z and t values) can be employed for composite indexing, it can be transformed in the form of ordinal response scales for surveys results, or it can be scaled on conventional linear scaling transformation method.

Weighting system and method employed in aggregating component scores plays a predominant role for development of composite index [93]. Multivariate techniques provide relatively better option for weight selection. Some of the key methods of aggregation employed are principal components analysis, factor analysis, distance to targets, expert's opinion (budget allocation), and analytic hierarchy process. Principal component analysis is one of the widely used multivariate analysis tools for weighting of components based on the proportion of variance. Once the weights have been assigned to each indicator and this is transformed into component score, these scores are aggregated into a composite score [93]. Sensitivity analysis along with proper validation should be done on composite indices [99]. Based on the validation results, indices need to be improved and adjusted. Validation is normally performed by using either item analysis or external validation [93]. There is always a requirement for demonstrating proper evidence through the reliable results while using composite index [100].

Using composite indices does not solve the problem, as there are controversies for defining the weight attached to each indicator. Methodological frameworks are needed for the selection of appropriate indicators and in the integration and transformation of the information to set the basis for the design of more sustainable alternatives. Conway [101] and Garcia [102] suggested that for an interdisciplinary analysis it has to produce insights that significantly transcend those of the individual participating disciplines. Systems theory holds that certain principles stand for all systems regardless of its hierarchical level [101, 103]. Identifying a set of central systemic attributes (or properties) that holds across disciplines or scales is therefore fundamental to keep the evaluation of sustainability and the derivation of indicators theoretically consistent.

The development of evaluation frameworks and indicators that make explicit the environmental, economic, social, and cultural advantages and disadvantages of the different NRMS let to improve not only the system's productivity or profitability but also the stability, resilience, reliability of resources management, adaptability, equity, and self-reliance [62].

To provide useful indicators based on benchmarking, trend analysis, and decoupling, Kovanda and Hak [104] developed Material Flow Analysis (MFA), and other attempts to conceptualize sustainable resource management were developed based on the idea of 'carrying capacity' [105] to express the idea of biophysical limit to use of resources. Wackernagel and Rees [106] developed the Ecological Footprint (EF) indicator based on the amount of biologically productive land and water area required to support a population at its current level of consumption. EF is used to estimate environmental sustainability at national and global level. And the Eco-Index Methodology [107] measures the impact of different products, services, and lifestyles. It takes care of entire life cycle data for assessing the EF conversion factors for most of the key components. The ecological footprint (as measured using global average yields) is normalized by the application of equivalence factors. Table 1 presents some of the environmental indices developed through the time.


Table 1. Some environmental indices used.

temporal scales. The farmers validate the tool by evaluating their own results. Through this validation, reference values will need to be established as farmers adopt new practices [59].

The construction of composite indicators involves selection of various methods at different stages of development process [94]. Development of composite indicators is considered to be a unique approach for evaluating sustainable development. Composite indices can be constructed with or without weights depending on its application. Indices are very useful in focusing attention and often simplify the problem [95]. The selection of the appropriate methods depends on the data and the scope of the study. After aggregation of indicators, an index requires to be checked for

There is a critical need to develop indicators to assess the relative degree of sustainability of the production systems, especially those throughout the rural sector of the developing world [62]. This is important for the Natural Resource Management Systems (NRMS) in the peasant context, because despite being highly resilient, diverse and based on the use of renewable local natural resources, have been undervalued on the basis of criteria that focus on short-term economic benefits. Its complexity has been alluding to the tight interactions among the different activities related to natural resource management and their repercussion in the satisfaction

For constructing a composite index, policy goal has to be clearly defined [93]. When empirical analysis is used for selection, bivariate and multivariate statistical techniques can be employed. Bivariate analysis measures the correlation between all pairs of variables using correlation matrices, while multivariate analysis assesses the strength of any set of variables to measure any other variable, using discriminant, principal component, and factor analyses. The objective of these techniques is to determine the number of key variables that influence the composite

For performing the scaling for composite indexing purposes, Booysen [93] defined that the use of standard scores (z and t values) can be employed for composite indexing, it can be transformed in the form of ordinal response scales for surveys results, or it can be scaled on

Weighting system and method employed in aggregating component scores plays a predominant role for development of composite index [93]. Multivariate techniques provide relatively better option for weight selection. Some of the key methods of aggregation employed are principal components analysis, factor analysis, distance to targets, expert's opinion (budget allocation), and analytic hierarchy process. Principal component analysis is one of the widely used multivariate analysis tools for weighting of components based on the proportion of variance. Once the weights have been assigned to each indicator and this is transformed into component score, these scores are aggregated into a composite score [93]. Sensitivity analysis along with proper validation should be done on composite indices [99]. Based on the validation results, indices need to be improved and adjusted. Validation is normally performed by using either item

of a multiplicity of economic, environmental, and social objectives [96, 97].

conventional linear scaling transformation method.

5. Compound indexes

40 Sustainability Assessment and Reporting

robustness and sensitivity.

index [98].

Rockstrom et al. [113] have introduced the concept of planetary boundaries. It is based on the knowledge that the Earth's subsystems react in a nonlinear way and often are particularly sensitive around the threshold levels of variables such as CO2 concentration. The authors identified nine processes and thresholds associated to an unacceptable environmental change: climate change, rate of biodiversity loss (terrestrial and marine), interference with the nitrogen and phosphorus cycles, stratospheric ozone depletion, ocean acidification, global freshwater use, change in land use, chemical pollution, and atmospheric aerosol loading.

The degree of complexity with which each indicator is obtained, for example through field measurements, mathematical models, and simulation models, also presents drawbacks in the comparison between systems evaluated by different methodologies. Many of the mentioned indicators lack the capacity to predict the state and the variation of the human system with the natural system, having to be looked at together with other indicators to obtain those properties, complicating the understanding of the results [114].
