Watershed Level Sustainable Development Index in Rondônia, Western Amazon: Index Construction from Factor Analysis

Objective: to build a sustainable development index for the river basins of Rondônia, using factor analysis as an analytical model. Method: factor analysis was used as a tool for building environmental, economic, social and institutional performance indices. The adapted FECAM classification scale was adopted to express the results achieved by each river basin. Results: The set of current sustainable performance indices for the Mamoré River watersheds (0.444) was considered a low index, although the best compared to other basins; the Madeira River (0.419, low index); the Guaporé River (0.378, low index); the Machado River (0.289, low index); the Jamari River (0.307, low index) and the Roosevelt River (0.227, low index). There has been a really insignificant improvement in the rates from 10 years ago. Conclusions: the factor analysis showed efficiency as a multivariate statistical method in the construction of sustainable development indices for the river basins of Rondônia. The management of watersheds is still very ineffective, despite being regulated by state law. It is highly recommended to institutionalize regional public policies in the form of a Master Plan for the Rondônia Watershed.


Watershed Level Sustainable Development Index in Rondônia, Western Amazon: Index Construction from Factor Analysis
to the exploitation of natural resources, technological development and institutional structure are considered.
On the other hand, qualitative aspects related to equity, resource use and environmental damage are considered.
In this sense, the author emphasizes that development must be focused on overcoming social deficiencies, basic needs and changes in living standards considered unsustainable, in order to conserve basic resources, especially agricultural, energy, minerals, air and water [19].
In this sense, Lustosa [22] describes sustainable development as the combination of "economic growth, quality of life, environmental protection, equity in income distribution, democracy, citizen participation and appreciation of culture"; in short, it is development that encompasses political, social, economic and cultural aspects. In this way, there is an interrelationship between environmental protection and economic development.
Therefore, the principle of sustainability is not limited to economic and ecological issues, it is about a balance between all the elements that make up the environment, whether natural, artificial or cultural [22]; [23]; [24].
The concept of sustainable development, despite being treated as a world reference, serving as the basis for several international conferences, is a "term much criticized and fought by researchers from different areas" [25]. This is a contradictory concept, since its defenders emphasize the need to impose limits on the use of natural resources, while at the same time emphasizing advances in economic growth. In this way, the Brundtland Report is criticized, for not giving any direction to the concept, as it does not defend the position of ecologists or defenders of the inalterability of production and consumption models, which characterizes, for the author, duality, which under the appearance of an environmental preservation policy hides questionable practices, seeking to control new business opportunities.
Corroborating, Carvalho et al., [26] from their studies, denote that in addition to bringing a new perception of the environmental crisis, the concept of sustainable development ended up generating a series of questions regarding its understanding, which creates difficulties for the operationalization of the same. Although there is resistance to adopting sustainable development as an alternative model of development, and there is no consensual definition among researchers [27], the fusion between environmental risk and social insecurity is evident, making it clear that environmental issues go far beyond mere questions, of the utilitarian market reason [28]. In the view of Grubba and Hamel [29], to establish sustainable development, it is necessary to take into account the complexity of the environment and integrate it as part of this process. Faced with an anthropocentric notion, it can be said that "ecological effects have repercussions on human life, in its conservation, reproduction and evolution". In this way, the authors affirm that there cannot be a development that is not sustainable. Based on this logic, Lacerda and Cândido [30] point out that, in practice, sustainable development is a great challenge for society, as it requires a holistic, systemic and interdisciplinary vision regarding the rational use of natural and built environments, in order to integrate local communities in the elaboration of strategies and plans. In summary, Melo Neto and Ribeiro [31] state that all development takes place at the local level, since this is the space for negotiations, conflict resolutions and initiatives. From this point on, community involvement in local projects results in transformations that possibly imply the creation of a sustainable environment.  (UN, 2017). In these meetings, alternatives are discussed to reduce consumerism, use natural resources rationally and minimize environmental damage, with the aim of promoting a better quality of life for populations [32]. The principles of sustainable development are based on Agenda 21, a document approved by more than 180 countries during the United Nations Conference on Environment and Development, held in Rio de Janeiro in 1992 (RIO 92). The ideas contained in the document were assimilated by the organizations of the United Nations system and several international organizations [33]. Brazil and other countries in Latin America, as well as in the Caribbean, only started the changes towards sustainable development, 20 years after Rio-92 [34]. For the authors, much remains to be done to confront the multiple challenges of the future for the consolidation of this process. The realization of Rio-92 turned the Amazon into a target of public policies and international collaborations, such as the creation of protected areas, demarcation of indigenous lands and expansion of reserves [35]. For Sawyer, policies were a way of separating society and nature, except in the case of indigenous lands and extractive areas. The author states that although protected areas can prevent the extinction of endangered species, they are not enough to maintain ecological functions that require a wider space, since environmental sustainability is not limited to ecological corridors or isolated points, it depends on the entire territory, including human presence. Based on this understanding, Abramovay [36] concludes that the most important element in a sustainable development strategy in the Amazon is the systematic application of science and technology for the sustainable use and exploitation of its biodiversity, which presupposes business and political activities, very much different from those prevailing today.
Copetti and Lottermann [37] state that environmental inequalities regarding protection and access to natural resources demonstrate that the central point is not the promotion of nature's sustainability, but the way in which society appropriates and makes use of these resources, the that highlights and relates social inequalities with environmental ones. Thus, the authors emphasize that poverty and inequalities trigger environmental crises. In this sense, sustainable development happens as long as human needs are met, increasing the productive potential and equality among all, since poverty limits individuals, making it impossible to use the environment sustainably, which ends up increasing the pressure on it [38]. Currently, the values linked to sustainable development and respect for environmental policies have been institutionalized to a greater or lesser extent, worldwide, through the media, social and environmental movements, as well as through governments [39]. This development will be achieved through the creation and implementation of public policies that ensure an increase in national income, access to basic services (health, education and economy) and the reduction of environmental impacts arising from production and consumption systems [40].
Corroborating this understanding, Custodio and Vieira [24]  place, the population must have the right to intervene in the processes of activities that may cause some environmental damage. Given the above, even if there is no consensus on the concept of sustainable development, the difficulties related to the studies of this process and the diversity of understandings on the subject, should serve as motivation to create new visions and tools, in order to present and measure sustainability [41]. In view of the above, the spatial clipping at the level of the hydrographic basins of the State of Rondônia was adopted as a central element of analysis, due to its important role for strategic planning and environmental management. In this context, the objective of the study was to build a sustainable development index for watersheds in Rondônia, using factor analysis as an analytical model. With this, it is expected that the model presented by the research can contribute to future studies and, thus, serve as a basis for academic, technical-scientific discussion within this theme.

II. Analytical Model Proposal
Factor analysis was used as a mechanism to build performance indices for each parameter studied. Factor analysis is a generic name given to a class of multivariate statistical methods whose main purpose is to define the underlying structure in a data matrix. In general terms, factor analysis addresses the problem of analyzing the structure of interrelationships (correlations) between a large number of variables, defining a set of dimensions, called factors. With factor analysis, the researcher can first identify the separate dimensions of the structure and then determine the degree to which each variable is explained by each dimension. Once these dimensions and the explanation of each variable are determined, the two main uses of factor analysis -data summarization and reduction -can be achieved. When summarizing the data, factor analysis obtains dimensions that, when interpreted and understood, describe the data in a much smaller number of concepts than the original individual variables. Data reduction can be achieved by calculating scores for each latent dimension and replacing the original variables with the same ones [42]. Santana [43]; Santana [44]; Santana [45]; Santana [46]; Santana [47]; and Cavalcante [48] are some of the important authors that corroborate the study by Hair et al., [42].
For the analysis of environmental, social, economic and political-institutional parameters, the municipalities were grouped by hydrographic basins, based on the distribution adopted by the Rondônia Secretariat for Environmental Development (SEDAM), as shown in table 1. It is also noteworthy that the Abunã river basin was not included in this work, as there are no cities in its coverage area.

Watershed Level Sustainable Development Index in Rondônia, Western Amazon: Index Construction from Factor Analysis
International Journal for Innovation Education and Research, Vol.10 No.9 (2022), pg. 291 F = is the q-dimensional vector transposed from non-observable variables or latent variables called common factors, denoted by F = (f1, f2,..., fq), where q < P; ε = is the p-dimensional vector transposed from random variables or unique factors, denoted by ε = (e1, e2,..., ep); α = is the array (p, q) of unknown constants, called factorials loads.
According to the authors, the initial structure used to determine the array of factorials loads, in general, may not provide a significant pattern of variable loads, so it is not definitive. This initial structure can be done by several methods of rotation of the factors, as Dillon and Goldstein [58]; Johnson and Wichern [58]. It was used the VARIMAX method of orthogonal rotation of the factors for this study.
The VARIMAX method is a process where the reference axes of the factors are rotated around the source until some other position is reached. The objective is to redistribute the variance of the first factors to others and to achieve a simpler and more theoretically significant factorial [42]; [43]; [47]; [50]; [49].
The choice of factors was carried out through the technique of latent root. So, the array of factorials loads, which measures the correlation between the common factors and observable variables, is determined by means of the correlation matrix, as Dillon and Goldstein [58].
For the determination of sustainable development indexes, the matrix of factor scores estimated by the factorial basis orthogonal rotation process was adopted, as pointed out by Santana [45]. The factor score, by definition, places each observation in the space of common factors. For each factor fj, the i-th factor score extracted factorial score is defined by FIj, expressed as follows [58]: To arrive at the equation that represents the Performance Index, Gama et al., [50]; Santana [46], show the evolutionary sequence of formulas from the previous equation. It turns out that even if the variable FIj is not observable it can be estimated through the factorial analysis techniques, using the matrix of observations of the vector x of observable variables. In factorial notation, equation 2 becomes: (p,q) =R (p,p) (p,q) (6) If the matrix R is non-singular, one can pre-multiply both sides of equation 6 by the inverse of R, obtaining: Substituting the β vector into equation 4, we obtain the factorial score associated with each observation, as follows: In this way, the main formula of the Performance Index (I.D.) is arrived at, where the ID is defined as a linear combination of these factor scores and the proportion of the variance explained by each factor in relation to the common variance. The mathematical expression is now represented by the following formula: Then: i = 1,2,..., n. λ = is the variance explained by each factor; ∑ λ = is the total sum of the variance explained by the set of common factors.
The factorial score was standardized (FP) to obtain positive values from the original scores and allow the hierarchy of the municipalities since the values of the performance index are between zero and one. The formula that allows this hierarchy can be seen by the following equation: It can be seen that min e max are the maximum and minimum values observed for the factor scores associated with the parameters observed by municipalities in Rondônia, framed in the level of hydrographic basins, for a period of 10 years. Thus, it is based on this understanding that it was possible to determine the performance indices adopted by this research.

Tests of adequacy of the factorial method to the mass of data
According to Gama et al., [50]; Santana [46], the two main tests with the objective of assessing the adequacy of the method to the mass concern, first, the Bartlett sphericity test, which has the property of evaluating the general significance of the correlation matrix, that is, it tests the null hypothesis that the correlation matrix is an identity matrix. In addition to the Bartlett test, the Kaiser-Meyer-Olkin (KMO) test is also widely used and is based on the principle that the inverse of the correlation matrix approaches the diagonal matrix, in this case, it seeks to compare the correlations between the observable variables. Thus, both methods were used by this research as techniques for assessing the adequacy of the method to the surveyed database.
According to Dillon; Goldstein [58]; Reis [49]; Mingoti [60]; Gama et al., [50]; Santana [46] the mathematical formulas of these tests can be seen by the following equations: Like this, ij = is the sample correlation coefficient between variables xi and xj; ij = is the partial correlation coefficient between the same variables that is simultaneously an estimate of the correlations between the factors, eliminating the effect of the other variables.
According to Hair et al., [42], the ij should assume values close to zero, since it is assumed that the factors are orthogonal to each other. Thus, according to this same author, values of this test below 0.50 are unacceptable.
Bartlett's sphericity test tests the null hypothesis that the variables are independent, against the alternative hypothesis that the variables are correlated with each other. That is, H0: R = 1 or H0: 1 =λ 2 = ⋯ =λ , which allows us to arrive at the following mathematical formula:

Analysis tool
The SPSS program, version 17, was used as an analysis tool, which enabled the application of mathematical knowledge and allowed the construction of performance indices based on each parameter analyzed: environmental, economic, social and political-institutional.

Watershed Level Sustainable Development Index in Rondônia, Western Amazon: Index Construction from Factor Analysis
International Journal for Innovation Education and Research, Vol.10 No.9 (2022), pg. 294

Levels of scale
The classification adopted by the research to express the results achieved by the river basins in  Source: FECAM.
The scale of analysis allowed classifying the indexes presented by the river basins of Rondônia in low, medium low, medium, medium high and high, according to the results obtained in this research.

Indicators raised by the survey
The model was built based on the following indices: environmental, economic, social and political institutional.
The combination of these four indexes resulted in the sustainable development index, as indicated in the methodology (methodological script). The indicators raised and the respective research sources, which were part of the analysis of this work, are listed in tables 3, 4, 5 and 6, below.  Source: Own elaboration. Source: Own elaboration. Source: Own elaboration.

Methodological roadmap
Next, the steps taken in this work will be described, which were considered essential for the consolidation of the process of construction of sustainable development indexes due to the object of the present study.

4
Use the SPSS tool, through factor analysis, based on the Varimax method.

5
Observe the data adequacy criteria for factor analysis.

6
Determine the performance indexes by municipalities aggregated by river basins.

7
Using the average performance indexes of the municipalities, determine the indexes for each parameter for each hydrographic basin.

8
Using the average of the parameters, determine the index of sustainable development by hydrographic basins.

III. Analysis of The Sustainable Development Indices of The Water Basins in The State of Rondônia.
From the 20th century, when environmental issues gained worldwide repercussion and the concept of sustainable development became a development model to be achieved, the need arose to measure the process towards sustainability, through instruments such as indicators. of development, "tools constituted by one or more variables that, associated through different ways, reveal broader meanings about the phenomena to which they refer" [63]. At first, traditional indicators (macroeconomic and pollution measurements) were not viable to indicate sustainability, making it necessary to develop new indicators that would be useful for public management decisions. Thus, it was foreseen in Agenda 21, the elaboration of effective methods for collecting and evaluating data, in the economic, social, institutional and environmental dimensions, from the local to the international scope [64]. The great challenge of sustainable development is to reconcile economic growth with environmental preservation and social justice. In this sense, indicators can be suitable instruments to assist this process, since they contain information on the economic, social and environmental situation of a given location. It is worth mentioning that sustainable development is a process under construction, so the formulation of indicators is an open work.
The main objective of indicators is to aggregate and quantify complex information, and facilitate their understanding [20]. Corroborating this understanding, Guimarães and Feichas [63] state that indicators can only be considered instruments of the sustainable development process if they add characteristics that allow the evaluation of social phenomena, enabling society's participation in the search for development, as well as offering subsidies for decision-making and project elaboration, by public managers, pointing out the possible

Watershed Level Sustainable Development Index in Rondônia, Western Amazon: Index Construction from Factor Analysis
variables, since society is built daily. The choice of indicators should "enable the temporal comparison within the same territory as well as the comparison between territories on a spatial and temporal scale" [63], which allows governments and society to project trends, analyze scenarios and direct public policies in the search for improvements. What is expected is that these indicators can facilitate the comparison of objectives with results, as well as the management process and indicate the gaps between the planning and execution processes of policies [63]. In this sense, "We seek to use a reduced number of truly binding indicators that provide systemic information relevant to different dimensions and sectors" [63]. The results obtained from the indicators present a partial view of reality, however, the studies must be carried out within a context that allows subsidizing analyzes and recommendations for local management. Therefore, it is necessary to "choose and develop methodologies, guidelines, parameters, criteria and instruments that adapt to the object of analysis" [64]. The complexity of problems related to sustainable development demands integrated indicators or aggregated indices that are easy to understand, as they will be the basis for the decision-making process in the search for solutions [65].
From the combination of indicators, it is possible to generate indices, "powerful tools in the process of consolidating ideas and also offering more tangible information to public policy makers" [66]. Assisting in numerous governmental actions, the indexes are also widely used by public managers, as a way of facilitating their communication, given the importance of strategic planning at the local level for the implementation of policies [66]. The formulation of sustainable development indices is a way of synthesizing a series of quantitative and semi-quantitative information, where each index results in a numerical value, the product of mathematical operations based on information collected, and which will serve as a basis for the evaluation of sustainability. According to these authors, among the existing indices, the ones that best fit the theme of sustainable development are the Sustainability Barometer, the Environmental Sustainability Index (ISA), the Sustainability Panel and the Ecological Footprint.
The construction of a sustainable development index must focus efforts so that a tool is acquired that addresses the complexity of the system in an accessible way. In this sense, even the simplest model of presentation of indices or aggregated indicators can contribute to achieving the goals of sustainable development [66].
Although several indicator systems address the dimensions of sustainable development, they cannot be adopted without being in the context of the analysis to be carried out, due to the differences that exist between the environments and the peculiarities of each place. However, this does not prejudice the use of indicators, which may vary according to the object of study [68]. A set of sustainable development indicators has been developed, tested and improved, however, this is justified by the fact that there is no consolidated methodology [68]. Choosing and considering the dimensions and aspects of the indicators of a given location are one of the main difficulties encountered, as the results will serve as a basis for decision-making, determining the sustainable development indices. The choice of indicators is important and deserves attention, so that they "reflect not only the knowledge of government institutions, but also the expectations of society" [69], since the results presented from these indicators determine a pattern normative, making a diagnosis viable, which will serve as a basis for formulating and evaluating public policies [67].
Next, the results achieved by the present study will be presented, aiming to demonstrate the scope of the model and the possibilities of analysis, depending on the proposed methodological instrument, as a suggestion of scientific criteria for decision making involving the theme of environmental management in hydrographic basins.  The evaluation of environmental, political-institutional, social, and economic parameters, based on the hydrographic basins of the Madeira, Mamoré, Guaporé, Jamari, Machado and Roosevelt rivers, allowed us to present the indices identified in each basin, as can be seen in tables 8 and 9 and in figures 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. Subsequent to the results obtained, it was possible to determine the sustainable development index at the level of watersheds in the state of Rondônia. Table 8 and Figure  Only the Madeira River basin currently improves its environmental performance index to medium low (0.597).
The Roosevelt River basin with the lowest rates is a region that has high rates of deforestation and aggression to the environment. The results found, in general, reflect the way in which the State has been developing and the difficulties faced to maintain a balance between environmental preservation, economic growth, social equality and institutional political structure.
In the context of watersheds, the state of Rondônia has a low sustainable development index, according to the research, a scenario that needs to be urgently transformed, taking into account that sustainable development is the guarantee of better living conditions and well-being. performance and future generation, as defined in the Brudtland report.
This result indicates that the objectives and guidelines of the state policy for water resources need to be applied efficiently, with the help of management tools and all the actors involved, so that in this way a development can actually be achieved that is considered sustainable.  The results found, in general, reflect the way in which the State has been developing and the difficulties faced to maintain a balance between environmental preservation, economic growth, social equality and institutional political structure. It was also found that the incipient public policy of strengthening the paradigm of sustainable development at the level of river basins in Rondônia, has contributed to the advance of deforestation in Rondônia.
In the context of watersheds, the state of Rondônia has a low sustainable development index, according to the research, a scenario that needs to be urgently transformed, taking into account that sustainable development is the guarantee of better living conditions and well-being, performance and future generation, as defined in the Brudtland report.
This result indicates that the objectives and guidelines of the state policy for water resources need to be applied efficiently, with the help of management tools and all the actors involved, so that in this way a development can actually be achieved that is considered sustainable. Finally, it is highly recommendable to institutionalize regional public policies in the form of a Master Plan for the Rondônia Watersheds as a mechanism for planning and managing the respective areas, from the perspective of sustainable, integrated and inseparable development of their local communities.