Endeavor

variables "Density of roads", "Number of direct flights" and "Distance to the nearest port." Once the variables are added, you can apply the same process of standardization of variables for the result. The standardization of sub determinants prevents that, later on, one sub determinant presents an average value higher then another just for being composed of more variable. However, instead of focusing the scores on average zero, as we did with the indicators, we moved the average to 6. For example, in the "Market" pillar, the sub determinants "Economic Development" and "Potential Leads" will always mean 6 and standard deviation 1, with scores of each city indicating its position relative to the others. Basically, mov - ing the average to 6 avoids misinterpretation and nega- tive connotation (below average score), while not affecting the results. Sub determinant_x = Indicator_1' + Indicator_2' + ... + Indicator_k' Sub determinant_x' = (Sub determinant_x – Average (Sub deter- minants) / Stand.dev (Sub determinants)) + 6 The choice of adding variables directly within a sub determinant has consequences. The most notable is that it is implicitly assumed that the indicators have the same weight within a sub determinant. Rankings and other comparison tools must necessarily adopt an arbitrary criterion to weigh different indicators and combine them, even if the criterion is to assign equi- valent weights. A suitable way around the arbitrari- ness of that choice is the careful evaluation of each of the determinants, sub determinants and indicators that compose them. Instead of adopting weights for the variables in this step of the study, it was decided to organize them hierarchically. In the early steps of the study 380 indicators were appointed. At first, these indicators were grouped into the determinants and their sub determinants fol - lowing the guidelines of existing frameworks and the opinion of the experts consulted. In the process of collecting variables, we eliminate those unavailable, with excessive errors of measurement or redundant, and sought out different sources for the same mea- surements. For example, the number of direct flights to a city and the total number of passengers carried are quite similar measures. Using two indicators that, once standardized, are almost identical would be like adopting twice the weight for a specific aspect of a sub determinant. Even after the initial elimination of redundant indica- tors, it is still possible that two indicators have very sim- ilar measurements and highly correlate with one anoth- er, even if their definitions and titles seem completely different. Then, with an already limited set of indicators, one Principal Component Analysis is produced for each determinant, showing how each indicator behaved in relation to the other. Intuitively, the application of Principal Component Analysis resembles discovering all the dimensions of each of the determinants and creating a component that represents each dimension. Sometimes a set of 10 indicators can be represented by a single component. For example, we can imagine that human capital has two dimensions, quality of education and total educated population, and that the average score of students in the county in the IDEB and the percentage of the population who finished high school are possibly related to these two dimensions. In producing the Principal Component Analysis, you can see how these two indicators are situated in the dimensions found and decide whether they are redundant, conflicting or complementa - ry. With this, one could also evaluate and reconstruct the sub determinants, improving existing tools in international studies and designing a suitable framework for Brazilian cities. A more detailed explanation of the principal compo- nent analysis is found below, where performance aspects are analyzed. Once the sub determinant category is built, the result of each pillar (determinant) is the simple sum between them and overall standardization, again with standard deviation 1 and average 6. Each determinant's ranking, presented throughout this report, and the scores of each city for a specific determinant comes from this last operation. The sub determinants always have the same weight within each determinant. Determinant_x = Sub determinant_1' + Sub determinant_2' + ... + Sub determinant_k' Determinant_x' = (Determinant_x – Average (Determinants) / Stand.dev (Determinants)) + 6 The final framework, presented on page 94, results, therefore, from an initial inductive process — consulta - tion with similar international studies and experts — and 91

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