## 4 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Original** & \multicolumn{3}{c}{**Expected Association**} \\ \hline  & **Depression** & **Negative** & **Positive** & **Total** \\ \hline Count & Negative & 27 & 0 & 27 \\  & Positive & 0 & 27 & 27 \\  & Negative & 100 & 0 & 100 \\  & Positive & 0 & 100 & 100 \\ \hline \hline \end{tabular} Note: 100% of cross-validated clustered cases are classified correctly.  
\end{table} 
Table 5: Discriminant analysis cross-validation. The analysis of the maps illustrated in Figure 2 highlights the difficulty in analyzing multiple sub-indicators simultaneously and understanding the multidimensional phenomenon [15; 52]. This highlights the importance of developing a composite indicator to represent the multidimensional diagnosis of depression. Figure 2: Maps of the determining factors for a positive and negative depression diagnosis in the states of Brazil. In this sense, understanding multidimensional depression through a composite indicator requires the analysis of its factors and respective weights. Table 6 shows the directions of the correlations between the factors and the multidimensional depression diagnostic index. The factors, including a limiting chronic illness and the male gender, are significantly correlated with a positive diagnosis of depression. In other words, individuals who have a limiting chronic illness and who are female are more likely to have a self-reported positive diagnosis of multidimensional depression. Education, having someone's support, and performing unhealthy work contribute to building a multidimensional depression diagnosis composite indicator that separates individuals with positive and negative diagnoses of depression. However, these factors do not significantly correlate with the multidimensional depression diagnostic index individually. It is worth noting that the total weight of these three factors in the multidimensional depression diagnostic index accounts for 43%. According to Figure 1, the weights assigned to having someone's support, performing unhealthy work, and having an education are 0.12, 0.15, and 0.16, respectively. From these factors, it is possible to represent the diagnosis of multidimensional depression in Brazilian states using the map in Figure 3.  
The map indicates that states in the northeastern region have higher scores on the multidimensional depression diagnostic index, while states in the southern and southeastern \begin{table}
\begin{tabular}{l c c} \hline \hline
**Factor** & \(\mathbf{R_{1}}\) & \(\mathbf{R_{2}}\) \\ \hline \(\alpha\) Having a limiting chronic illness & 0.43 * & 0.06 \\ \(\beta\) Education level & 0.19 & 0.05 \\ \(\gamma\) Having someone’s support & 0.24 & \(-\)0.28 \\ \(\delta\) Performing unhealthy work & \(-\)0.10 & \(-\)0.00 \\ \(\varepsilon\) Male gender & \(-\)0.45 * & \(-\)0.21 \\ \hline \hline \end{tabular} Note: * Correlation significance level: 0.10. Except for the factor education level (one basic and five superior), all factors represent the percentage of the state’s population.  
\end{table} 
Table 6: Correlations between factors and positive (\(R_{1}\)) and negative (\(R_{2}\)) self-reported depression diagnoses. Figure 3: Map of the multidimensional depression diagnostic index in Brazil. regions have lower scores. These results are consistent with the per capita incomes of these states and align with the supporting literature that correlates income and depression [64; 65]. At this point, it is important to highlight that a relationship between income and depression occurs in Brazil, although the discriminant function did not capture this effect. Table 7 shows the rankings of the states regarding each of the determining factors of multidimensional depression. Alagoas, in the northeastern region, is the worst-positioned state in the ranking of the multidimensional depression index. This state has the third-lowest level of education, the second-lowest percentage of people who have someone's support and perform unhealthy work, and the highest percentage of males.