## 1 Introduction
Studies exploring multidimensional phenomena and depression are limited to correlating depression with composite indicators [36], considering depression as a factor associated with composite indicators of mental health [37; 38], and diagnosing an individual based on factors linked to depression [39; 40]. Therefore, to the best of the authors' knowledge, this study is the first to construct a composite indicator that captures the various factors of multidimensional depression. This context enables us to assert that a depression diagnosis composite indicator offers methodological and phenomenological contributions. From a methodological perspective, this research demonstrates that discriminant analysis objectively selects and weights sub-indicators, providing a more comprehensive explanation of the multidimensional phenomenon based on a categorical dependent variable. This objective selection of sub-indicators is a unique property of discriminant analysis, preventing sub-indicators that are not highly relevant from being aggregated into the composite indicator. From a phenomenological perspective, this research offers a novel composite indicator to represent the multidimensional nature of depression diagnosis. The depression diagnosis composite indicator provides valuable information for public authorities to plan investments in public health in Brazilian states and prioritize actions in states with populations with a self-reported positive diagnosis of depression. Furthermore, the research reveals which factors contribute most to discriminating between positive and negative diagnoses of depression in Brazilian states, providing public managers with information to plan specific actions to offer support to individuals with depression, according to the characteristics of each Brazilian state. These new developments have a high degree of appropriateness among researchers and academics, as they can be applied to other countries, regions, and cities and explored in the representation of multidimensional social, environmental, and managerial phenomena. However, it is essential to note that the determinants of multidimensional depression are context-sensitive, which limits direct comparisons. On the one hand, comparing the determinants of depression across different contexts provides valuable insights into local similarities and differences. On the other hand, the consideration of different factors and weights in obtaining the scores of the multidimensional depression diagnostic index makes it impossible to indicate locations that are more or less vulnerable to multidimensional depression, hindering the development of policies across different contexts. This limitation also applies to the use of discriminant analysis in constructing composite social, environmental, and managerial indicators. This research is organized into six sections. In addition to this Introduction, Section 2 presents limitations, gaps, and opportunities in understanding mental health, especially depression, from a multidimensional perspective. Section 3 illustrates the application of discriminant analysis in creating a multidimensional depression diagnostic index for the 27 states of Brazil. Section 4 presents the results, while Section 5 discusses the index for the diagnosis of multidimensional depression and the study's limitations and outlines future research directions. Finally, the research conclusions are presented in Section 6.