## 1 Introduction  
Composite indicators are one-dimensional representations resulting from the weighted aggregation of different factors associated with a multidimensional phenomenon [1, 2]. The ability of composite indicators to provide a simultaneous and easy-to-understand visualization of the different factors associated with a multidimensional phenomenon makes them a popular approach among researchers from diverse areas [3, 4]. The construction of composite indicators involves many aspects, from defining the conceptual framework to validating and visualizing the results [3; 5]. Specifically, composite indicator scores are derived from the normalization, weighting, and aggregation of factors [6]. These steps are critical in constructing composite indicators due to their direct relationship with the composite indicator score [7; 8]. Weighting, in particular, can be carried out based on data or expert opinion [9]. Weighting based on data is carried out using statistics [10]. For example, principal component analysis (PCA) defines weights that maximize the variance extracted from input factors [11]. Entropy weighting assigns weights that account for the informational diversity of input factors [12; 13]. Factor analysis (FA) defines weights that maximize the correlations between input factors [7]. The concept of benefit of the doubt (BoD) defines weights that maximize the scores of the composite indicator [14]. Weighting based on expert opinion involves the application of multicriteria methods such as the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), the analytic hierarchy process (AHP), and Elimination and Choice Expressing Reality (ELECTRE) [15]. These statistical and multicriteria methods apply to different situations, offering solutions to represent multidimensional phenomena of a social [16], business [17; 18], economic [19; 20], environmental [21; 22], governmental [23; 24], and industrial [25; 26] nature. However, both classes of methods consider all factors selected in the conceptual framework in the composite indicator. Although this approach appears appropriate, it overlooks the fact that not all input factors are significantly correlated with the multidimensional phenomenon. This research examines this flaw and proposes a new approach to constructing composite indicators, focusing only on factors that explain the multidimensional phenomenon. The proposed approach leverages two valuable properties of discriminant analysis for the construction of composite indicators, preventing factors that are not highly relevant to the multidimensional phenomenon from being included in the composite indicator. This ensures that the composite indicator scores have a significant correlation with the dependent variable. Despite its advantages, the adoption of discriminant analysis as a method of constructing composite indicators is rare. Studies that review methods for the construction of composite indicators rarely mention discriminant analysis [10; 15]. Research using this method has focused on finding variables that indicate the quality of surface waters [27], identifying the human labor variables that best classify countries' quality of life levels [28], or determining factors that can be used to discriminate between diseases [29; 30], rather than on the construction of the composite indicator itself. This method's advantages have also been overlooked in research that employs discriminant analysis to validate a composite indicator constructed by other methods [31]. The applicability of discriminant analysis to represent multidimensional phenomena is demonstrated through the construction of the so-called multidimensional depression diagnostic index. This application example is especially timely for two reasons. Depression impairs the ability of people worldwide to carry out routine activities, resulting in social and economic consequences [32; 33; 34; 35]. The multidimensional nature of depression is poorly explored in the literature.