Exploratory Hierarchical Factor Analysis with an Application to Psychological Measurement

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Key words and phrases: Hierarchical factor model, augmented Lagrangian method, exploratory hier- archical factor analysis 1 Introduction Many constructs in social and behavioural sciences are conceptualized to be hierarchically structured, such as psychological traits (e.g., Carroll, 1993; DeYoung, 2006), economic factors (e.g., Kose et al., 2008; Moench et al., 2013), health outcomes measures (e.g., Chen et al., 2006; Reise et al 2007) and constructs in marketing research (e g Sharma et al 2022) Exploratory Hierarchical Factor Analysis Hierarchical factor models (Brunner et al., 2012; Schmid and Leiman, 1957; Thomson, 1939; Yung et al., 1999), which include the bi-factor model (Holzinger and Swineford, 1937) as a special case with two factor layers, are commonly used to measure hierarchically structured constructs. In these models, hierarchically structured zero constraints are imposed on factor loadings to define the hierarchical factors. When the hierarchical factor structure is known or hypothesized a priori, the statistical inference of a hierarchical factor model only requires standard confirmatory factor analysis techniques (Brunner et al., 2012). However, for many real-world scenarios, little prior information about the hierarchical factor structure is avail- able, so we need to learn this structure from data. This analysis is referred to as exploratory hierarchical factor analysis