A Tutorial on Hierarchically Structured Constructs

Abstract

Many psychological constructs are conceived to be hierarchically structured and thus to operate at various levels of generality. Alternative confirmatory factor analytic (CFA) models can be used to study various aspects of this proposition: (a) The one-factor model focuses on the top of the hierarchy and contains only a general construct, (b) the first-order factor model focuses on the intermediate level of the hierarchy and contains only specific constructs, and both (c) the higher order factor model and (d) the nested-factor model consider the hierarchy in its entirety and contain both general and specific constructs (e.g., bifactor model). This tutorial considers these CFA models in depth, addressing their psychometric properties, interpretation of general and specific constructs, and implications for model-based score reliabilities. The authors illustrate their arguments with normative data obtained for the Wechsler Adult Intelligence Scale and conclude with recommendations on which CFA model is most appropriate for which research and diagnostic purposes.

Analyzing Models of Career Decision Self-Efficacy: First-Order, Hierarchical, and Bifactor Models of the Career Decision Self-Efficacy Scale

“…However, we also took into consideration that internal consistency and Cronbach's α values can be lower if the number of items of a given scale is lower (Cortina 1993). We followed the guidelines of several methodologists (Brunner et al 2012;Rodriguez, Reise, and Haviland 2015) for assessing reliability in nested models, omega values were assessed which can more precisely grasp the reliability of bifactor models. The value of omega (ω) informs on the measurement precision "with which a scale score assesses the blend of the general/higher order and specific constructs".…”

“…In the present study, we intend to resolve the paradox of one-vs. multifactor structures by using a bifactorial (or nested) model. These models can be applied when one general factor (in the present case career decision selfefficacy) and multiple specific factors (in the present case self-appraisal, occupational information, goal selection, planning, and problem solving) can be supposed to account for the commonality of the items (Brunner, Nagy, and Wilhelm 2012;Chen, Hayes, Carver, Laurenceau, and Zhang 2012;Chen, West, and Souza 2006). Bifactor models have several advantages over other structural solutions (Chen et al 2006;Reise, Morizot, and Hays 2007):…”

Repetitive negative thinking as a predictor of depression and anxiety: A longitudinal cohort study

“…The ω estimates for the general, perseverative thinking, rumination, and worry factors were: 0.98, 0.97, 0.85, and 0.96, respectively. The ω h revealed the following values for the same factors above: 0.92, 0.02, 0.36, and 0.29, indicating a low capacity of the scales -in particular of the PTQ-to reliably measure the variance due to the specific factors by themselves, beyond reliability provided by the general factor (Brunner et al, 2012).…”

Analyzing Models of Work Addiction: Single Factor and Bi-Factor Models of the Bergen Work Addiction Scale

“…However, regarding nested models, the guidelines of Brunner et al (2012) were followed and computed omega (ω) coefficients for assessing reliability. This coefficient provides information concerning reliable variance accounted for by all general and specific latent variables of work addiction.…”

“…There were no missing data in the current study. In the CFA analyses, first-order, higher-order, and nested-factor models (Brunner et al 2012) were tested. Following the guidelines of Brown (2006) and Schreiber et al (2006).…”