Parafac2 Component Analysis of Multiple Groups with Nested Mean-Structures

• Activity Number: 391
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Korean International Statistical Society
• Author(s): Sungjin Hong*+
• Companies: PepsiCo
• Keywords: Parafac ; Parafac2 ; tensor decomposition ; component mean structure ; bootstrap ; emotion space

Abstract

Parallel factor analysis (Parafac) is a multilinear component model that provides a unique decomposition of tensors under mild conditions. As a relaxed hybrid model, Parafac2 allows for component analysis of nested data, which can be useful for uncovering an invariant component structure across multiple groups. When several alternative grouping variables are available (e.g., nationality vs. age), however, an added nested mean-structure makes less optimally grouped data spuriously fitted more. A bootstrap-based reliability index (BRI) has been successfully developed for choosing the most optimal grouping among several alternatives. This study will show the algebraic form of nested component mean-structure that leads to a spurious fit. A simulation experiment will be presented to evaluate the performance of BRI, followed by a psychological application to emotion data. Given four alternatively grouped data (by nationality, age, gender, or wealth) of 14 self-reported emotion adjectives, BRI clearly suggested that an invariant component structure existed most reliably across 6 geographically distinctive countries (Brazil, China, Greece, Iran, Nigeria, and USA).