Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization

Abstract

Exploratory Factor Analysis (EFA) is a widely used statistical technique to discover the structure of latent unobserved variables, called factors, from a set of observed variables. EFA exploits the property of rotation invariance of the factor model to enhance factors’ interpretability by building a sparse loading matrix. In this paper, we propose an optimization-based procedure to give meaning to the factors arising in EFA by means of an additional set of variables, called explanatory variables, which may include in particular the set of observed variables. A goodness-of-fit criterion is introduced which quantifies the quality of the interpretation given this way. Our methodology also exploits the rotational invariance of EFA to obtain the best orthogonal rotation of the factors, in terms of the goodness-of-fit, but making them match to some of the explanatory variables, thus going beyond traditional rotation methods. Therefore, our approach allows the analyst to interpret the factors not only in terms of the observed variables, but in terms of a broader set of variables. Our experimental results demonstrate how our approach enhances interpretability in EFA, first in an empirical dataset, concerning volumes of reservoirs in California, and second in a synthetic data example.     

When My Object Becomes Me: The Mere Ownership of an Object Elevates Domain‐Specific Self‐Efficacy

Past research on the mere ownership effect has shown that when people own an object, they perceive the owned objects more favorably than the comparable non‐owned objects. The present research extends this idea, showing that when people own an object functional to the self, they perceive an increase in their self‐efficacy. Three studies were conducted to demonstrate this new form of the mere ownership effect. In Study 1, participants reported an increase in their knowledge level by the mere ownership of reading materials (a reading package in Study 1a, and lecture notes in Study 1b). In Study 2, participants reported an increase in their resilience to sleepiness by merely owning a piece of chocolate that purportedly had a sleepiness‐combating function. In Study 3, participants who merely owned a flower essence that is claimed to boost creativity reported having higher creativity efficacy. The findings provided insights on how associations with objects alter one's self‐perception.