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Probabilistic Latent Factor Induction with BayesiaLab

A Side-By-Side Comparison with Traditional Factor Analysis

Bayesian networks have been gaining prominence among scientists over the recent decade and the new insights generated by this powerful research method can now be found in studies that circulate well beyond the academic communities. As a result, many practitioners and managerial decision-makers see more and more references to Bayesian networks in all kinds of scientific and business research, ranging from biostatistics to marketing analytics.

It is not surprising that the new Bayesian network paradigm prompts comparisons to more conventional methods. In the field of market research, for instance, long-established methods, such as factor analysis remain in daily use today. Given that there exists a direct counterpart to factor analysis in the Bayesian network framework, we want to highlight similarities as well as fundamental differences. The goal of this paper is to present both methods side-by-side and thus help researchers to correctly compare and understand the respective results. More specifically, we want to establish the semantic equivalents between the traditional statistical factor analysis approach and BayesiaLab’s method based on Bayesian networks, which we refer to as Probabilistic Latent Factor Induction.

Factor Analysis is a statistical method used to describe variability among observed variables in terms of a potentially lower number of unobserved variables called factors. It is possible, for example, that variations in three or four observed variables mainly reflect the variations in a single unobserved variable, or in a reduced number of unobserved variables. The observed variables can be seen as manifestations of abstract underlying (and unobserved) dimensions or (latent) factors.

Factor analysis originated in psychometrics and is used in behavioral sciences, social sciences, marketing, product management, operations research, and other applied sciences that deal with a large number of variables in their data.

Probabilistic Latent Factor Induction is a workflow within the BayesiaLab software package, which has the same objective as the traditional factor analysis, i.e. variable reduction, but works entirely with the framework of Bayesian networks and is based on principles derived from information theory.

It is important to point out that this comparison is not meant to favor one approach over the other (and to declare a winner and loser), although it is clearly in the authors’ interest to promote Bayesian networks in general and BayesiaLab in particular. Rather, this paper should serve as a reference for research practitioners and those who use research results in their decision-making processes, so they can correctly interpret insights produced with either approach.