Applied Bayesian Modelling, 2nd Edition

Chapter 9Latent variable and structural equation models

9.1 Introduction

Structural equation models (or SEM methods) describes multiple equation representations that include latent or unmeasured variables (‘factors’, ‘constructs’, or ‘domains’) for which multiple observed indicators (or ‘items’) are available (e.g. Kelloway, 1995; Bollen, 1998; Tu, 2009; Kline, 2011; Ullman and Bentler, 2012). The intention is often the representation of causal relationships (Song and Lee, 2012, Section 2.2.2). Particular types of SEM include confirmatory and explanatory factor analysis (Hurley et al., 1997), latent class analysis and item response models (Fox, 2010).

Such methods have found a major application in areas such as psychology, education, marketing and sociology where underlying constructs (depression, product appeal, teacher style, anomie, authoritarianism, etc.) are not possible to measure directly. Among issues that often occur are the treatment of non-normality or discrete manifest indicators (Muthen, 1984; Quinn, 2004), missing data (Muthen et al., 1987; Kamakura and Wedel, 2000; Allison, 2003), and invariance of measurement structures (Meredith and Teresi, 2006).

Bayesian approaches to factor analysis and structural equation models are discussed by Song and Lee (2012), Lee (2007), Muthen and Asparouhov, (2012), MacCallum et al. (2012), Palomo et al. (2007), and Ghosh and Dunson (2009), with applications exemplified by Arhonditsis et al. (2006), Wu et al. (2010) and Ho and ...