Latent factors are variables that cannot be observed directly but can be inferred from a set of observable variables. For example, in psychology, bad conduct (latent factor) can be measured by how much one engages in fighting, bullying, stealing, swearing, cheating, lying and losing temper (observable variables). In marketing, customer satisfaction can be measured by indicators such as price perception, product quality and customer service.
Structural equation modelling (SEM) provides a holistic theoretical framework that assesses both the relationship between observed variables and a latent factor, and also relationships between latent factors. SEM is used extensively in several research areas, particularly in psychology to validate instruments that measure people’s attitudes; and in marketing to assess the impact of marketing strategies on consumer behaviour.
The foundation of SEM can be traced back to exploratory factor analysis (EFA), regression analysis and path analysis. It started in various disciplines, including psychometrics, sociology, econometrics and biometric path analysis. However, a conference on structural equation models in 1970 brought together a wide variety of social scientists whose research interests were the development and use of quantitative methods for analysing causation in various types of data.
The foundation of SEM can be traced back to exploratory factor analysis (EFA), regression analysis and path analysis
The seminal work of Bentler (1970), Blalock (1971), Jöreskog (1974), Muthen (1984) and Bollen (1989) laid the foundation for a comprehensive theoretical SEM framework. Moreover, the development of the EQS software in 1970 was another turning point for the application of SEM in several research fields. Other software, including MIMIC, FASEM, PLS and GLLAMM, have extended the application of SEM techniques to a higher level.
SEM consists of three main processes: path analysis, confirmatory factor analysis (CFA) and structural regression models. Path analysis includes the analysis of structural models of observed variables, while CFA deals with the analysis of a priori measurement models where one specifies beforehand both the number of latent factors and their corresponding observable variables.
On the other hand, structural regression models deal with estimating the effects between latent factors. The general SEM consists of two models, the measurement model and the structural model. The measurement model is obtained through CFA and the structural model is obtained through SEM.
CFA tests how well the observable variables represent the number of latent factors, while a measurement model depicts the relationships existing between the observable variables and the latent factors.
Liberato Camilleri is a statistics professor at the University of Malta.
Sound Bites
• From the local scene: The author of this page (Liberato Camilleri) together with other researchers applied structural equation models to two studies. The first study validated the structural framework of the strengths and difficulties questionnaire (SDQ) using a data set collected from Malta. This instrument included five latent factors (conduct problems, hyperactivity, emotional difficulty, peer problems and prosocial behaviour) described by 25 observable variables.
The second study validated the structural framework of the social emotional learning (SEL) tool using a data set collected from six European countries. This instrument included five latent factors (self-awareness, self-management, social awareness, relationship skills and responsible decision-making) described by 20 observable variables. The two studies are found at: ‘Examining the structural validity of the Strengths and Difficulties Questionnaire (SDQ) in a multilevel framework’ (2018). (Xjenza Journal, Volume 6, Issue 1, p.16-24.) ‘Exploring the structural validity of the Social Emotional Learning (SEL) Questionnaire’ (2024). (ESM Conference Proceedings, p.59-63.)
For more soundbites, listen to Radio Mocha every Saturday at 7.30pm on Radju Malta and the following Monday at 9pm on Radju Malta 2 https://www.fb.com/RadioMochaMalta/.
DID YOU KNOW?
From the PISA 2022 survey:
• Malta’s mean scores for parental educational support (0.145) and for students’ curiosity in learning (0.136) were significantly higher than the international average (-0.008 and 0.055 respectively).
• Unfortunately, this was also the case for school bullying (-0.039 vs -0.268), showing that school bullying is more prevalent in Malta.
• Maltese students also have a lower sense of school belonging than the international average (-0.232 vs -0.081).
For more trivia, see: www.um.edu.mt/think.