Purpose
This study aims to more deeply examine the various types of testing mediations and use the comparison test by using test-based mediation Sobel models and Bayesian approach. The purpose of this study are to apply the traditional (using indirect effect) and Sobel test, extend Yuan and MacKinnon (2009) work on Bayesian mediation analysis. Both analysis methods of mediation (Traditional, Sobel Test and Bayesian estimation) should apply in the research of management, by using structural equation modeling (SEM) in a structural model, with one mediation, one exogenous (independent) and one endogenous variable. The meta-analysis approximation has been used to investigate the job satisfaction as a mediation in the relationship between employee competence and performance (endogenous).
Design/methodology/approach
Data were collected from ten dissertations of students of the Management Doctoral Program at the Brawijaya University from 2009 until 2013; data were analyzed for the mediation variable of job satisfaction (M) in the relationship between employee competence (X) and employee performance (Y) (Muindi and Obonyo, 2015; Olcer, 2015; Sattar et al., 2015; Khan and Ahmed, 2015). A researcher can determine the mediating variable and whether it is complete or partial or if mediation exists in several ways.
Findings
The results of the above findings using meta-analysis showed that 60% of previous research states that job satisfaction is a partial mediation on relationship competence of the performance, 10% of previous research states that job satisfaction is a full mediation on relationship competence of the performance and 30% stated that job satisfaction is not pemediasi (pemediasi means Mediation variable) on the relationship between competence and performance. This research found that all three approaches provide similar conclusions for ten previous research.
Research limitations/implications
The findings showed that the Sobel approach and the Bayesian approach provide results that are more sensitive than the traditional approach.
Practical implications
In my opinion, the rule to investigate the mediation variable should be completed with the conditions (1) q (theta) is not statistically significant, (2) α (alpha) and β (beta) are significant, and (3) q’ (theta) is significant, and increase when M is include as an additional predictor. This condition called partial mediation.
Social implications
The traditional method is simpler and easy. The method is less sensitive and is not sufficient for investigating the mediating variables. In general, the method results in a mediation variable, but it cannot be used to determine either partial or complete mediation variables. So, investigation by Baron and Kenny Methods (in Hair et al., 2010), the rule or testing called Sobel Test and another approach such as Bayesian to determine the mediation variable is necessary.
Originality/value
Various methods for detecting mediating/intervening have been widely used in previous research as a method of measurement using indirect effect (Hair et al., 2010), and calculations have been performed using Sobel test (Baron and Kenny, 1986) and Bayesian approach (Enders, 2013). In this study, I wanted to more deeply examine the various types of testing mediations, and use the comparison test by using the test-based mediation Sobel models and Bayesian approach (Baron and Kenny, 1986; Enders, 2013). The statistical application should not be complicated and difficult, it but must rather be simple and easy, so that it is user-friendly. The traditional method is simpler and easier than the other methods, but how sensitive is it? This research is conducted to investigate this problem. The evaluation of mediating mechanisms has become a critical element of behavioral science research (Enders, 2013), especially in the field of management, not only to assess whether (and how) interventions achieve their effects but also, more, broadly, to understand the cause of behavioral change. Methodologists have developed mediation analysis techniques for a broad range of substantive applications. However, methods for estimating mediation mechanisms with various methods have been understudied. The purpose of this study is to apply the traditional (using indirect effect) and Sobel tests and extend Yuan and MacKinnon’s (2009) work on the Bayesian mediation analysis. Both analyses methods of mediation (traditional and Sobel test and Bayesian estimation) should apply in the research of management, by using structural equation modeling (SEM) in a structural model, with one mediation, one exogenous (independent) and one endogenous variable. The meta-analysis approximation has been used to investigate job satisfaction as the mediation in the relationship between employee competence and performance (endogenous). This study uses software R to complete the mediating effect (Enders, 2013). R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers et al. R provides a wide variety of statistical analyses such as SEM and Mediation test. R provides an open source route for participation in that activity. The Bayesian estimation approach provides an R function and a macro that applies the method of mediation analysis.
An Investigation of the Relationship between School Principals' Empowering Leadership Style and Teachers’ Job Satisfaction: The Role of Trust and Psychological Empowerment
