The mediation analysis represents one of my core analytical methods applied in this thesis. To test for mediation effects, I applied different approaches in research paper I and III, which also demonstrates my journey and progress in empirical analysis in the course of preparing this thesis. I will therefore discuss in more detail the mediation analysis and why different approaches were selected in the research papers.
A mediator can be considered as a variable that partly or entirely carries an effect of a given independent variable to a given dependent variable (Baron & Kenny, 1986; Sobel, 1990). In doing so, the independent variable significantly affects the dependent variable in the absence of the mediator. When additionally taking the mediator into account, the effect of the independent variable on the dependent variable declines or disappears completely, while the independent variable significantly affects the mediator, which in turn significantly affects the dependent variable. Different analytical approaches are available, allowing testing for mediation.
A causal multi-step procedure suggested by Baron and Kenny (1986) allows to informally test the mentioned series of hypothesis to evaluate whether or not a variable is mediating a relationship between an independent and a dependent variable by using OLS regressions or structural equation modeling. Although this procedure is most commonly used for testing mediation, it does not provide statistical evidence of the mediated effect and is thus limited in its predictive power to detect real effects particularly for small sample sizes (MacKinnon et al., 2002; Preacher & Hayes, 2004).
This shortcoming is frequently addressed by using a set of statistical methods based on the ratio of the product of the coefficients of the indirect path to the estimated standard error, which is in contrast to the multi-step procedure focusing the single paths in a mediation model (Preacher & Hayes, 2008). The most popular product-of- coefficient method was proposed by Sobel (1982). It allows testing whether the indirect effect differs significantly from zero, i.e., the paths from the independent variable to the dependent variable through the mediator. Since the product-of-coefficient method is well established and is frequently applied in recent research – even with small sample sizes – (e.g. Bhagavatula et al., 2010; Lee et al., 2011) I rely on this method in the first research paper of this dissertation in order to statistically investigate mediating effects.
However, product-of-coefficient methodological approaches have some limitations that should be taken into account. As these approaches are of a parametric nature, a normal distribution of the indirect effect is assumed for the calculation of its p-value, which is oftentimes questionable, at least in small samples such as that in research paper I. Therefore, it is recommended to use product-of-coefficient mediation tests, such as the Sobel’s test, only when the sample is large, when the effects are large, and/or in the event that raw data are not available (Preacher & Hayes, 2008). Although it is difficult to estimate the impact of a skewed, non-normally distributed indirect effect on the results, it reduces the predictive power of studies and thus the results of research paper I. Besides this, in the first research paper, I tested for the mediating effect of two mediators in two separate product-of-coefficient calculations. I used the values of the coefficients and standard errors obtained from a structural equation modeling which included both mediators at the same time. Thus, the effect of the other mediator is indirectly considered in each of the product-of-coefficient calculations. However, by using this approach, I was unable to evaluate several additional aspects (cf. Preacher & Hayes, 2008): First, the chosen methodological approach did not allow us to calculate the
total indirect effect in order to investigate whether a joint mediating effect caused by all expected mediators exists. Second, I am unable to provide evidence for the significance and relative size of the specific indirect effect of each of the mediators when other mediators are included in the model at the same time. Finally, it is more likely that I have obtained biased parameter estimates, as I rely on the single-mediator models which exclude the effects of other mediators, and thus potential effects between the mediators (Judd & Kenny, 1981). Overall, it must be emphasized that, although the chosen analytical approach in paper I is commonly used for mediation analyses in recent studies, it has some limitations, i.e., it does not investigate relevant issues related to models with multiple mediators.
Driven by theory, I also ended up with a multiple mediation model in the third paper of this dissertation. In order to address some of the limitations associated with the approach chosen in the first paper, I looked for a more appropriate approach. In the context of mediation models with multiple mediators, a bootstrapping method is thought to have advantages over the causal-multi-step procedure as well as the product- of-coefficients approach (e.g. Bollen & Stine, 1990; MacKinnon et al., 2004; Preacher & Hayes, 2004, 2008): First, as a nonparametric re-sampling procedure, bootstrapping does not require normality of the sampling distribution of indirect effects; it can be applied even when a given sample is small. Second, bootstrapping procedures allow mediation models with multiple mediators to be estimated. These procedures thereby allow an investigation of the effect and significance of each single mediator in the presence of the others, the differences between two mediators in terms of their relevance, and the total indirect effect of the given set of mediators. Finally, the abovementioned problem with biased parameter estimates is reduced. Overall, the bootstrapping method used in paper III provides more comprehensive and valid results compared to the approach chosen in paper I.