Link between mindfulness, self-control, and aggression

The associations amongst self-reported measures were explored using zero-order correlations. On examination of these correlations, Hypothesis 1 would be confirmed if there is a positive correlation between trait mindfulness and trait self- control and negative correlations between these traits and trait aggression.

The possible relationships between mindfulness, self-control, and aggression were tested with bootstrapping method. Specifically, we used (i) Preacher and A. F. Hayes’s (2011) macro called INDIRECT (for Hypothesis 2 and 3), and (ii) A. F. Hayes’s (2012a) macro called PROCESS (for Hypothesis 4).

For Hypothesis 2 and 3, we tested whether the relationship between trait mindfulness (predictor) and aggression (outcome) would be mediated by trait self- control (proposed mediator). The main outcome was trait aggression. Additionally, the four aggression subscales (physical and verbal aggression, anger, and hostility) were analysed separately as outcomes. A mediation model with only one mediating variable is known as simple mediation (see Figure 2.1).

Traditionally, mediation testing followed a four-step causal approach popularised by R. M. Baron and Kenny (1986; see also Kenny, 2013). With this approach, several

examined at each step. At Step 1, the outcome (Y) is regressed on the predictor (X) to determine a significant total effect (c path). At Step 2, the proposed mediator (M) is regressed on the predictor (a path). At Step 3, the outcome is regressed on both the mediator and the predictor. As such, the predictor is controlled to establish the effect of the mediator on the outcome (b path). One would proceed to Step 4 if there are significant relationships from Step 1 to 3. However, current researchers have strongly advocated that it is not always necessarily for the c path to be significant in order to establish mediation (for a review, see e.g., MacKinnon, Fairchild, & Fritz, 2007; Zhao, Lynch & Chen, 2010). At Step 4, if the direct effect of the predictor on the outcome is zero after controlling for the mediator (c’ path) then the finding supports full mediation. If the direct effect decreases but the reduction is still different from zero then the finding supports partial mediation. It should be noted that statistically, Step 3 and Step 4 are estimated in the same equation. The amount of mediation is called the indirect effect (ab path).

Figure 2.1. Simple mediation model. The causal effect of X on Y (c) is apportioned through its indirect effect on Y through M (ab) and its direct effect on Y (c’). X = predictor (trait mindfulness), Y = outcome (trait aggression or self-harm), M = proposed mediator (trait self-

control). a, b, c, c’ = unstandardised regression coefficient. Reprinted from Kenny (2013).

In the causal approach, the size of the mediation is not directly estimated, but is mathematically derived as the product of the a and b paths. Since the total effect of the predictor on the outcome is equal to the sum of the direct and indirect effects, c

= c’+ ab, the indirect effect is calculated as ab = c – c’. The main problem with this calculation is that a confidence interval for the population indirect effect could not be obtained (Pituch, Whittaker, & Stapleton, 2005; for a thorough discussion on the limitations of the causal approach consult MacKinnon, Lockwood, Hoffman, West, & Sheets, 2002; Preacher & A. F. Hayes, 2008). An initial attempt to perform a single test of ab was proposed by Sobel (1982). The Sobel test, however, assumes normality of the sampling distribution of the indirect effect, which is typically violated in practice (e.g., MacKinnon, Lockwood & Williams, 2004; Preacher & A. F. Hayes, 2004; Shrout & Bolger, 2002).

Conversely, with bootstrapping method, the sampling distribution of ab is estimated empirically; therefore no assumptions are made about this distribution (see e.g., MacKinnon et al., 2004; Preacher & A. F. Hayes, 2008). To bootstrap an indirect effect, the available sample size n is re-sampled with replacement intensively for a total of k times to estimate the a and b as usual (Preacher & A. F. Hayes, 2008, suggest using 5,000 resamples for final reporting). These estimates of a and b are used to calculate ab* (the indirect effect in a single resample), and the distribution of the k values of ab* provides a nonparametric approximation of the sampling distribution of ab. The mean of the k estimates of ab* represents the indirect effect. Since the mean of the k is not exactly equal with the indirect effect, a correction for bias is made, typically using confidence intervals (MacKinnon et al., 2004; Preacher & A. F. Hayes, 2008). If the bias-corrected confidence intervals does not include zero, one can be confident that a significant mediation has occurred.

Hypothesis 2 would be supported if there is a zero in the bias-corrected confidence intervals of path ab (indirect effect of self-control on the link between mindfulness and aggression). Hypothesis 3 would be confirmed if path c’ (the direct effect of mindfulness on aggression) is still significant after the inclusion of trait self-control. For Hypothesis 4, we tested whether the relationship between trait self-control (predictor) and aggression (outcome) would be moderated by trait mindfulness (proposed moderator). Trait aggression was used again as the main outcome, and the four aggression subscales were analysed separately as outcomes. A moderator

model with only one moderator variable is known as simple moderation (see Figure 2.2). The variables are mean-centered so that their coefficients are interpretable within the range of the data (A. F. Hayes, 2012b).

Figure 2.2. Conceptual and statistical models for simple moderation. In the statistical model, Y is estimated as a weighted function of X, M, and the product of X and M (XM).

X = predictor (trait self-control), Y = outcome (trait aggression or self-harm), M =

moderator (trait mindfulness). c1, c2, c3 = unstandardised regression coefficient.

Reprinted from A. F. Hayes (2012b, p.33).

Theoretically, X is depicted to exert an influence on Y, and this effect is proposed to be influenced or moderated by M (the Conceptual Model in Figure 2.2). These effects are estimated mathematically (the Statistical Model in Figure 2.2, Statistical Model) in the form of a linier equation: Y = i + c1X + c2M + c3XM + ey. From this equation, it

can be seen that the effect of X on Y is a function of M, since Y = i + (c1+ c3M)X + c2M

+ ey (for further details, consult A. F. Hayes, 2012b). The (c1 + c3M) function

represents the conditional effect of X on Y or “simple slope” for X, in which c1

estimates the effect of X on Y when M = 0, and c3estimates how much the effect of X

on Y changes as M changes by one unit. The main focus in a moderation model is whether c3, the interaction coefficient between X and M, is statistically different

from zero. Additionally, the significance of the change in the total variance in Y due to this interaction is also useful. When the null hypothesis is rejected, the magnitude of the conditional effect of X at various values of M is elaborated, along with a standard error, t, and p-value. For dichotomous M, this effect is derived at each of the two values of M. If M is continuous, M can be set to various values that

represent low (a standard deviation below the mean), moderate (the mean), and

high (a standard deviation above the mean).

Hypothesis 4 would be confirmed if c3, the interaction coefficient between self-

control and mindfulness, is statistically different from zero.