Statistical Analysis

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2.5.1 Univariate and multivariate analyses.

Data analysis was completed using SPSS version 20 (IBM Corporation 2011). All continuously distributed data were screened to ensure they met the assumptions for parametric testing. Specifically, they were inspected to identify outliers and spurious data points, tested for deviation from a normal distribution and checked to ensure equality of variance in the care-leaver and non-care leaver groups (see Section 3.1).

Independent samples t-tests, using published means and standard deviations, were used to compare MASC, ECR-R and DERS data from the current study with other studies.

Bivariate relationships between demographic characteristics of the sample and the main study variables were assessed to identify possible confounders that would need to be controlled for in subsequent analyses. Categorical and continuously distributed data were assessed using the χ2

test, Cramér's V test of association or independent samples t-tests as appropriate. Pearson’s correlation coefficients, t-tests and ANOVA were used to investigate the relationship between age, gender, years of education, participants’ level of qualifications and the main study variables (e.g. DERS, ECR-R and MASC variables).

Analysis of covariance (ANCOVA) was used to compare DERS and MASC total scores between care–leavers and non-care-leavers, controlling for participant’s level of qualifications. Separate MANCOVAs were conducted to explore the relationship between care-leaver status and 1) subscales of the DERS; 2) errors categories of the MASC (e.g. ‘No TOM’, ‘reduced TOM’ and ‘excess TOM’ errors); and 3) mental state modalities on the MASC (e.g. emotions and cognitive mental state inferences).

Fraley and colleagues recommend carrying out multivariate analyses of the two attachment dimensions assessed by ECR-R (e.g. anxiety and avoidance) within a regression framework (e.g. Y = α + β(anxiety) + β(avoidance) + ε; see

http://internal.psychology.illinois.edu/~rcfraley/measures/ecrr.htm). Simultaneous inclusion of the two dimensions in a regression framework allows the results to be interpreted in a manner that is conceptually aligned with Bartholomew's four

attachment prototypes, without having to impose arbitrary cut-offs on the attachment dimensions to classify individuals as having secure, fearful, preoccupied or

dismissing attachment classifications As such, the relationships between attachment and total scores on the DERS and MASC were assessed using a three-step linear regression model. In the first step, care-leaver status and participants’ level of qualification were added to the model. In the second step, the two attachment

final step, separate interaction terms (group*anxiety and group*avoidance) were entered into the model to test whether the relationship between attachment and the dependent variable (DERS or MASC) differed in care-leavers compared to non care- leavers. Multivariate multiple regression was used to test the relationship between the two attachment dimensions and 1) errors categories of the MASC (e.g. ‘No TOM’, ‘reduced TOM’ and ‘excess TOM’ errors); and 2) mental state modalities on the MASC (e.g. cognitive and emotional), controlling for the confounding effects of care leaver status and level of qualifications.

Before completing regression analyses, scatterplots were inspected to ensure that the relationship between the independent and dependent variables was approximately linear. Additionally, statistical checks were carried out to ensure that all regression models met the assumptions relevant to regression analyses. Specifically, a histogram of the standardised residuals was inspected to ensure that they were approximately normally distributed; standardised residuals were plotted against predicted Y values to check for homoscedasticity; outliers were inspected and removed where necessary (utilising a cut of Cook’s Distance ≥ 1 and standardised residual ≥ 3, (Cook, 2000)). Finally, the variance inflation factor (adopting a cut off of ≥ 5; O’Brien, 2007) and condition index (adopting a cut off of ≥ 30; Kirkwood & Sterne, 2003) were inspected to identify issues of multi-collinearity.

2.5.2 Mediation analysis

Mediation analysis was used to further dissect the relationship between care-leaver status, MASC performance, difficulties with emotional regulation and romantic attachment. Mediation analyses are typically conducted when it is hypothesised that a significant amount of the variance in the relationship between an independent variable (Variable X; e.g. care-leaver status) and dependent variable (Variable Y; e.g.

difficulties with emotional regulation) is explained by a third variable (Variable M; e.g. erroneous social cognition). Put simply, X causes M, and M causes Y. Mediation models, illustrated in Figure 2.1, offer an opportunity to test such predictions.

In such models the total effect of X on Y is denoted as path c (See Figures 2.1a). Adding a mediator variable, M, allows the a coefficient for X to be calculated in a model predicting M from X, as well as the b coefficient derived from predicting Y

from M (Figure 2.2b). The c’ coefficient represents the direct effect of X on Y

controlling for a and b, whereas the product of a and b quantifies the indirect effect of

X on Y through M (Baron & Kenny, 1986). The indirect effect (or mediation effects)

represents the difference between the total and direct effect of X (e.g. ab = c – c’). More complex, multiple mediator models can be calculated by adding additional mediators, where the indirect effect through a given mediating variable is called the specific indirect effect (Hayes, 2009). This is conceptualised graphically in Figure 2.1(c), where M and W represent different potential mediator variables, with corresponding specific indirect effects labelled, a1b1 and a2b2, respectively.

a. Total effects of X on Y.

b. Simple mediation model representing the direct (c’) and indirect effects (ab) of X on Y.

c. Multiple mediator model, with specific (a1b1 and a2b2) and total (ab) indirect effects

Figure 2.1 (a) Total effect of X and Y model; (b) a simple mediation model; and (c) a multiple mediator model. Adapted from Hayes (2009)

X" Y" c" X" Y" c’" M" a" b" X" Y" M" a1" b1" c’" W" a2" b2"

In such a model the total effect is equal to the direct effects of X on Y, plus the sum of indirect affects though all possible mediators (e.g. c = c’ + a1b1 + a2b2).

Traditionally, mediation has been assessed using the ‘causal steps approach’

(Baron & Kenny, 1986). This involves completing a two-step hierarchical regression; first, testing the relationship between the independent and dependent variable; and then adding the proposed mediator to the model. Using this approach a mediation effect is indicated if both a and b paths are statistically significant and the relationship between X and Y becomes statistically less significant when M is added to the model (Baron & Kenny, 1986). However, this approach has been criticised for lacking power (Fritz & Mackinnon, 2007; Mackinnon et al., 2002) and failing to directly test for mediation (Hayes, 2009). Inferential approaches, such as the Sobel test (Sobel, 1982), have sought to address these shortcomings. However, they typically assume that the sampling distribution of the indirect effect is normal, an assumption that is frequently violated (Bollen & Stine, 1990; Lockwood & Mackinnon, 1997). Non-parametric bootstrapping approaches do not make this assumption and have been shown in simulation studies to be more powerful and to have more accurate overall Type-I error than the Sobel test and the causal steps approach, especially in small samples

(Williams & Mackinnon, 2008).

In this study, mediation analysis with bootstrapping was carried out in SPSS, utilising the custom PROCESS dialogue box available from: http://www.afhayes.com/spss- sas-and-mplus-macros-and-code.html. The non-parametric bootstrap approach directly tests the significance of the indirect (or mediating) effects. Empirical

representations of the sampling distribution of the indirect effect are obtained through bootstrapping, where k ‘mimic’ samples are obtained from the obtained data by repeatedly resampling the original sample with replacement. Once a sample size equivalent to the original n is sampled, a and b are estimated in the resampled dataset. The process is repeated k times, with a and b coefficients recorded in each sample. In this study, 10,000 bootstrap samples (k) were generated. The distribution of a and b coefficients in the permuted datasets serves as an empirical approximation of the sampling distribution and is used to generate bias-corrected percentile-based confidence intervals for indirect effects. Although, p-values are not computed

explicitly, the null hypothesis can be rejected at the p < .05 level of significance if the lower and upper bounds of the 95% confidence intervals do not cross zero. Multiple mediators can be analysed within the same model, producing estimates of specific and total indirect effects (i.e. the sum of all specific effects in the model) (Preacher & Hayes, 2008). Specific effects can be contrasted with one another to determine whether the indirect effect of X on Y through a proposed mediator (M) differs in size from specific indirect effect through another proposed mediator (W) (e.g. whether