2.3. Statistical analysis

The hypothesised mediation model was tested using structural equation modeling (e.g., Kline, 1998) as implemented in LISREL 8.8 (Jo"reskog & So"rbom, 1996). Simpler statistical techniques for the test of mediation, such as Baron and Kenny (1986) four-step regression procedure, assume that the mediator is measured with no error, and tend to produce unstable estimates when the sample is small and the variables are strongly intercorrelated. Structural equation modeling allows for controlling the measurement error of the mediator and of other study variables thus coping more efficiently with small sample size and multicollinearity.

Structural equation modeling requires defining a measurement model and a structural model. The measurement model is a confirmatory factor model in which each of the study variables is defined as a latent variable imperfectly measured by a set of directly measurable indicator variables. The relationships between a latent variable and its indicators are graphically represented as arrows heading from the latent variable to its indicators, meaning that the latent construct “produces” the indicators as its manifestations; the coefficients of these paths are equivalent to factor loadings. The structural model is a path model that specifies the relationships between latent variables. A relationship between two latent variables is graphically represented as an arrow heading from one latent variable to the other latent variables, meaning that the first variable “causes” or “predicts” the second one; the coefficients of these paths are equivalent to regression coefficients. Although the language of structural equation modeling is causal, when a model is fitted to cross-sectional (not-experimental and not-longitudinal) data, the structural paths should be prudently interpreted as indicative of causal relationships.

The three study variables (negative emotions, metacognitions, and PIU) were defined as latent variables. The two sub-scale scores of the HADS and the scale scores of the BPS were defined as the indicators of the latent variable negative emotions. The five sub-scale scores of the MCQ-30 were defined as the indicators of the latent variable metacognitions. Indicators for the latent variable PIU were created using parcelling as follows. We first fitted a single-factor Principal Components model to the item score of the IAT. The scree-plot indicated that a single-factor was sufficient, confirming that the scale is unidimensional. The item factor pattern coefficients were all positive. We then created parcels using the item factor pattern coefficients as a guide, following the “item-to-construct balance” method (e.g., Little et al., 2002 T.D. Little, W.A. Cunningham, G. Shahar and K.F. Widaman, To parcel or not to parcel?: Exploring the question, weighing the merits, Structural Equation Modeling 9 (2002), pp. 151–173. Full Text via CrossRefLittle, Cunningham, Shahar, & Widaman, 2002). We created two parcels of seven items and one of six items.

The indicators of the latent variables MCQ-30 and HADS are specific constructs, that is, facets of the underlying latent construct that are measured as sub-scales of an overall scale. Instead, the indicators of the latent variable PIU are unspecific constructs, that is, aggregate parcels of items that are designed to measure the same underlying construct, not different facets of the underlying construct. Three parcels were used instead of two because three indicators allow a considerably more efficient estimation of the PIU error variance, which is what the model is primarily intended to explain. Three parcels were used instead of four or more because, due to the small sample size, the addition of parameters would result in overall less stable estimation of the model.

Lisrel 8.8 employs a range of goodness-of-fit indices to estimate the adequacy of the proposed model under investigation. The most common statistic test for the assessment of the model fit is the Chi-square goodness of fit test (?2). This test estimates the discrepancies between the observed covariance matrices and those implied by the model. A non-significant Chi-square value indicates adequacy of a model. The Chi-square statistic assesses the absolute fit of the model to the data however it is sensitive to sample size and often inflates Type 1 error ([Bollen, 1989] and [Cohen, 1988]). Therefore it is necessary to use additional indices to evaluate the model fit. We have chosen the Root Mean Square Error of Approximation (RMSEA) which indicates the closeness of fit and is sensitive to the mis-specification of the measurement model (the factor loadings). Cut-off values close to .08 demonstrate adequate fit of the model, whereas between 0 and .05 indicate a good fit ([Browne and Cudeck, 1993] and [Hu and Bentler, 1999]). The relative Comparative Fit Index (CFI) was selected as an incremental fit index. The minimally acceptable fit is indicated by threshold values of .90 with values close to or above .95 indicating a good model fit (Hu & Bentler, 1999).

The analysis was conducted in two steps. In the first step, we defined three structural paths: (a) a path from negative emotions to PIU, (b) a path from negative emotions to metacognitions, and (c) a path from metacognitions to PIU. These paths represent the correlated antecedents of PIU which are consistent with a partial mediation process, in which negative emotions has both a direct effect on PIU and an indirect effect through the mediation of metacognitions.

In the second step of the analysis, we tested the model of the previous step but without the path (a) from negative emotions to PIU. The remaining two paths (b) and (c) represent the correlated antecedents of PIU which are consistent with a complete mediation process, in which negative emotions only has an indirect effect on PIU through the mediation of metacognitions. The comparison in goodness of fit between the models of the first and second step provided useful information on the nature and strength of the hypothesised mediation process.