Prior to the evaluation of the models, a parceling procedure was undertaken for the two attachment subscales. Parceling enables the researcher to create several measures (rather than one) of each of the latent variables thereby reducing measurement error (for discussion see Russell, Kahn, Spoth, and Altmaier, 1998). Parcels were created for each of the attachment variables (i.e., IWMs of self and of others) by factor analyzing each of the attachment subscales separately using maximum-likelihood extraction. Then, the items were rank-ordered on the basis of the magnitude of their factor loadings, and pairs of the highest and lowest items were successively assigned to each parcel. This equalizes the average loadings of each parcel such that the three parcels reflect the underlying construct to an equal degree. In the case of OC symptoms (PI-R) and cognitions (OBQ), the established subscales were used to create the corresponding latent variables . The latent variable of Sensitive Self was constructed using the four domain specific dichotomous variables (i.e., Morality, Job Competence, School Competence and Social Acceptability) previously shown to relate to OC symptoms and cognitions (see Chapter 5 of this thesis). The world view latent variable was created using the two components of the benevolence of world subscale (i.e., benevolence of world and benevolence of people).
Analysis was undertaken using the AMOS 6.0 program. Several studies have found that parameter estimates remain valid in SEM analysis even when the data are non-normal (see McDonald & Ho, 2002). Nevertheless, to increase normality, a square-root transformation of the Padua-Inventory (PI) subscales and the OBQ Important of thoughts subscale was undertaken. Following transformation, evaluation of the assumptions of normality of sampling distributions were satisfactory for all continuous indicator variables (i.e., critical ratio of skewness and kurtosis ranged from -2.33 to +2.54), except for the PI impulse of harm subscale showing somewhat higher skewness (critical ratio skewness = 5.45). Means, standard deviations, and zero-order correlations for the 19 measured variables are shown in Table 10.
In order to test the hypotheses the following analytic procedures were undertaken. Firstly, a confirmatory factor analysis was performed to develop a measurement model with an acceptable fit to the data. Secondly, multi-group analysis was conducted to confirm invariance in fit across the two samples. Finally, an evaluation of the several nested structural models was taken to find the best fitting model of the data. The following recommended indices were used in the present study (see Hu, & Bentler; 1999; Quintana, & Maxwell, 1999): the comparative fit index (CFI; values of .95 or greater are desirable), the standardized root-mean-square residual (SRMR; values of .08 or less are desirable), the root-mean-square error of approximation (RMSEA; values of .06 or less are desirable), and the chi-square difference test was used to compare nested models (significance indicates poorer fit).
Table 10. Means, Standard Deviations, and Correlations Among 19 Observed Variables
|1||PI-R chk||2.33 (0.07)|
|2||PI-R cont||.52||2.43 (0.06)|
|3||PI-R imph||.33||.24||0.91 (0.06)|
|4||PI-R obsh||.61||.50||.36||1.52 (0.06)|
|6||OBQ PR||.48||.35||.20||.35||.56||59.17 (1.02)|
|7||OBQ IT||.28||.32||.14||.36||.59||.42||5.53 (0.06)|
|12||Was BW||.14||.16||.13||.16||.09||.11||.14||.15||.13||.07||.21||3.09 (0.06)|
|13||Was BP||.21||.28||.22||.26||.25||.22||.22||.13||.15||.12||.16||.53||2.75 (0.05)|
|14||IWO 1||.19||.17||.26||.27||.06||.15||.07||.16||.13||.13||.18||.14||.08||21.75 (0.35)|
|15||IWO 2||.21||.22||.18||.25||.20||.19||.12||.18||.19||.17||.16||.15||.19||.81||19.77 (0.45)|
|16||IWO 3||.20||.18||.15||.20||.15||.16||.10||.10||.18||.11||.10||.17||.19||.67||.80||17.65 (0.40)|
|17||IWS 1||.17||.18||.26||.28||.30||.23||.32||.19||.20||.25||.11||.10||.13||.20||.16||.01||20.21 (0.39)|
|18||IWS 2||.25||.21||.25||.32||.30||.27||.34||.15||.19||.17||.11||.14||.14||.20||.16||.01||.79||21.54 (0.39)|
|19||IWS 3||.20||.23||.21||.32||.29||.27||.35||.24||.20||.16||.15||.22||.14||.19||.17||.01||.80||.79||24.81 (0.42)|
Note. N =273. Means and Standard deviations (in brackets) are shown on the diagonal. Absolute values of correlation greater than .11 were significant at p < .0.05. PI-R= Padua Inventory Revised; PI-R chk= PI-R checking subscale; PI-R cont= PI-R contamination subscale; PI-R imph= PI-R impulses of harm subscale; PI-R obsh= PI-R obsessions of harm subscale; OBQ=Obsessive Beliefs Questionnaire; OE= overestimation of threat/responsibility subscale; PR=perfectionism/uncertainty subscale; IT=importance of/need to control thoughts subscale ; SsSC=sensitive self social competence domain; SsJC=sensitive self job competence domain; SsSA=sensitive self social acceptability domain; SsMor=sensitive self morality domain; WasBW=World Assumption Scale benevolence of World subscale; WasBW=World Assumption Scale benevolence of people subscale; IWS 1, 2, 3 = item parcels from the Anxiety subscale of the Experiences in Close Relationships Scale; IMO 1, 2, 3 = item parcels from the Avoidance subscale of the Experiences in Close Relationships Scale.
A measurement model is the same as a confirmatory factor analysis and involves allowing the latent factors to correlate. The measurement model was estimated using the maximum-likelihood method. Test of the measurement model resulted in a good fit to the data, Χ² (137, N =273) = 185.69, p < .01, CFI = .98, SRMR = .04, and RMSEA =.04 (90% confidence interval [CI]: .02, .05). All of the loadings of the measured variables on the latent variables were statistically significant ( p < .001; see Table 18). Therefore, all of the latent variables appear to have been adequately measured by their respective indicators.
Table 11. Factor Loadings for the Measurement Model
|Measure and variable||b||SE||Z||B|
|OC related cognitions|
|Benevolence of World|
|IMW of Other|
|IMW of Self|
Note. N = 273. * p<.05; ** p<.01; *** p<.001; PI-R= Padua Inventory Revised; PI-R chk= PI-R checking subscale; PI-R cont= PI-R contamination subscale; PI-R imph= PI-R impulses of harm subscale; PI-R obsh= PI-R obsessions of harm subscale; OBQ=Obsessive Beliefs Questionnaire; OBQOE= OBQ overestimation of threat/responsibility subscale; OBQ PR= OBQ perfectionism/uncertainty subscale; OBQIT= OBQ importance of/need to control thoughts subscale; SsSC=sensitive self social competence domain; SsJC=sensitive self job competence domain; SsSA=sensitive self social acceptability domain; SsMor=sensitive self morality domain; WasBW=World Assumption Scale benevolence of World subscale; WasBW=World Assumption Scale benevolence of people subscale; IWMsS 1, 2, 3 = item parcels from the Anxiety subscale of the Experiences in Close Relationships Scale; IMWO 1, 2, 3 = item parcels from the Avoidance subscale of the Experiences in Close Relationships Scale; a=square root score were used
In addition, the correlations among the independent (exogenous) latent variables were statistically significant ( p < .05; see Table 19). Thus, this measurement model was used to test the theoretical structural model.
Table 12. Correlations Among Latent Variables for the Measurement Model
|2||OC related cognitions||1||.44**||.34***||.20**||.44***|
|4||Benevolence of World||1||.23**||.19**|
|5||IMW of Others||1||.13*|
|6||IMW of Self||1|
Note. N = 273. * p<.05; ** p<.01; *** p<.001; IWMs=internal working model.
A multiple group analysis was undertaken to ascertain whether any statistically significant differences were evident between the two data sets in the way they responded to the measurement model. We examined whether the patterns of factor loadings and the intercorrelations among the factors were invariant across groups (see Bollen, 1989). Two models (a freely estimated model and a constrained model) were used to determine whether the measurement model was the same across the two groups. The freely-estimated model does not restrict the estimation of factor loadings and intercorrelations among factors. The constrained model restricts the factor loadings and intercorrelations among factors such that they are identical values for the two data groups. Both models indicated acceptable fit indices and comparison of the freely estimated model [Χ² (274, N =273) = 368.73, p < .001, CFI = .96, SRMR = .04, RMSEA =.04 (90% confidence interval [CI]: .02, .05)] and the constrained model [Χ² (308, N =273) = 398.13, p < .001, CFI = .96, SRMR = .04, RMSEA =.03 (90% confidence interval [CI]: .02, .04)] resulted in a non-significant chi-square difference [ΔΧ² (34, N =273) = 129.40, p=.ns.]. This indicates that it is appropriate to assume that the measurement model was equivalent for both sample groups.
The 4 alternative models were then compared. The four alternative models were as follows: (a) Model A (see figure 5), the default model, included both direct and indirect paths of IWMs of self and IWMs of others on OC symptoms (b) Model B, the partially mediated IWMs of others model, constrained to zero the direct path between IWMs of self and OC symptoms, but allowed for both direct and indirect links between IWMs of others and OC symptoms; (c) Model C, the partially mediated IWMs of self model, constrained to zero the direct path between IWMs of other and OC symptoms, but allowed for both direct and indirect links between IWMs of self and OC symptoms and; (d) Model D, the fully mediated model constrained both direct links between attachment representations and OC symptoms to zero.
As can be seen in Table 13, all models showed a good fit to the data. The Χ² difference analysis between Model A (default model) and Models C was statistically significant (see Table 13) suggesting that the default model is superior. However, the differences between the default model and Models B and Model D were not statistically significant (a,b= Χ²(N=273)=0.95, p=ns; a,d= Χ²(N=273)=4.71, p=ns) suggesting that the most simple model (Model D) should be preferred (see Figure 5).
Table 13. Structural Paths, Chi-Square, and Fit Indices Among Different Models
|Path coefficients and fit indices||Model A||Model B||Model C||Model D|
|IWMs other||>>||Sensitive Self||.27*||.27*||.28**||.29**|
|IMW self||>>||Sensitive Self||.34**||.34**||.34**||.35**|
|IWMs other||>>||Sensitive Self||.18**||.18**||.19**||.19**|
|IWMs other||>>||OC related cognitions||.05||.13||.07||.07|
|Sensitive Self||>>||OC related cognitions||.34*||.25*||.24*||.24*|
|IMW self||>>||OC related cognitions||.25***||.31***||.30***||.30**|
|OC related cognitions||>>||OC related cognitions||.53***||.56***||.53***||.55***|
|IWMs other||>>||OC symptoms||.13*||.13*|
|IMW self||>>||OC symptoms||.08||.15|
|Standard ??||>>||OC symptoms||232.14||233.09*||236.16*||236.85*|
|CI for RAMSEA||.04 - .06||.04 - .06||.04 - .06||.04 - .06|
|ΔΧ² (df)||A and B:
|A and C:
|A and D:
Note. N = 273. Boldface type represents the best model; dashes indicate that the paths were constrained to zero. Model A= the default structural model (see Figure 5) in which every all hypothesized paths were estimated; Model B (the best fit model, see Figure 6) in which the direct path from IWMs of self to OC symptoms was constrained to zero; Model C= the partially mediated model in which the direct paths from IMW of other to OC symptoms was constrained to zero; Model D= the fully mediated model in which the paths from IMW of self and IMW of other to OC symptoms were constrained to zero; CFI=comparative fit index; RMSEA=root-mean-square error of approximation; CI=confidence interval; SRMR=standardized root-mean-square residual; IMO=internal working model of other; IMS=internal working model of self.
In addition, a multiple group comparison was conducted on the superior model (model D) to ascertain whether there was a significant difference between the two samples. Both models indicated acceptable fit indices and comparison of the freely estimated model [Χ² (280, N =273) = 385.64, p < .001, CFI = .95, SRMR = .04, RMSEA =.04 (90% confidence interval [CI]: .03, .05)] and the constrained model [Χ² (307, N =273) = 407.44, p < .001, CFI = .95, SRMR = .04, RMSEA =.04 (90% confidence interval [CI]: .03, .04)] resulted in a non-significant chi-square difference [ΔΧ² (27, N =273) = 23.58, p=.ns.] This suggests that Model D reflects the structure of both sample groups to an equivalent degree.
Finally, following recent recommendation regarding the interpretation of indirect effects (e.g., MacKinnon, Lockwood, Hoffman, West, & Sheets, 2002; MacKinnon, Lockwood, & Williams, 2004), a sampling with replacement, bias corrected, bootstrapping procedure was used for examination of all indirect effects in Model D. An important advantage of the bootstrapping procedure is that no assumptions about the shape of the sampling distribution of the indirect effect or its constituent paths are made. All such procedures assume that the distributions of the measured variables in the sample closely approximate the population distributions. The bootstrapping procedure generates an empirical approximation of the sampling distribution of a statistic from the available data. This approximation is than used to calculate p-values and construct confidence intervals (CIs).
Table 14 shows the indirect effects of the attachment dimensions, sensitive self construct and world view assumptions on OC symptoms and cognitions (all indirect effects are over and above the direct effects). As can be seen in table 14, both attachment dimensions show a significant indirect effect on OC symptoms and on OC cognitions. The results also indicated a statistically significant indirect effect of sensitive self and world view assumptions on OC symptoms.
Table 14. Bootstrapped Standardized Point Estimates and Confidence Intervals for the Total Indirect Effects (2000 Bootstrap Samples) predicting PI-R with Sensitive Self, OC related cognitions and World View assumptions as mediators
|Path coefficients and fit indices||Point Estimate||BC 95% CI|
|OC related cognitions||.11*||.04||.25|
|IMW of self|
|OC related cognitions||.12**||.04||.39|