To check for the adequacy of running EFA on the data, we used Bartlett’s test of sphericity and the KMO measure of sampling adequacy. To determine the initial number of factors, Horn´s parallel analysis was used. The initial solution was generated using least-squares factors extraction with Oblimin rotation due to potential correlations between factors.
The second subsample was then used to run a CFA with WLSMV estimation. An exhaustive assessment of the overall fit of the EFA model was conducted, including as parameters for fit estimation the comparative fit index (CFI), the Tucker-Lewis Index (TLI), and the root mean square error of approximation (RMSEA). CFI and TLI values of 0.95 or higher were considered acceptable, while RMSEA values of lower than 0.05 were considered as good and lower than 0.08 as acceptable.
Results
An overall KMO value of 0.83 showed good sampling adequacy, and Bartlett's test of sphericity was significant (Chi-square(66)=2209.46, p<0.001), indicating adequacy of the correlation matrix; together, these confirmed the dataset's appropriateness for factor analysis.
We also conducted analyses on both 2- and 3- factor solutions, using polychoric correlation matrix, weighted least squares, oblimin rotation. The two-factor solution explained 55% of variance. There were no items showing cross-loading above 0.3, and the correlation coefficient for the two factors was 0.22. The 3-factor solution explained 63% of the variance, however, the solution included some cross-loadings [ghq3]. Factor correlation coefficients were 0.12 (factors 1 / 2), 0.41 (factors 1 / 3), and 0.30 (factors 2 / 3).
We further tested a recent model from the literature that used ESEM on a large sample, to see how our solutions compared. This model showed improved goodness-of-fit indices. Besides, we determined the modified three-factor solution as the best solution. The reliability of the modified 3-factor solution showed acceptable alphas and omegas for all subscales (f1: α = 0.82, ω = 0.82; f2: α = 0.81, ω = 0.81; f3: α = 0.73, ω = 0.74).
Results for measurement invariance for the modified three-factor model show an acceptable fit (RMSEA=0.074; CFI=0.964), thus corroborating configural invariance. Although the absolute metric and scalar invariance were rejected using scaled difference chi-square tests, both were supported using the relative indices of differences in CFI (-0.004 and 0.002) and RMSEA (0.000 and -0.003).
In sum, our results showed the multidimensionality of the instrument, with a three-factor model; invariance was demonstrated considering length of imprisonment; a factor structure similar to other studies was demonstrated: anxiety, social dysfunction and loss of confidence. Since many prison systems face challenges on the mental health of both incarcerated individuals, we think that testing the suitability of GHQ-12 might be a positive contribution to a more humane, effective reintegration.
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