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The paper proposes a novel model assessment paradigm aiming to addressshortcoming of posterior predictive $p-$values, which provide the defaultmetric of fit for Bayesian structural equation modelling (BSEM). The modelframework of the paper focuses on the approximate zero approach, according towhich parameters that would before set to zero (e.g. factor loadings) are nowformulated to be approximate zero via informative priors (Muthen andAsparouhov, 2012). The introduced model assessment procedure monitors theout-of-sample predictive performance of the fitted model, and together with alist of guidelines we provide, one can investigate whether the hypothesisedmodel is supported by the data. We incorporate scoring rules andcross-validation to supplement existing model assessment metrics for BayesianSEM. The proposed tools can be applied to models for both categorical andcontinuous data. The modelling of categorical and non-normally distributedcontinuous data is facilitated with the introduction of an item-individualrandom effect that can also be used for outlier detection. We study theperformance of the proposed methodology via simulations. The factor model forcontinuous and binary data is fitted to data on the `Big-5' personality scaleand the Fagerstrom test for nicotine dependence respectively.

Model Assessment for a Generalised Bayesian Structural Equation Model