Deep Neural Networks for Detecting Statistical Model Misspecifications. The Case of Measurement Invariance

While in recent years a number of new statistical approaches have been proposed to model group differences with a different assumption on the nature of the measurement invariance of the instruments, the tools for detecting local specifications of these models have not been fully developed yet. The main type of local misspecification concerning comparability is the non-invariance of indicators (called also differential item functioning; DIF). Such non-invariance could arise from poor translations or significant cultural differences. In this study, we present a novel approach to detect such misspecifications using a Deep Neural Network (DNN). We compared the proposed model with the most popular traditional methods: modification indices (MI) and expected parameters change (EPC) indicators from the confirmatory factor analysis (CFA) modelling, logistic DIF detection, and sequential procedure introduced with the CFA alignment approach. Simulation studies show that proposed method outperformed traditional methods in almost all scenarios, or it was at least as accurate as the best one. We also provide an empirical example utilizing European Social Survey (ESS) data including items known to be miss-translated, which are correctly identified by our approach and DIF detection based on logistic regression. This study provides a strong foundation for the future development of machine learning algorithms for detection of statistical model misspecifications.