A maximum likelihood approach for asymmetric non-normal data using a transformational measurement model

A transformational measurement model for structural equation modeling (SEM) of asymmetric non-normal data is proposed. This measurement model aligns with the expectation-maximization (EM) algorithm of the maximum likelihood estimation (MLE) method, creating adaptability to data that deviate from normality. Distinctive properties of the connection of the measurement model and EM algorithm are maintenance of the normality assumption, which is at the core of EM algorithm, and applicability to asymmetric non-normality of observed data mediated by distortion coefficients. An evaluation using a mixture of normal and severely asymmetric non-normal data analyzed by MLE for asymmetric non-normal data (MLE for ASN) demonstrated efficiency of the model. Comparisons with robust DWLS and WLS yielded better fit results under MLE for ASN estimation.