Statistical Approaches for Highly Skewed Data: Evaluating Relations between Maltreatment and Young Adults’ Non-Suicidal Self-injury

Abstract

Objective: Clinical phenomena often feature skewed distributions with an overabundance of zeros. Unfortunately, empirical methods for dealing with this violation of distributional assumptions underlying regression are typically discussed in statistical journals with limited translation to applied researchers. Therefore, this investigation compared statistical approaches for addressing highly skewed data as applied to the evaluation of relations between child maltreatment and non-suicidal self-injury (NSSI). Method: College students (N = 2,651; 64.2% female; 85.2% nonwhite) completed the Child Abuse and Trauma Scale and the Functional Assessment of Self-Mutilation. Statistical models were applied to cross-sectional data to provide illustrative comparisons across predictions to a) raw, highly skewed NSSI outcomes, b) natural log, square-root, and inverse NSSI transformations to reduce skew, c) zero-inflated Poisson (ZIP) and negative-binomial zero-inflated (NBZI) regression models to account for both disproportionate zeros and skewness in the NSSI data, and d) the skew-t distribution to model NSSI skewness. Results: Child maltreatment was significantly and positively related to NSSI frequency in the raw, transformation, and zero-inflated models, but this relation was negative in the skew-t model. Conclusions: These findings highlight the importance of using zero-inflated models rather than transformation approaches to address data skew. Moreover, whereas the skew-t distribution has been used to model skewed non-clinical data, this study suggests that the skew-t approach may not be well-suited to address skewed clinical data.