Transforming wealth: Using the inverse hyperbolic sine (IHS) and splines to predict youth’s math achievement

• Published in: Social science research 2015-01, Vol.49, p.264-287
• Main Authors: Friedline, Terri, Masa, Rainier D., Chowa, Gina A.N.
• Format: Article
• Language: English
• Subjects: Academic achievement; Achievement; Adolescent; Child; Child, Preschool; Children & youth; Debt; Educational Measurement; Family Characteristics; Female; Ghana; History of medicine and histology; Households; Humans; Inverse hyperbolic sine (IHS) transformation; Male; Math achievement; Mathematics; Mathematics education; Models, Statistical; Panel study of income dynamics; Quality of Life; Research Design; Social Class; Social research; Socioeconomic Factors; U.S.A; United States; Wealth; Well-being; Youth; YouthSave Ghana Experiment
• ISSN: 0049-089X; 1096-0317
• DOI: 10.1016/j.ssresearch.2014.08.018

•The inverse hyperbolic sine (IHS) is presented as a way to transform wealth data.•IHS is compared to natural log and categorical transformations of wealth data.•IHS performs similarly in models predicting youth’s math achievement.•Non-linearity and accumulation thresholds exist with IHS transformation and splines.•Wealth accumulation thresholds relate to improved math scores. The natural log and categorical transformations commonly applied to wealth for meeting the statistical assumptions of research may not always be appropriate for adjusting for skewness given wealth’s unique properties. Finding and applying appropriate transformations is becoming increasingly important as researchers consider wealth as a predictor of well-being. We present an alternative transformation—the inverse hyperbolic sine (IHS)—for simultaneously dealing with skewness and accounting for wealth’s unique properties. Using the relationship between household wealth and youth’s math achievement as an example, we apply the IHS transformation to wealth data from US and Ghanaian households. We also explore non-linearity and accumulation thresholds by combining IHS transformed wealth with splines. IHS transformed wealth relates to youth’s math achievement similarly when compared to categorical and natural log transformations, indicating that it is a viable alternative to other transformations commonly used in research. Non-linear relationships and accumulation thresholds emerge that predict youth’s math achievement when splines are incorporated. In US households, accumulating debt relates to decreases in math achievement whereas accumulating assets relates to increases in math achievement. In Ghanaian households, accumulating assets between the 25th and 50th percentiles relates to increases in youth’s math achievement.