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

Soc Sci Res. 2015 Jan;49:264-87. doi: 10.1016/j.ssresearch.2014.08.018. Epub 2014 Sep 3.

Abstract

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.

Keywords: Inverse hyperbolic sine (IHS) transformation; Math achievement; Panel study of income dynamics; Wealth; YouthSave Ghana Experiment.

Publication types

  • Comparative Study

MeSH terms

  • Achievement*
  • Adolescent
  • Child
  • Child, Preschool
  • Educational Measurement*
  • Family Characteristics
  • Female
  • Ghana
  • Humans
  • Male
  • Mathematics*
  • Models, Statistical*
  • Quality of Life
  • Research Design*
  • Social Class*
  • Socioeconomic Factors
  • United States