An Application of Univariate Bootstrapping to DeFries-Fulker Regression Models

Abstract

The univariate bootstrap is a relatively recently developed version of the bootstrap (Lee & Rodgers, 1998). Currently, research on the univariate bootstrap has largely focused on individual, bivariate correlations. DeFries-Fulker (DF) analysis is a regression model used to estimate parameters in behavioral genetic models (DeFries & Fulker, 1985). It is appealing for its simplicity; however, it violates certain regression assumptions such as homogeneity of variance and independence of errors that make calculation of standard errors and confidence intervals problematic. Methods have been developed to account for these issues (Kohler & Rodgers, 2001), however the univariate bootstrap represents a unique means of doing so that is presaged by suggestions from previous DF research (e.g., Cherny, Cardon, Fulker, & DeFries, 1992). DF analysis also presents an ideal area for application of univariate bootstrapping in that DF analysis primarily relies on a bivariate (intraclass) correlation, however it provides a convenient stepping off point for potential future applications of univariate bootstrapping to more complex models.