Collections > Electronic Theses and Dissertations > Fungible Simple Slopes in Moderated Regression

This thesis concerns an application of fungible weights methodology to the question of moderation in least squares (LS) regression. Fungible weights are weights that produce predictions correlated to a given degree with the LS predictions and scaled so that they produce minimal sum of squared errors. Waller (2008) proposes that fungible weights be used to determine if LS weights should be interpreted as representing relative contributions of predictors or only as a composite effect. In this project, data were simulated from regression models with a variety of structures and fungible weights were generated for each dataset. For each set of fungible weights, corresponding simple slopes were computed. The variability of fungible weights and simple slopes across samples was examined, as well as the conditions under which fungible solutions suggest a qualitatively different regression model. Factors that were varied include the coefficient of determination of the model, the correlation of the predictors, the relative weights of predictors, the presence of the interaction, and the sample size. Tentative recommendations of conditions for which sample fungible solutions give good approximations of population fungible solutions are made, and a simple bootstrapping method for generating confidence sets around fungible weights is proposed.