Analysis of proportions
Maarten L. BuisSAGE Research Methods Foundations: An Encyclopedia (forthcoming)
This entry discusses the challenges that proportions pose when including them in an analysis, and solutions that have been proposed to those challenges. Analyzing a single proportion as a dependent variable is hard because the upper and lower bound of the proportion will result in non-linearity of effects. Moreover, these bounds will typically result in heteroscedasticity. Multiple proportions that add to one as dependent variables have the additional challenge that these variables are mutually dependent; if you spent an extra minute a day watching television, then that minute cannot be spent on other activities. So the proportions tend to be negatively correlated. The mutual dependence of proportions also poses a challenge when proportions are added as explanatory variables. Effects of explanatory variables are often interpreted as the expected change in the explained variable for a unit change in the explanatory variable while keeping all other variables constant. This latter part is logically impossible when adding multiple proportions as explanatory variables.