Analysis of Proportions


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 nonlinearity 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.

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