One approach to variance partitioning is to use what has become known as **hierarchical regression analysis**, which has also been called *incremental partitioning of variance*. The idea is pretty simple: You dump all the variables in your study into a regression model. You get R^{2} for that model. You then run the model again, adding your variable of interest. If your new variable contributes some new explanatory power, then R^{2} will rise. (Any time two models are compared, you can examine the change in R^{2}. This “change” is often footnoted using the Greek letter delta: ΔR^{2}). The logic is that such a rise indicates the “independent contribution” of that variable. Pedhazur (1997) warns against such an interpretation (p. 245). He does suggest, however, that such as method is perfectly fine when the researcher wants to examine the effect of the one variable while controlling for the effects of the others (we’ll consider the idea of statistical control in a later section). Simply put, *incremental partitioning of variance is not a valid way of determining the relative importance of a variable*.

Last Modified: 02/14/2019