Final Report to the EPA on Multilevel Models for Generalization

Multilevel statistical models are characterized by analyses undertaken simultaneously at different levels of aggregation or spatial/temporal scales. For example, one might study several reaches in a stream for a number of different research sites. Or one might study several transects in each of several forests. The basic idea in multilevel models is to have a regression equation characterizing relationships at the smaller, or micro, level and then have one or more of the regression coefficients at the micro level a function of predictors at the macro level. At the micro level, for instance, taxa richness may be a function of stream velocity (and other things). Then at the macro level, the regression coefficient linking stream velocity to taxa richness may be a function of proximity of the stream to land used for agriculture. Thus, one can address how the relationship between stream velocity and taxa richness varies (or not) in different locations, here with locale characterized by proximity to land use for agriculture. That is, one can learn when to generalize over sites and when not to generalize over sites. One can also learn how different temporal and/or spatial scales are linked