This post is my fourth contribution to JustScience week.
Multiple regression is an empirical, data-driven approach for modelling the response of a single (dependent) variable from a suite of predictor (independent) variables. Mac Nally (2002) suggests that multiple regression is generally used for two purposes by ecologists and biologists; 1) to assess the amount of variance exhibited by the dependent variable that can be attributed to each predictor variable, and 2) to find the ‘best’ predictive model (the model that explains most total variance). Yesterday I discussed the use of logistic regression (a form of multiple regression) models for predictive purposes in Land Use/Cover Change (LUCC) studies. Today I’ll present some work on an explanatory use of these methods.
Finding a multivariate model that uses the ‘best’ set of predictors does not imply that those predictors will remain the ‘best’ when used independently of one another. Multi-collinearity between predictor variables means that the use of the ‘best’ subset of variables (i.e. model) to infer causality between independent and dependent variables provides little valid ‘explanatory power’ (Mac Nally, 2002). The individual coefficients of a multiple regression model can only be interpreted for direct effects on the response variable when the other predictor variables are held constant (James & McCulloch, 1990). The use of a model to explain versus its use to predict must therefore be considered (Mac Nally, 2000).
Hierarchical partitioning (HP) is a statistical method that provides explanatory power, rather than predictive. It allows the contribution of each predictor to the total explained variance of a model, both independently and in conjunction with the other predictors, to be calculated for all possible candidate models. The use of the HP method developed by Chevan and Sutherland (1991) by ecologists and biologists in their multivariate analyses was first suggested by Mac Nally (1996). More recently, the method has been extended to help provide the ability to statistically choose which variables to retain once they have been ranked for their predictive use (Mac Nally, 2002). Details of how HP works can be found here.
With colleagues, I examined the use of hierarchical partitioning for understanding LUCC in my PhD study area, leading to a recent publication in Ecosystems. We examined the difference in using two different land-cover (LC) classifications for the same landscape, one classification with 10 LC classes, another with four. Using HP we found that more coarse LC classifications (i.e. fewer LC classes) causes the joint effects of variables to suppress total variance explained in LUCC. That is, the combined effect of explanatory variables increases the total explained variance (in LUCC) in regression models using the 10-class LC classification, but reduces total explained variance in the dependent variable for four-class models.
We suggested that (in our case at least) this was because the aggregated nature of the four-class models means broad observed changes (for example from agricultural land to forested land) masks specific changes within the classes (for example from pasture to pine forest or from arable land to oak forest). These specific transitions may have explanatory variables (causes) that oppose one another for the different specific transitions, decreasing the explanatory power of models that use both variables to explain a single broader shift. By considering more specific transitions, the utility of HP for elucidating important causal factors will increase.
We concluded that a systematic examination of specific LUCC transitions is important for elucidating drivers of change, and is one that has been under-used in the literature. Specifically, we suggested hierarchical partitioning should be useful for assessing the importance of causal mechanisms in LUCC studies in many regions around the world.