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Matthew Kramer

Abstract

The R2 statistic, when used in a regression or ANOVA context, is appealing because it summarizes how well the model explains the data in an easy-to-understand way. R2 statistics are also useful to gauge the effect of changing a model. Generalizing R2 to mixed models is not obvious when there are correlated errors, as might occur if data are georeferenced or result from a designed experiment with blocking. Such an R2 statistic might refer only to the explanation associated with the independent variables, or might capture the explanatory power of the whole model. In the latter case, one might develop an R2 statistic from Wald or likelihood ratio statistics, but these can yield different numeric results. Example formulas for these generalizations of R2 are given. Two simulated data sets, one based on a randomized complete block design and the other with spatially correlated observations, demonstrate increases in R2 as model complexity increases, the result of modeling the covariance structure of the residuals.

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Apr 24th, 3:00 PM

R2 STATISTICS FOR MIXED MODELS

The R2 statistic, when used in a regression or ANOVA context, is appealing because it summarizes how well the model explains the data in an easy-to-understand way. R2 statistics are also useful to gauge the effect of changing a model. Generalizing R2 to mixed models is not obvious when there are correlated errors, as might occur if data are georeferenced or result from a designed experiment with blocking. Such an R2 statistic might refer only to the explanation associated with the independent variables, or might capture the explanatory power of the whole model. In the latter case, one might develop an R2 statistic from Wald or likelihood ratio statistics, but these can yield different numeric results. Example formulas for these generalizations of R2 are given. Two simulated data sets, one based on a randomized complete block design and the other with spatially correlated observations, demonstrate increases in R2 as model complexity increases, the result of modeling the covariance structure of the residuals.