An R² statistic for fixed effects in the generalized linear mixed model

Computation of $R_{{\beta }^{\ast }}^2$ in SAS and R

Proc Glimmix in SAS [30 SAS Institute Inc., Cary, NC, 2003. Available at http://www.sas.com/. [Google Scholar]] fits GLMMs using PQL as the default estimation technique. The procedure is based on a more general macro, %Glimmix, which applies the PQL algorithm by performing repeated calls to Proc Mixed. Our procedure to calculate $R_{{\beta }^{\ast }}^2$ in SAS utilizes this macro, saving output parameters from a full model contrast statement upon the convergent iteration of the PQL algorithm. The approximate F-statistic and denominator degrees of freedom from the pseudo linear mixed model are then used to compute $R_{{\beta }^{\ast }}^2$. The method outlined here is implemented in a SAS macro available in [18 B. Jaeger, Software in SAS and R to compute $R^2$ for fixed effects in the linear and generalized linear mixed model. Available at https://github.com/bcjaeger/R2FixedEffectsGLMM/. [Google Scholar]].

The r2glmm package computes $R_{{\beta }^{\ast }}^2$ for the LMM using the Kenward-Roger approach as well as the method proposed by Nakagawa and Schielzeth [17 U. Halekoh and S. Højsgaard, A Kenward–Roger approximation and parametric bootstrap methods for tests in linear mixed models–the R package pbkrtest, J. Statist. Softw. 59 (2014), pp. 1–30, http://www.jstatsoft.org/v59/i09/. doi: 10.18637/jss.v059.i09[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. In addition to semi-partial R squared values, the package supplies confidence limits. As a note of caution, the authors of the pbkrtest package cannot guarantee that the results agree with other implementations of the Kenward–Roger approach. Therefore, it is highly encouraged to compare $R_{{\beta }^{\ast }}^2$ values calculated with R to corresponding calculations in SAS when performing inference. We recommend favoring results from SAS.