Showing papers by "Pranab Kumar Sen published in 2017"

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

Abstract: Measuring the proportion of variance explained (R2) by a statistical model and the relative importance of specific predictors (semi-partial R2) can be essential considerations when building a parsimonious statistical model. The R2 statistic is a familiar summary of goodness-of-fit for normal linear models and has been extended in various ways to more general models. In particular, the generalized linear mixed model (GLMM) extends the normal linear model and is used to analyze correlated (hierarchical), non-normal data structures. Although various R2 statistics have been proposed, there is no consensus in statistical literature for the most sensible definition of R2 in this context. This research aims to build upon existing knowledge and definitions of R2 and to concisely define the statistic for the GLMM. Here, we derive a model and semi-partial R2 statistic for fixed (population) effects in the GLMM by utilizing the penalized quasi-likelihood estimation method based on linearization. We show that...