Generalized linear mixed models(GLMMs)have been widely used in contemporary ecology studies.However,determination of the relative importance of collinear predictors(i.e.fixed effects)to response variables is one of th...Generalized linear mixed models(GLMMs)have been widely used in contemporary ecology studies.However,determination of the relative importance of collinear predictors(i.e.fixed effects)to response variables is one of the challenges in GLMMs.Here,we developed a novel R package,glmm.hp,to decompose marginal R2^(2)explained by fixed effects in GLMMs.The algorithm of glmm.hp is based on the recently proposed approach‘average shared variance’i.e.used for multivariate analysis.We explained the principle and demonstrated the use of this package by simulated dataset.The output of glmm.hp shows individual marginal R2^(2)s that can be used to evaluate the relative importance of predictors,which sums up to the overall marginal R2^(2).Overall,we believe the glmm.hp package will be helpful in the interpretation of GLMM outcomes.展开更多
This paper considers a widely used mixed effects model in repeated measures under het- eroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise diffe...This paper considers a widely used mixed effects model in repeated measures under het- eroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise differences are discussed. A generalized F-test has been proposed to test the equality of the fixed effects in the model, but simulation results for evaluating its performance have not been shown in the literature. Moreover, the generalized F-test cannot be used to deduce the simultaneous confidence intervals for all pair-wise differences of the fixed effects. The authors propose two new p-values to test the hypotheses of equality of the fixed effects and simultaneous confidence intervals of the differences of the effects based on the generalized pivotal quantities derived in this paper. The authors also compare the empirical performances of the proposed tests and the generalized F-test. The type I error rates and powers of these tests are evaluated using the Monte Carlo simulation. The simulation studies show that the generalized F-test does not perform well in terms of type I error rate under various sample size and parameter combinations. However, the type I error probabilities of the proposed tests are always close to the nominal value. It can also be seen that the simultaneous confidence intervals perform well.展开更多
基金This work was supported by the National Natural Science Foundation of China(32271551)the Metasequoia funding of Nanjing Forestry University.Conflict of interest statement.The authors declare that they have no conflict of interest.
文摘Generalized linear mixed models(GLMMs)have been widely used in contemporary ecology studies.However,determination of the relative importance of collinear predictors(i.e.fixed effects)to response variables is one of the challenges in GLMMs.Here,we developed a novel R package,glmm.hp,to decompose marginal R2^(2)explained by fixed effects in GLMMs.The algorithm of glmm.hp is based on the recently proposed approach‘average shared variance’i.e.used for multivariate analysis.We explained the principle and demonstrated the use of this package by simulated dataset.The output of glmm.hp shows individual marginal R2^(2)s that can be used to evaluate the relative importance of predictors,which sums up to the overall marginal R2^(2).Overall,we believe the glmm.hp package will be helpful in the interpretation of GLMM outcomes.
基金supported by the National Natural Science Foundation of China under Grant Nos.11126243 and 11071015Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality(PHR 201107123)School Scientific Found under Grant No. 101002207
文摘This paper considers a widely used mixed effects model in repeated measures under het- eroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise differences are discussed. A generalized F-test has been proposed to test the equality of the fixed effects in the model, but simulation results for evaluating its performance have not been shown in the literature. Moreover, the generalized F-test cannot be used to deduce the simultaneous confidence intervals for all pair-wise differences of the fixed effects. The authors propose two new p-values to test the hypotheses of equality of the fixed effects and simultaneous confidence intervals of the differences of the effects based on the generalized pivotal quantities derived in this paper. The authors also compare the empirical performances of the proposed tests and the generalized F-test. The type I error rates and powers of these tests are evaluated using the Monte Carlo simulation. The simulation studies show that the generalized F-test does not perform well in terms of type I error rate under various sample size and parameter combinations. However, the type I error probabilities of the proposed tests are always close to the nominal value. It can also be seen that the simultaneous confidence intervals perform well.
