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回归模型中随机效应的简单检验AI 解读

Testing that random effects are zero is difficult, because the null hypothesis restricts the corresponding variance parameter to the edge of the feasible parameter space. In the context of generalized linear mixed models, this paper exploits the link between random effects and penalized regression to develop a simple test for a zero effect. The idea is to treat the variance components not being tested as fixed at their estimates and then to express the likelihood ratio as a…

扩展广义可加模型中平滑分量的p值AI 解读

The problem of testing smooth components of an extended generalized additive model for equality to zero is considered. Confidence intervals for such components exhibit good across-the-function coverage probabilities if based on the approximate result ⁠, where f is the vector of evaluated values for the smooth component of interest and Vf is the covariance matrix for f according to the Bayesian view of the smoothing process. Based on this result, a Wald-type test of f=0 is…

多重二次惩罚下的建模与平滑参数估计AI 解读

Summary Penalized likelihood methods provide a range of practical modelling tools, including spline smoothing, generalized additive models and variants of ridge regression. Selecting the correct weights for penalties is a critical part of using these methods and in the single-penalty case the analyst has several well-founded techniques to choose from. However, many modelling problems suggest a formulation employing multiple penalties, and here general methodology is lacking.…