mplot: An R Package for Graphical Model Stability and Variable Selection Procedures

The mplot package provides an easy to use implementation of model stability and variable inclusion plots (M\"uller and Welsh 2010; Murray, Heritier, and M\"uller 2013) as well as the adaptive fence (Jiang, Rao, Gu, and Nguyen 2008; Jiang, Nguyen, and Rao 2009) for linear and generalised linear models. We provide a number of innovations on the standard procedures and address many practical implementation issues including the addition of redundant variables, interactive visualisations and approximating logistic models with linear models. An option is provided that combines our bootstrap approach with glmnet for higher dimensional models. The plots and graphical user interface leverage state of the art web technologies to facilitate interaction with the results. The speed of implementation comes from the leaps package and cross-platform multicore support.Comment: 28 pages, 9 figure

The Performance of the Turek-Fletcher Model Averaged Confidence Interval

We consider the model averaged tail area (MATA) confidence interval proposed by Turek and Fletcher, CSDA, 2012, in the simple situation in which we average over two nested linear regression models. We prove that the MATA for any reasonable weight function belongs to the class of confidence intervals defined by Kabaila and Giri, JSPI, 2009. Each confidence interval in this class is specified by two functions b and s. Kabaila and Giri show how to compute these functions so as to optimize these intervals in terms of satisfying the coverage constraint and minimizing the expected length for the simpler model, while ensuring that the expected length has desirable properties for the full model. These Kabaila and Giri "optimized" intervals provide an upper bound on the performance of the MATA for an arbitrary weight function. This fact is used to evaluate the MATA for a broad class of weights based on exponentiating a criterion related to Mallows' C_P. Our results show that, while far from ideal, this MATA performs surprisingly well, provided that we choose a member of this class that does not put too much weight on the simpler model

Designing experiments for an application in laser and surface Chemistry

We consider the design used to collect data for a Second Harmonic Generation (SHG) experiment, where the behaviour of interfaces between two phases, for example the surface of a liquid, is investigated. These studies have implications in surfactants, catalysis, membranes and electrochemistry. Ongoing work will be described in designing experiments to investigate nonlinear models used to represent the data, relating the intensity of the SHG signal to the polarisation angles of the polarised light beam. The choice of design points and their effect on parameter estimates is investigated. Various designs and the current practice of using equal-spaced levels are investigated, and their relative merits compared on the basis of the overall aim of the chemical study

Estimating the Retransformed Mean in a Heteroscedastic Two-Part Model

Two distribution free estimators are proposed to estimate the mean of a dependent variable after fitting a semiparametric two-part heteroscedastic regression model to a transformation of the dependent variable. We show that the proposed estimators are consistent and have asymptotic normal distributions. We also compare their finite-sample performance in a simulation study. Finally, we illustrate the proposed methods in a real-world example of predicting in-patient health care costs

Hierarchical selection of fixed and random effects in generalized linear mixed models

In many applications of generalized linear mixed models(GLMMs), there is a hierarchical structure in the effects that needs to be taken into account when performing variable selection. A prime example of this is when fitting mixed models to longitudinal data, where it is usual for covariates to be included as only fixed effects or as composite (fixed and random) effects. In this article, we propose the first regularization method that can deal with large numbers of candidate GLMMs while preserving this hierarchical structure: CREPE (Composite Random Effects PEnalty) for joint selection in mixed models. CREPE induces sparsity in a hierarchical manner, as the fixed effect for a covariate is shrunk to zero only if the corresponding random effect is or has already been shrunk to zero. In the setting where the number of fixed effects grow at a slower rate than the number of clusters, we show that CREPE is selection consistent for both fixed and random effects, and attains the oracle property. Simulations show that CREPE outperforms some currently available penalized methods for mixed models

Peter Hall on Extremes: Research, Teaching And Supervision

We examine Peter Hall's early research, undergraduate teaching, and PhD supervision, using the theme of extreme order statistics to highlight interesting aspects of these activities. Focusing on this period allows us to see Peter when, like all academics in the early part of their careers, he was becoming an academic and still establishing himself. That he succeeded so greatly and rapidly began to make the many remarkable contributions that adorn his distinguished career, makes this early, formative stage particularly interesting to explore

Finite sample properties of the Buckland-Burnham-Augustin confidence interval centered on a model averaged estimator

We consider the confidence interval centered on a frequentist model averaged estimator that was proposed by Buckland, Burnham & Augustin (1997). In the context of a simple testbed situation involving two linear regression models, we derive exact expressions for the confidence interval and then for the coverage and scaled expected length of the confidence interval. We use these measures to explore the exact finite sample performance of the Buckland-Burnham-Augustin confidence interval. We also explore the limiting asymptotic case (as the residual degrees of freedom increases) and compare our results for this case to those obtained for the asymptotic coverage of the confidence interval by Hjort & Claeskens (2003).Comment: Journal of Statistical Planning and Inference (2019