This paper introduces the R package ordinalCont, which implements an ordinal regression framework for response variables which are recorded on a visual analogue scale (VAS). This scale is used when ...recording subjects' perception of an intangible quantity such as pain, anxiety or quality of life, and consists of a mark made on a linear scale. We implement continuous ordinal regression models for VAS as the appropriate method of analysis for such responses, and introduce smoothing terms and random effects in the linear predictor. The model parameters are estimated using constrained optimization of the penalized likelihood and the penalty parameters are automatically selected via maximization of their marginal likelihood. The estimation algorithm is shown to perform well, in a simulation study. Two examples of application are given: the first involves the analysis of pain outcomes in a clinical trial for laser treatment for chronic neck pain; the second is an analysis of quality of life outcomes in a clinical trial for chemotherapy for the treatment of breast cancer.
High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and ...scientific discoveries. The traditional idea of best subset selection methods, which can be regarded as a specific form of penalized likelihood, is computationally too expensive for many modern statistical applications. Other forms of penalized likelihood methods have been successfully developed over the last decade to cope with high dimensionality. They have been widely applied for simultaneously selecting important variables and estimating their effects in high dimensional statistical inference. In this article, we present a brief account of the recent developments of theory, methods, and implementations for high dimensional variable selection. What limits of the dimensionality such methods can handle, what the role of penalty functions is, and what the statistical properties are rapidly drive the advances of the field. The properties of non-concave penalized likelihood and its roles in high dimensional statistical modeling are emphasized. We also review some recent advances in ultra-high dimensional variable selection, with emphasis on independence screening and two-scale methods.
Frailty models are very useful for analysing correlated survival data, when observations are clustered into groups or for recurrent events. The aim of this article is to present the new version of ...anR package called frailtypack. This package allows to t Cox models andfour types of frailty models (shared, nested, joint, additive) that could be useful for several issues within biomedical research. It is well adapted to the analysis of recurrent events such as cancer relapses and/or terminal events (death or lost to follow-up). The approach uses maximum penalized likelihood estimation. Right-censored or left-truncated data are considered. It also allows stratication and time-dependent covariates during analysis.
This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency ...refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the covariance matrix, its inverse or its Cholesky decomposition. We study these three sparsity exploration problems under a unified framework with a general penalty function. We show that the rates of convergence for these problems under the Frobenius norm are of order (s n log p n /n) 1/2 , where s n is the number of nonzero elements, p n is the size of the covariance matrix and n is the sample size. This explicitly spells out the contribution of high-dimensionality is merely of a logarithmic factor. The conditions on the rate with which the tuning parameter λ n goet to 0 have been made explicit and compared under different penalties. As a result, for the L₁-penalty, to guarantee the sparsistency and optimal rate of convergence, the number of nonzero elements should be small: $s_{n}^{\prime}=O(p_{n})$ at most, among $O(p_{n}^{2})$ parameters, for estimating sparse covariance or correlation matrix, sparse precision or inverse correlation matrix or sparse Cholesky factor, where $s_{n}^{\prime}$ is the number of the nonzero elements on the off-diagonal entries. On the other hand, using the SCAD or hard-thresholding penalty functions, there is no such a restriction.
HIGH-DIMENSIONAL ADDITIVE MODELING Meier, Lukas; Van de Geer, Sara; Bühlmann, Peter
Annals of statistics,
12/2009, Volume:
37, Issue:
6B
Journal Article
Peer reviewed
Open access
We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for ...finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, for optimizing the penalized likelihood. Furthermore, we provide oracle results which yield asymptotic optimality of our estimator for high dimensional but sparse additive models. Finally, an adaptive version of our sparsity-smoothness penalized approach yields large additional performance gains.
Hidden semi-Markov models generalise hidden Markov models by explicitly modelling the time spent in a given state, the so-called dwell time, using some distribution defined on the natural numbers. ...While the (shifted) Poisson and negative binomial distribution provide natural choices for such distributions, in practice, parametric distributions can lack the flexibility to adequately model the dwell times. To overcome this problem, a penalised maximum likelihood approach is proposed that allows for a flexible and data-driven estimation of the dwell-time distributions without the need to make any distributional assumption. This approach is suitable for direct modelling purposes or as an exploratory tool to investigate the latent state dynamics. The feasibility and potential of the suggested approach is illustrated in a simulation study and by modelling muskox movements in northeast Greenland using GPS tracking data. The proposed method is implemented in the R-package PHSMM which is available on CRAN.
• Premise of the study: Land plants play an essential role in the evolution of terrestrial life. Their time of origin and diversification is fundamental to understanding the evolution of life on ...land. We investigated the timing and the rate of molecular evolution of land plants, evaluating the effects of different types of molecular data, including temporal information from fossils, and using different molecular clock methods.• Methods: Ages and absolute rates were estimated independently with two substitutionally different data sets: a highly conserved 4-gene data set and matK, a fast-evolving gene. The vascular plant backbone and the crown nodes of all major lineages were calibrated with fossil-derived ages. Dates and absolute rates were estimated while including or excluding the calibrations and using two relaxed clocks that differ in their implementation of temporal autocorrelation.• Key results: Land plants diverged from streptophyte alga 912 (870–962) million years ago (Mya) but diversified into living lineages 475 (471–480) Mya. Ages estimated for all major land-plant lineages agree with their fossil record, except for angiosperms. Different genes estimated very similar ages and correlated absolute rates across the tree. Excluding calibrations resulted in the greatest age differences. Different relaxed clocks provided similar ages, but different and uncorrelated absolute rates.• Conclusions: Whole-genome rate accelerations or decelerations may underlie the similar ages and correlated absolute rates estimated with different genes. We suggest that pronounced substitution rate changes around the angiosperm crown node may represent a challenge for relaxed clocks to model adequately.
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