Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

/pdf/fitting-linear-mixed-effects-models-using-lme4-4zzrpoy9lh.pdf

Fitting Linear Mixed-Effects Models Using lme4

In comparative high-throughput sequencing assays, a fundamental task is the analysis of count data, such as read counts per gene in RNA-seq, for evidence of systematic changes across experimental conditions. Small replicate numbers, discreteness, large dynamic range and the presence of outliers require a suitable statistical approach. We present DESeq2, a method for differential analysis of count data, using shrinkage estimation for dispersions and fold changes to improve stability and interpretability of estimates. This enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression. The DESeq2 package is available at http://www.bioconductor.org/packages/release/bioc/html/DESeq2.html
 .

/pdf/moderated-estimation-of-fold-change-and-dispersion-for-rna-3ywnbkcan0.pdf

Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2

Summary: It is expected that emerging digital gene expression (DGE) technologies will overtake microarray technologies in the near future for many functional genomics applications. One of the fundamental data analysis tasks, especially for gene expression studies, involves determining whether there is evidence that counts for a transcript or exon are significantly different across experimental conditions. edgeR is a Bioconductor software package for examining differential expression of replicated count data. An overdispersed Poisson model is used to account for both biological and technical variability. Empirical Bayes methods are used to moderate the degree of overdispersion across transcripts, improving the reliability of inference. The methodology can be used even with the most minimal levels of replication, provided at least one phenotype or experimental condition is replicated. The software may have other applications beyond sequencing data, such as proteome peptide count data. Availability: The package is freely available under the LGPL licence from the Bioconductor web site (http://bioconductor.org).

http://dmrocke.ucdavis.edu/Class/BST226.2014.Winter/edgeR%20bioinformatics%202010.pdf

edgeR: a Bioconductor package for differential expression analysis of digital gene expression data.

limma is an R/Bioconductor software package that provides an integrated solution for analysing data from gene expression experiments. It contains rich features for handling complex experimental designs and for information borrowing to overcome the problem of small sample sizes. Over the past decade, limma has been a popular choice for gene discovery through differential expression analyses of microarray and high-throughput PCR data. The package contains particularly strong facilities for reading, normalizing and exploring such data. Recently, the capabilities of limma have been significantly expanded in two important directions. First, the package can now perform both differential expression and differential splicing analyses of RNA sequencing (RNA-seq) data. All the downstream analysis tools previously restricted to microarray data are now available for RNA-seq as well. These capabilities allow users to analyse both RNA-seq and microarray data with very similar pipelines. Second, the package is now able to go past the traditional gene-wise expression analyses in a variety of ways, analysing expression profiles in terms of co-regulated sets of genes or in terms of higher-order expression signatures. This provides enhanced possibilities for biological interpretation of gene expression differences. This article reviews the philosophy and design of the limma package, summarizing both new and historical features, with an emphasis on recent enhancements and features that have not been previously described.

/pdf/limma-powers-differential-expression-analyses-for-rna-4yl7ae3arh.pdf

limma powers differential expression analyses for RNA-sequencing and microarray studies

In comparative high-throughput sequencing assays, a fundamental task is the analysis of count data, such as read counts per gene in RNA-Seq data, for evidence of systematic changes across experimental conditions. Small replicate numbers, discreteness, large dynamic range and the presence of outliers require a suitable statistical approach. We present DESeq2, a method for differential analysis of count data. DESeq2 uses shrinkage estimation for dispersions and fold changes to improve stability and interpretability of the estimates. This enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression and facilitates downstream tasks such as gene ranking and visualization. DESeq2 is available as an R/Bioconductor package.

/pdf/moderated-estimation-of-fold-change-and-dispersion-for-rna-59glcgpwlk.pdf

When creating the R Matrix package, which provides access to the Fortran Lapack and BLAS3 routines, we patterned the functions after the corresponding S-PLUS library but chose a completely dierent implementation. We based the R implementation on the lapack++ classes that provide C++ wrappers for the Lapack code. There are several advantages to using C++ instead of C for code that will be called from R. In particular it is possible to encapsulate some of the Slanguage class structure in the C++ classes. There are also disadvantages to using C++. We discuss these for the particular example of the Matrix package and also describe a more general approach of reecting basic R object types in C++ classes.

/pdf/c-classes-for-r-objects-3wziw8swst.pdf

C++ Classes for R Objects

: As greater computing power becomes routinely available to researchers, analyses based on Bayesian or likelihood methods become easier to perform, especially since the increase in computing power has been accompanied by development of inventive statistical algorithms for inference. We consider here the nonlinear regression model but these approaches to inference are applicable in more general circumstances and we feel the comparisons will remain useful. Several methods can be used for inference in nonlinear regression: propagation of errors, likelihood profiles, approximate marginal likelihoods and posteriors, and Monte Carlo methods such as importance sampling, and the Gibbs sampler. These methods vary in computing intensity and in their ability to handle poorly conditioned situations. Furthermore, since some of these methods have only been recently developed, it is not easy for the practitioner to compare them and choose between them because they are not widely implemented. We demonstrate the respective merits of these methods in a small but instructive example. Nonlinear Models; Profile Likelihood; Importance Sampling; Gibbs Sampler, Approximate Marginalization.

A Comparison of Approaches to Inference for Nonlinear Models

Grace Wahba (nee Goldsmith, born August 3, 1934), I. J. Schoenberg-Hilldale Professor of Statistics at the University of Wisconsin-Madison (Emerita), is a pioneer in methods for smoothing noisy data. Her research combines theoretical analysis, computation and methodology motivated by innovative scientific applications. Best known for the development of generalized cross-validation (GCV), the connection between splines and Bayesian posterior estimates, and “Wahba’s problem,” she has developed methods with applications in demographic studies, machine learning, DNA microarrays, risk modeling, medical imaging and climate prediction. Grace grew up in the Washington, DC area and New Jersey, and graduated from Montclair High School. She was educated at Cornell (B.A. 1956), University of Maryland, College Park (M.A. 1962) and Stanford (Ph.D. 1966), and worked in industry for several years before receiving her doctorate in 1966 and settling in Madison in 1967. Although holding several visiting appointments, she has made Madison her home for over 50 years. She is the author of Spline Models for Observational Data which has garnered more than 8000 citations. Grace is treasured as an academic advisor and has mentored 39 Ph.D. students that have resulted in more than 330 academic descendants. She was elected to the United States National Academy of Sciences in 2000 and received an honorary degree of Doctor of Science from the University of Chicago in 2007. Wahba is a Fellow of several academic societies including the American Academy of Arts and Sciences, the American Association for the Advancement of Science, the American Statistical Association and the Institute of Mathematical Statistics. Over the years, she has received a selection of notable awards in the statistics community: R. A. Fisher Lectureship (2014), Gottfried E. Noether Senior Researcher Award (2009), Committee of Presidents of Statistical Societies Elizabeth Scott Award (1996) and the first Emanuel and Carol Parzen Prize for Statistical Innovation (1994).

/pdf/a-conversation-with-grace-wahba-kq0t55h020.pdf

Douglas M. Bates

Papers

C++ Classes for R Objects

A Comparison of Approaches to Inference for Nonlinear Models

A Conversation with Grace Wahba

Response to Beal and Sheiner

Probability and Statistics with R by Maria Dolores Ugarte, Ana F. Militino, Alan T. Arnholt