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

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1977.tb01600.x

Maximum likelihood from incomplete data via the EM algorithm

Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Deep Learning

Meta-Analysis in Clinical Trials*

We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

/pdf/latent-dirichlet-allocation-4gmscb06en.pdf

Latent dirichlet allocation

On estimating the causal effects of DNR orders.

Publisher Summary This chapter explores those statistical issues that arise from missing data and uses current population surveys to illustrate these ideas. Many basic problems are introduced via simple examples. The chapter presents the taxonomy of these methods. The explicit modeling approach is a flexible but principled way to proceed in practice. The chapter discusses the computational methods for the analysis of incomplete data. It also outlines various methods for handling incomplete data and describes the modeling approach to incomplete data. A principled approach to the problem of missing data in large databases requires a plausible model for the missing data mechanism and estimation procedures that remove or minimize biases introduced by the incompleteness of the data.

Missing data in large data sets

For estimating causal effects of treatments, randomized experiments are appropriately considered the gold standard, although they are often infeasible for a variety of reasons. Nevertheless, nonran ...

Outcome-free Design of Observational Studies: Peer Influence on Smoking

This document presents the results of an investigation into the prediction of first-year average in graduate management school based on undergraduate grade point average and GMAT scores. It is found that the use of a single prediction equation for both black students and white students tends to produce over predictions of the former's graduate school performance. Substantial effort is devoted to developing a prediction system which takes into account ethnic status. This approach is made practicable by employing the empirical Bayes estimation paradigm, and the new predictions represent a substantial improvement over the ones based on a single equation for both races.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/j.2333-8504.1981.tb01260.x

Donald B. Rubin

Papers

On estimating the causal effects of DNR orders.

Missing data in large data sets

Outcome-free Design of Observational Studies: Peer Influence on Smoking

The graduate management admission test prediction bias study

On optimal rerandomization designs