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

The research area of interpersonal expectancy effects originally derived from a general consideration of the effects of experimenters on the results of their research. One of these is the expectancy effect, the tendency for experimenters to obtain results they expect, not simply because they have correctly anticipated nature's response but rather because they have helped to shape that response through their expectations. When behavioral researchers expect certain results from their human (or animal) subjects they appear unwittingly to treat them in such a way as to increase the probability that they will respond as expected.In the first few years of research on this problem of the interpersonal (or interorganism) self-fulfilling prophecy, the “prophet” was always an experimenter and the affected phenomenon was always the behavior of an experimental subject. In more recent years, however, the research has been extended from experimenters to teachers, employers, and therapists whose expectations for their pupils, employees, and patients might also come to serve as interpersonal self-fulfilling prophecies.Our general purpose is to summarize the results of 345 experiments investigating interpersonal expectancy effects. These studies fall into eight broad categories of research: reaction time, inkblot tests, animal learning, laboratory interviews, psychophysical judgments, learning and ability, person perception, and everyday life situations. For the entire sample of studies, as well as for each specific research area, we (1) determine the overall probability that interpersonal expectancy effects do in fact occur, (2) estimate their average magnitude so as to evaluate their substantive and methodological importance, and (3) illustrate some methods that may be useful to others wishing to summarize quantitatively entire bodies of research (a practice that is, happily, on the increase).

Interpersonal expectancy effects: the first 345 studies

We introduce the binomial effect size display (BESD), which is useful because it is (a) easily understood by researchers, students, and lay persons; (b) widely applicable; and (c) conveniently computed. The BESD displays the change in success rate (e.g., survival rate, improvement rate, etc.) attributable to a new treatment procedure. For example, an r of .32, the average size of the effect of psychotherapy, is said to account for "only 10% of the variance"; however, the BESD shows that this proportion of variance accounted for is equivalent to increasing the success rate from 34% to 66%, which would mean, for example, reducing an illness rate or a death rate from 66% to 34%. Traditionally, behavioral researchers have concentrated on reporting significance levels of experimental effects. Recent years, however, have shown a welcome increase in emphasis on reporting the magnitude of experimental effects obtained (Cohen, 1977; Fleiss, 1969; Friedman, 1968, Glass, Note 1, Hays, 1973; Rosenthal, 1978; Rosenthal & Rubin, 1978; Smith & Glass, 1977).

https://www.pbarrett.net/publications/BESD_Rosenthal_and_Rubin_1982.pdf

A Simple, General Purpose Display of Magnitude of Experimental Effect

/pdf/statistical-analysis-with-missing-data-second-edition-3ffdfm8al7.pdf

Statistical Analysis with Missing Data, Second Edition

For estimating causal effects of treatments, randomized experiments are generally considered the gold standard. Nevertheless, they are often infeasible to conduct for a variety of reasons, such as ethical concerns, excessive expense, or timeliness. Consequently, much of our knowledge of causal effects must come from non-randomized observational studies. This article will advocate the position that observational studies can and should be designed to approximate randomized experiments as closely as possible. In particular, observational studies should be designed using only background information to create subgroups of similar treated and control units, where 'similar' here refers to their distributions of background variables. Of great importance, this activity should be conducted without any access to any outcome data, thereby assuring the objectivity of the design. In many situations, this objective creation of subgroups of similar treated and control units, which are balanced with respect to covariates, can be accomplished using propensity score methods. The theoretical perspective underlying this position will be presented followed by a particular application in the context of the US tobacco litigation. This application uses propensity score methods to create subgroups of treated units (male current smokers) and control units (male never smokers) who are at least as similar with respect to their distributions of observed background characteristics as if they had been randomized. The collection of these subgroups then 'approximate' a randomized block experiment with respect to the observed covariates.

/pdf/the-design-versus-the-analysis-of-observational-studies-for-2ljp0kb09j.pdf

The design versus the analysis of observational studies for causal effects: parallels with the design of randomized trials.

The Bayesian bootstrap is the Bayesian analogue of the bootstrap. Instead of simulating the sampling distribution of a statistic estimating a parameter, the Bayesian bootstrap simulates the posterior distribution of the parameter; operationally and inferentially the methods are quite similar. Because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions, neither method should be applied without some consideration of the reasonableness of these model assumptions. In this sense, neither method is a true bootstrap procedure yielding inferences unaided by external assumptions.

/pdf/the-bayesian-bootstrap-1starnibum.pdf

Donald B. Rubin

Papers

Interpersonal expectancy effects: the first 345 studies

A Simple, General Purpose Display of Magnitude of Experimental Effect

Statistical Analysis with Missing Data, Second Edition

The design versus the analysis of observational studies for causal effects: parallels with the design of randomized trials.

The Bayesian Bootstrap