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

An observed score distribution for a multiple-choice test can often be cogently summarized using 3 statistics that are easily calculated functions of the first 3 moments of the distribution. These statistics can be interpreted as providing a mean ability in terms of probability of obtaining a correct response, a guessing threshold, and a reliability relative to binomial variability

Summarizing multiple-choice tests using three informative statistics.

(1984). Comment: Assessing the Fit of Logistic Regressions Using the Implied Discriminant Analysis. Journal of the American Statistical Association: Vol. 79, No. 385, pp. 79-80.

Comment: Assessing the Fit of Logistic Regressions Using the Implied Discriminant Analysis

A systematic study is presented of the effects of pulsed high power RF processing (HPP) as a method of reducing field emission (FE) in superconducting radio frequency (SRF) cavities to reach higher accelerating gradients for future particle accelerators. The processing apparatus was built to provide up to 150 kW peak RF power to 3 GHz cavities, for pulse lengths from 200 μs to 1 ms. Single-cell and nine-cell cavities were tested extensively. The thermal conductivity of the niobium for these cavities was made as high as possible to ensure stability against thermal breakdown of superconductivity. HPP proves to be a highly successful method of reducing FE loading in nine-cell SRF cavities. Attainable continuous wave (CW) fields increase by as much as 80% from their pre-HPP limits. The CW accelerating field achieved with nine-cell cavities improved from 8–15 MV/m with HPP to 14–20 MV/m. The benefits are stable with subsequent exposure to dust-free air. More importantly, HPP also proves effective against new field emission subsequently introduced by cold and warm vacuum “accidents” which admitted “dirty” air into the cavities. Clear correlations are obtained linking FE reduction with the maximum surface electric field attained during processing. In single cells the maximums reached were E peak = 72 MV/m and H peak = 1660 Oe. Thermal breakdown, initiated by accompanying high surface magnetic fields is the dominant limitation on the attainable fields for pulsed processing, as well as for final CW and long pulse operation. To prove that the surface magnetic field rather than the surface electric fields is the limitation to HPP effectiveness, a special two-cell cavity with a reduced magnetic to electric field ratio is successfully tested. During HPP, pulsed fields reach E peak = 113 MV/m ( H peak = 1600 Oe) and subsequent CW low power measurement reached E peak = 100 MV/m, the highest CW field ever measured in a superconducting accelerator cavity.

Reduction of field emission in superconducting cavities with high power pulsed RF

Differences were revealed in the age at which boys and girls attain developmental milestones during the first year of life and in the intervals between milestone attainments. Three of ten milestones were reached significantly earlier in boys than girls while none of the milestones appeared earier in girls than boys. Of the 45 intervals between milestones, seven were longer in boys and twelve were longer in girls. Data were recorded by the mothers of 4653 infants participating in the Copenhagen Consecutive Perinatal Cohort. Full-term gestation (38-41 weeks) and survival through the first year were the criteria for inclusion in the study. Nine potential confounding variables, including SES, birth weight and complications of pregnancy, were not responsible for the behavioral sex differences. This sexually dimorphic pattern of milestone achievement is discussed as supportive of hypothesized biologically-based sex differences in the ontogeny of social responsiveness and is consistent with sex differences ident...

Sex Differences in Developmental Milestones During the First Year of Life

Many outcomes of interest in the social and health sciences, as well as in modern applications in computational social science and experimentation on social media platforms, are ordinal and do not have a meaningful scale. Causal analyses that leverage this type of data, termed ordinal non-numeric, require careful treatment, as much of the classical potential outcomes literature is concerned with estimation and hypothesis testing for outcomes whose relative magnitudes are well defined. Here, we propose a class of finite population causal estimands that depend on conditional distributions of the potential outcomes, and provide an interpretable summary of causal effects when no scale is available. We formulate a relaxation of the Fisherian sharp null hypothesis of constant effect that accommodates the scale-free nature of ordinal non-numeric data. We develop a Bayesian procedure to estimate the proposed causal estimands that leverages the rank likelihood. We illustrate these methods with an application to educational outcomes in the General Social Survey.

Donald B. Rubin

Papers

Summarizing multiple-choice tests using three informative statistics.

Comment: Assessing the Fit of Logistic Regressions Using the Implied Discriminant Analysis

Reduction of field emission in superconducting cavities with high power pulsed RF

Sex Differences in Developmental Milestones During the First Year of Life

Causal inference for ordinal outcomes