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

There is a little doubt that the topic of the target article is extremely important—how to provide guidance for making medical decisions that are based on evidence concerning which interventions are likely to work well in practice. The hope for this enterprise, now called CER for ‘comparative effectiveness research,’ which is similar to the previously used ‘evidence-based medicine,’ is to use the voluminous amounts of data often routinely collected in our society, such as for insurance and other administrative uses, or from federal, state, and private sample surveys, to learn about the relative effectiveness of all sorts of medical interventions. The target article itself is rich in its statement of goals and general objectives, but it seems to me to be quite thin in its statement of (a) specific suggestions for what characteristics the data sets should possess to make such effectiveness comparisons plausibly accurate or (b) what methodological techniques are most likely to be appropriate to apply to the data sets to achieve these goals. Even the specific examples cited, at least those with which I am familiar, seem to me to be relatively poor sources of guidance for either the kinds of data sets needed or for the kinds of statistical techniques to be applied to them to achieve credible answers. In my limited experience in trying to address such topics, I find that there is too little thoughtful guidance for the correct design and analysis of investigations that use complex data sets, mostly non-randomized observational ones, to estimate the effects of medical interventions; an exception is Cochran [1], but that article does not reflect the substantial changes that have taken place over the last half century in statistics, computing, medicine, and routinely collected databases. It is important for me to emphasize that much of the required effort when attacking a causal question using observational data takes place before any of the usual statistical analyses of the data are initiated, just as with welldesigned randomized experiments. Moreover, often the inevitable conclusion of a thoughtful attack may be that there are no reliable answers available from existing data sets, or even from summaries of them based on meta-analyses [2], effect-size surface estimations [3], or from research syntheses [4]. It is my firm view that it is better, for eventual progress, to know that we cannot yet reliably answer questions than to pretend that we know the answers based on bogus assumptions and hopelessly inadequate data. My comments are admittedly somewhat idiosyncratic in that they rely largely on references to my own work or work with which I have substantial familiarity, although there are many fine sources of ideas on the topics. I do this mainly because, when thinking about the issues that the target article raises, many of these concern what is needed to create a reliable observational study, and I have spent a large amount of time thinking and writing about this in the context of real problems for more than four decades.

On the limitations of comparative effectiveness research

This article offers reflections on the development of the Rubin causal model (RCM), which were stimulated by the impressive discussions of the RCM and Campbell's superb contributions to the practical problems of drawing causal inferences written by Will Shadish (2010) and Steve West and Felix Thoemmes (2010). It is not a rejoinder in any real sense but more of a sequence of clarifications of parts of the RCM combined with some possibly interesting personal historical comments, which I do not think can be found elsewhere. Of particular interest in the technical content, I think, are the extended discussions of the stable unit treatment value assumption, the explication of the variety of definitions of causal estimands, and the discussion of the assignment mechanism.

Reflections stimulated by the comments of Shadish (2010) and West and Thoemmes (2010).

https://www.uobabylon.edu.iq/uobColeges/ad_downloads/5_3060_1069.pdf

Rumor and Gossip Research

This article proposes and evaluates two new methods of reweighting preliminary data to obtain estimates more closely approximating those derived from the final data set. In our motivating example, the preliminary data are an early sample of tax returns, and the final data set is the sample after all tax returns have been processed. The new methods estimate a predicted propensity for late filing for each return in the advance sample and then poststratify based on these propensity scores. Using advance and complete sample data for 1982, we demonstrate that the new methods produce advance estimates generally much closer to the final estimates than those derived from the current advance estimation techniques. The results demonstrate the value of propensity modeling, a general-purpose methodology that can be applied to a wide range of problems, including adjustment for unit nonresponse and frame undercoverage as well as statistical matching.

Projecting From Advance Data Using Propensity Modeling: An Application to Income and Tax Statistics

Multivariate matching methods are commonly used in the behavioral and medical sciences in an attempt to control bias when randomization is not feasible. Some examples of multivariate matching methods are discussed in Althauser and Rubin (1970) and Cochran and Rubin (1973), but otherwise seem to have received little attention in the literature. Here, we present examples of multivariate matching methods that will yield the same percent reduction in bias for each matching variable for a variety of underlying distributions. Eleven distributional cases are considered, and for each one, matching methods are defined which are equal percent bias reducing. Methods discussed in Section 8, which are based on the values of the estimated best linear discriminant or which define distance by a sample based inner-product, will probably be the most generally applicable in practice.

Donald B. Rubin

Papers

On the limitations of comparative effectiveness research

Reflections stimulated by the comments of Shadish (2010) and West and Thoemmes (2010).

Rumor and Gossip Research

Projecting From Advance Data Using Propensity Modeling: An Application to Income and Tax Statistics

Multivariate matching methods that are equal percent bias reducing, i: some examples