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.

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Fitting Linear Mixed-Effects Models Using lme4

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.

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Latent dirichlet allocation

We describe a model-based clustering method for using multilocus genotype data to infer population structure and assign individuals to populations. We assume a model in which there are K populations (where K may be unknown), each of which is characterized by a set of allele frequencies at each locus. Individuals in the sample are assigned (probabilistically) to populations, or jointly to two or more populations if their genotypes indicate that they are admixed. Our model does not assume a particular mutation process, and it can be applied to most of the commonly used genetic markers, provided that they are not closely linked. Applications of our method include demonstrating the presence of population structure, assigning individuals to populations, studying hybrid zones, and identifying migrants and admixed individuals. We show that the method can produce highly accurate assignments using modest numbers of loci— e.g. , seven microsatellite loci in an example using genotype data from an endangered bird species. The software used for this article is available from http://www.stats.ox.ac.uk/~pritch/home.html.

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Inference of population structure using multilocus genotype data

We propose a generative model for text and other collections of discrete data that generalizes or improves on several previous models including naive Bayes/unigram, mixture of unigrams [6], and Hof-mann's aspect model, also known as probabilistic latent semantic indexing (pLSI) [3]. In the context of text modeling, our model posits that each document is generated as a mixture of topics, where the continuous-valued mixture proportions are distributed as a latent Dirichlet random variable. Inference and learning are carried out efficiently via variational algorithms. We present empirical results on applications of this model to problems in text modeling, collaborative filtering, and text classification.

/pdf/latent-dirichlet-allocation-rkwbqihm3p.pdf

Latent Dirichlet Allocation

Fitting Linear Mixed-Effects Models using lme4

Genetic and environmental factors interact during sensitive periods early in life to influence mental health and disease. These influences involve modulating the function of neurons and neuronal networks via epigenetic processes such as DNA methylation. However, it is not known if DNA methylation changes outside the brain provide an "epigenetic signature" of early-life experiences in an individual child that may serve as a marker for vulnerability or resilience to mental illness. Here, to obviate the massive variance among individuals, we employed a novel intra-individual approach by testing DNA methylation from buccal cells of individual rats before and immediately after exposure to one week of typical or adverse life experience. We show that whereas inter-individual changes in DNA methylation reflect the effect of age, DNA methylation changes within paired DNA samples from the same individual reflect the impact of diverse neonatal experiences on the individual. The methylome signature of early-life experience is enriched in genes encoding transcription factors and key molecular cellular pathways. Specifically, genes involved in cell morphogenesis and differentiation were more methylated in pups exposed to the adverse environment whereas pathways of response to injury and stress were less methylated. Thus, intra-individual methylome signatures indicate large-scale transcription-driven alterations of cellular fate, growth and function. Our observations in rats--that distinct early-life experiences generate specific individual methylome signatures in accessible peripheral cells-- should be readily testable in humans.

/pdf/intra-individual-methylomics-detects-the-impact-of-early-1lfhnpitlj.pdf

Intra-individual methylomics detects the impact of early-life adversity

Abstract:The Mann-Whitney test is a popular nonparametric test for comparing two samples. It has been recently extended by Satten et al. (2018) to allow testing for the existence of treatment effects in observational studies. Their proposed adjusted Mann-Whitney test relies on the unconfoundedness assumption which is untestable in practice. It hence becomes important to assess the impact of violating this assumption on the degree to which causal conclusions remain valid. In this paper, we consider a marginal sensitivity analysis framework to address this problem by utilizing a bootstrap approach that provides a sensitivity interval for the estimand with a guaranteed coverage probability as long as the data generating mechanism is included in the set of pre-specified sensitivity models. We develop efficient optimization algorithms for computing the sensitivity interval and further extend our approach to a general class of adjusted multi-sample U-statistics. Simulation studies and two real data applications are discussed to demonstrate the utility of our proposed methodology.

Sensitivity Analysis for the Adjusted Mann-Whitney Test with Observational Studies

Letter to the Editors regarding Rodriguez-Cruz, S.E., and R.S. Montreuil. “Assessing the quality and reliability of the DEA drug identification process.” Forensic Chemistry 6 (2017): 36–43

We consider the problem of testing for treatment effect heterogeneity in observational studies, and propose a nonparametric test based on multisample U-statistics. To account for potential confounders, we use reweighted data where the weights are determined by estimated propensity scores. The proposed method does not require any parametric assumptions on the outcomes and bypasses the need for modeling the treatment effect for each study subgroup. We establish the asymptotic normality for the test statistic, and demonstrate its superior numerical performance over several competing approaches via simulation studies. Two real data applications including an employment program evaluation study and a mental health study of China's one-child policy are also discussed.

Nonparametric tests for treatment effect heterogeneity in observational studies

Directional data require specialized probability models because of the non-Euclidean and periodic nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional layer of complexity. This paper introduces a novel Bayesian nonparametric approach for directional-linear data based on the Dirichlet process. We ﬁrst extend the projected normal distribution to model the joint distribution of linear variables and a directional variable with arbitrary dimension as a projection of a higher-dimensional augmented multivariate normal distribution (MVN). We call the new distribution the semi-projected normal distribution (SPN); it possesses properties similar to the MVN. The SPN is then used as the mixture distribution in a Dirichlet process model to obtain a more ﬂexible class of models for directional-linear data. We propose a normal conditional inverse-Wishart distribution as part of the prior distribution to address an identiﬁability issue inherited from the projected normal and preserve conjugacy with the SPN distribution. A Gibbs sampling algorithm is provided for posterior inference. Experiments on synthetic data and the Berkeley image database show superior performance of the Dirichlet process SPN mixture model (DPSPN) in clustering compared to other directional-linear models. We also build a hierarchical Dirichlet process model with the SPN to develop a likelihood ratio approach to bloodstain pattern analysis using the DPSPN model for density estimation to estimate the likelihood of a given pattern from a set of training data.

Hal S. Stern

Papers

Intra-individual methylomics detects the impact of early-life adversity

Sensitivity Analysis for the Adjusted Mann-Whitney Test with Observational Studies

Letter to the Editors regarding Rodriguez-Cruz, S.E., and R.S. Montreuil. “Assessing the quality and reliability of the DEA drug identification process.” Forensic Chemistry 6 (2017): 36–43

Nonparametric tests for treatment effect heterogeneity in observational studies

A Dirichlet Process Mixture Model for Directional-Linear Data