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

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

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.

/pdf/inference-of-population-structure-using-multilocus-genotype-1x75ku6urs.pdf

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

Vulnerability to emotional disorders including depression derives from interactions between genes and environment, especially during sensitive developmental periods. Across evolution, maternal care is a key source of environmental sensory signals to the developing brain, and a vast body of work has linked quantitative and qualitative aspects of maternal care to emotional outcome in children and animals. However, the fundamental properties of maternal signals, that promote advantageous vs pathological outcomes in the offspring, are unknown and have been a topic of intense study. We studied emotional outcomes of adolescent rats reared under routine or impoverished environments, and used mathematical approaches to analyze the nurturing behaviors of the dams. Unexpectedly, whereas the quantity and typical qualities of maternal care behaviors were indistinguishable in the two environments, their patterns and rhythms differed drastically and influenced emotional outcomes. Specifically, unpredictable, fragmented maternal care patterns translated into high-entropy rates of sensory signals to the offspring in the impoverished cages. During adolescence, these offspring had significant reductions in sucrose preference and in peer-play, two independent measures of the ability to experience pleasure. This adolescent anhedonia, often a harbinger of later depression, was not accompanied by measures of anxiety or helplessness. Dopaminergic pleasure circuits underlying anhedonia are engaged by predictable sequences of events, and predictable sensory signals during neonatal periods may be critical for their maturation. Conversely, unpredictability maternal-derived signals may disrupt these developmental processes, provoking anhedonia. In sum, high-entropy and fragmented patterns of maternal-derived sensory input to the developing brain predicts, and might promote, the development of anhedonia in rodents, with potential clinical implications.

/pdf/fragmentation-and-high-entropy-of-neonatal-experience-4alegmgjh2.pdf

Fragmentation and high entropy of neonatal experience predict adolescent emotional outcome

Disease incidence or disease mortality rates for small areas are often displayed on maps. Maps of raw rates, disease counts divided by the total population at risk, have been criticized as unreliable due to non-constant variance associated with heterogeneity in base population size. This has led to the use of model-based Bayes or empirical Bayes point estimates for map creation. Because the maps have important epidemiological and political consequences, for example, they are often used to identify small areas with unusually high or low unexplained risk, it is important that the assumptions of the underlying models be scrutinized. We review the use of posterior predictive model checks, which compare features of the observed data to the same features of replicate data generated under the model, for assessing model fitness. One crucial issue is whether extrema are potentially important epidemiological findings or merely evidence of poor model fit. We propose the use of the cross-validation posterior predictive distribution, obtained by reanalyzing the data without a suspect small area, as a method for assessing whether the observed count in the area is consistent with the model. Because it may not be feasible to actually reanalyze the data for each suspect small area in large data sets, two methods for approximating the cross-validation posterior predictive distribution are described.

https://cfpub.epa.gov/ncer_abstracts/index.cfm/fuseaction/display.files/fileID/14734

Posterior predictive model checks for disease mapping models

This article develops a predictive model for National Football League (NFL) game scores using data from the period 1988–1993. The parameters of primary interest—measures of team strength—are expected to vary over time. Our model accounts for this source of variability by modeling football outcomes using a state-space model that assumes team strength parameters follow a first-order autoregressive process. Two sources of variation in team strengths are addressed in our model; week-to-week changes in team strength due to injuries and other random factors, and season-to-season changes resulting from changes in personnel and other longer-term factors. Our model also incorporates a home-field advantage while allowing for the possibility that the magnitude of the advantage may vary across teams. The aim of the analysis is to obtain plausible inferences concerning team strengths and other model parameters, and to predict future game outcomes. Iterative simulation is used to obtain samples from the joint ...

A State-Space Model for National Football League Scores

observed, and was often best supplied when the decision to increase the dose was left to the patient: this must, however, depend on an assessment of each individual's personality. Antibiotics given early during infections of the upper respiratory tract also appeared to reduce the risk of serious relapse. We reiterate the view that long-term steroid therapy is a valuable form of treatment, but it must be used circumspectly, with adequate supervision and full collaboration between the hospital consultant and the family physician. Though steroids often enable patients to lead a more active and useful life, attacks of severe asthma may still occur, and need urgent and thorough treatment.

https://www.bmj.com/content/bmj/1/5593/665.full.pdf

Isolation of cytomegalovirus and clinical manifestations of infection at different ages.

Maternal care is a critical determinant of child development. However, our understanding of processes and mechanisms by which maternal behavior influences the developing human brain remains limited. Animal research has illustrated that patterns of sensory information is important in shaping neural circuits during development. Here we examined the relation between degree of predictability of maternal sensory signals early in life and subsequent cognitive function in both humans (n = 128 mother/infant dyads) and rats (n = 12 dams; 28 adolescents). Behaviors of mothers interacting with their offspring were observed in both species, and an entropy rate was calculated as a quantitative measure of degree of predictability of transitions among maternal sensory signals (visual, auditory, and tactile). Human cognitive function was assessed at age 2 y with the Bayley Scales of Infant Development and at age 6.5 y with a hippocampus-dependent delayed-recall task. Rat hippocampus-dependent spatial memory was evaluated on postnatal days 49-60. Early life exposure to unpredictable sensory signals portended poor cognitive performance in both species. The present study provides evidence that predictability of maternal sensory signals early in life impacts cognitive function in both rats and humans. The parallel between experimental animal and observational human data lends support to the argument that predictability of maternal sensory signals causally influences cognitive development.

/pdf/exposure-to-unpredictable-maternal-sensory-signals-43boi9gzcf.pdf

Hal S. Stern

Papers

Fragmentation and high entropy of neonatal experience predict adolescent emotional outcome

Posterior predictive model checks for disease mapping models

A State-Space Model for National Football League Scores

Isolation of cytomegalovirus and clinical manifestations of infection at different ages.

Exposure to unpredictable maternal sensory signals influences cognitive development across species.