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.

/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

15. Answering Questions about Baseball Using Statistics.

BACKGROUND For young children, existing measures of children's health-related quality of life must be parent-reported or interviewer-administered for those who cannot read or complete measures independently. Parents' and childrens' reports about the child's health have been shown to disagree. AIMS (a) To test the reliability and validity of an animated, computer-administered Child Health Rating Inventories (CHRIS2.0) among children aged 4-12 undergoing surgery; and (b) to develop and test two CHRIS measures of preoperative anxiety and postoperative pain management. METHODS We conducted a longitudinal cohort study of a diverse group of 542 children aged 4-12 undergoing surgery. We compared the CHRIS measures to Pediatric Quality of Life Inventory (PedsQL), the Functional Disabilities Inventory (FDI), State-Trait Anxiety Inventory for children (STAI-CH), and the Parent Postoperative Pain Measure (PPPM). RESULTS Factor analyses supported the construct validity of the 12-item general physical health and the 8-item mental health CHRIS scales, as well as a composite 20-item scale, and the CHRIS preoperative anxiety and postoperative pain scales. Internal consistency reliability for all CHRIS scales exceeded the standard for group comparisons (Cronbach's α ≥0.70). The CHRIS general health composite was significantly correlated with composite PedsQL and FDI (r = 0.28, P < .001 and r = 0.43, P < .001, respectively). The CHRIS peri-operative anxiety measure was significantly correlated with the STAI-CH (r = 0.44, P < .001), as was the CHRIS postoperative pain scale with the PPPM (r = 0.52, P < .001). CONCLUSIONS The CHRIS measures were reliable and valid in this diverse sample of young children (4-12). Because CHRIS measures are self-administered, scored in real time, and run on multiple different platforms, this approach provides a feasible method for the collection of health-related quality of life in young children and those with limited literacy. Our data indicate that this approach is psychometrically sound and has the potential for adding the child's voice to pediatric outcomes.

Development and initial validation of self-report measures of general health, preoperative anxiety, and postoperative pain in young children using computer-administered animation.

Machine Learning and Statistics: Applications in Genomics and Computer Vision

We estimate the probabilities of informed trading (PIN) for small and large trades and then investigate their determinants. We model a competitive dealership market for equities with two order sizes using a Poisson process mixture model and use TORQ data to estimate the parameters for the model via the method of maximum likelihood. The PIN for small and large trades are functions of the resulting parameter estimates. In our empirical tests, we find that although for the majority of securities information contents in small and large trades are similar, the average PIN for small trades is significantly higher than that in large trades. We also find that trading volume and institutional trading are the primary determinants of information content in small and large trades, respectively, but not of both. A further investigation of the securities with the largest differences in terms of PINs for small and large trades reveals that trade size alone distinguishes those firms from the rest – all eight firms reside in the lowest quartile in terms of average trade size.

Information Content in Small and Large Trades

https://doi.org/10.1016/j.jadohealth.2022.12.020

Hal S. Stern

Papers

15. Answering Questions about Baseball Using Statistics.

Development and initial validation of self-report measures of general health, preoperative anxiety, and postoperative pain in young children using computer-administered animation.

Machine Learning and Statistics: Applications in Genomics and Computer Vision

Information Content in Small and Large Trades

Experiences of COVID-19-Related Racism and Impact on Depression Trajectories Among Racially/Ethnically Minoritized Adolescents