Generalized multilevel structural equation modeling

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent variables. The response model generalizes GLMMs to incorporate factor structures in addition to random intercepts and coefficients. As in GLMMs, the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower-level units in the higher-level units and missing data. A wide range of response processes can be modeled including ordered and unordered categorical responses, counts, and responses of mixed types. The structural model is similar to the structural part of a SEM except that it may include latent and observed variables varying at different levels. For example, unit-level latent variables (factors or random coefficients) can be regressed on cluster-level latent variables. Special cases of this framework are explored and data from the British Social Attitudes Survey are used for illustration. Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata.gllamm can be downloaded from http://www.gllamm.org. The paper was written while Sophia Rabe-Hesketh was employed at and Anders Skrondal was visiting the Department of Biostatistics and Computing, Institute of Psychiatry, King's College London.     

Extracting a maximum of useful information from statistical research data

The practice of statistical inference in psychological research is critically reviewed. Particular emphasis is put on the fast pace of change from the sole reliance on null hypothesis significance testing (NHST) to the inclusion of effect size estimates, confidence intervals, and an interest in the Bayesian approach. We conclude that these developments are helpful for psychologists seeking to extract a maximum of useful information from statistical research data, and that seven decades of criticism against NHST is finally having an effect.     

Bayes Factors Have Frequency Properties—This Should Not Be Ignored: A Rejoinder to Morey,Wagenmakers, and Rouder

Hoijtink, van Kooten, and Hulsker (2016 Hoijtink, H., van Kooten, P., &; Hulsker, K. (2016). Why Bayesian psychologists should change the way they used the Bayes factor. Multivariate Behavioral Research, 51, 1--9. doi: 10.1080/00273171.2014.969364.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) outline a research agenda for Bayesian psychologists: evaluate and use the frequency properties of Bayes factors. Morey, Wagenmakers, and Rouder (2016 Morey, R. D., Wagenmakers, E. -J., &; Rouder, J. N. (2016). Calibrated Bayes factors should not be used: A reply to Hoijtink, van Kooten, and Hulsker. Multivariate Behavioral Research, 51, 10--17. doi: 10.1080/00273171.2015.1052710.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) respond that Bayes factors calibrated using frequency properties should not be used. This paper contains the response of Hoijtink, van Kooten, and Hulsker to the criticism of Morey, Wagenmakers, and Rouder (2016 Morey, R. D., Wagenmakers, E. -J., &; Rouder, J. N. (2016). Calibrated Bayes factors should not be used: A reply to Hoijtink, van Kooten, and Hulsker. Multivariate Behavioral Research, 51, 10--17. doi: 10.1080/00273171.2015.1052710.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]).     

Using MCMC chain outputs to efficiently estimate Bayes factors

One of the most important methodological problems in psychological research is assessing the reasonableness of null models, which typically constrain a parameter to a specific value such as zero. Bayes factor has been recently advocated in the statistical and psychological literature as a principled means of measuring the evidence in data for various models, including those where parameters are set to specific values. Yet, it is rarely adopted in substantive research, perhaps because of the difficulties in computation. Fortunately, for this problem, the Savage–Dickey density ratio (Dickey & Lientz, 1970) provides a conceptually simple approach to computing Bayes factor. Here, we review methods for computing the Savage–Dickey density ratio, and highlight an improved method, originally suggested by Gelfand and Smith (1990) and advocated by Chib (1995), that outperforms those currently discussed in the psychological literature. The improved method is based on conditional quantities, which may be integrated by Markov chain Monte Carlo sampling to estimate Bayes factors. These conditional quantities efficiently utilize all the information in the MCMC chains, leading to accurate estimation of Bayes factors. We demonstrate the method by computing Bayes factors in one-sample and one-way designs, and show how it may be implemented in WinBUGS.     

An extended application ‘Brain Q’ processing EEG and MEG data of finger stimulation extended from ‘Zeffiro’ based on machine learning and signal processing

GoalTo apply signal processing and machine learning skills and knowledge in processing the EEG and MEG signal and further localize and evaluate the source of the finger stimulation.MethodsCognitive control is usually applied in information processing and behavioral response. In the preprocessing, baseline correction is implemented to analyze the pre-stimuli, combining ERP to mark the event related potential, studying the time-locked only behavior. Z-score transform, coherence and spec trum are calculated and analyzed in the functional connectivity analysis.In addition to the functional analysis, Bayes Optimizer evaluates the neuro imaging according to the hierarchical Bayes. The introduction of the application is described from both user and developer’s prospects. Results: Introduction of both user and developers aspects, on its modules from pre-processing, functional analysis and results visualization and evaluation is conducted with one specific clinical data case, including the correlation is higher especially on gamma band and the MVAR coherence on the whole source space depicting the relation between different regions, especially on somatosensory (compared by thalamus) when stimulated by finger activity, phase-lock property of the E/MEG signal and etc. Compared to a manual selection, the scaling parameter prediction can be improved with support vector machine (SVM). The evaluation results with Bayes Optimization, location prediction is superior in the somatosensory area and in the thalamus, the total reconstructed source space is larger, one of the realization of cognitive system comparing different kernels and classifiers. The SVM and discriminant classifier gives similar results evaluating the dipole localization and the parameter choice related as well to the shape parameter, noise level, hyperprior and etc.ConclusionApproaches of Brain Q are found to be suitable for pre-processing for the EEG and MEG data. The system is capable of functional analysis including coherence and spectral related computation. Machine learning techniques are conducted as well to analyze and evaluate the result of the dipole reconstruction and help to predict the better model parameters and the localization of the origin dipoles. A case on finger stimulation clinical data is conducted and the results of the analysis temporarily and spatially manifests its functionality for users and potential extensions for developers.     

Bayesian evaluation of informative hypotheses for multiple populations

The software package Bain can be used for the evaluation of informative hypotheses with respect to the parameters of a wide range of statistical models. For pairs of hypotheses the support in the data is quantified using the approximate adjusted fractional Bayes factor (BF). Currently, the data have to come from one population or have to consist of samples of equal size obtained from multiple populations. If samples of unequal size are obtained from multiple populations, the BF can be shown to be inconsistent. This paper examines how the approach implemented in Bain can be generalized such that multiple-population data can properly be processed. The resulting multiple-population approximate adjusted fractional Bayes factor is implemented in the R package Bain.     

Playing the long game: A multivariate multilevel non-linear growth curve model of long-term effects in a randomized trial of the Good Behavior Game

This cluster randomized controlled trial (RCT) examined the impact of the Good Behavior Game (GBG) on children's developmental trajectories of disruptive behavior, concentration problems, and prosocial behavior from middle childhood (ages 6–7 years) to early adolescence (ages 10–11 years). Seventy-seven schools in England were randomly assigned to intervention and control groups. Allocation was balanced by school size and the proportion of children eligible for free school meals. Children (N = 3084) ages 6–7 years at baseline were the target cohort. Outcome measures, assessed via the Teacher Observation of Child Adaptation Checklist, were taken prior to randomization (baseline – Time 1) and annually for the next 4 years (Time 2 to Time 5). During the 2-year main trial period (Time 1 to Time 3), teachers of this cohort in intervention schools implemented the GBG, whereas their counterparts in the control group continued their usual practice. A multivariate multilevel non-linear growth curve model indicated that the GBG reduced concentration problems over time. In addition, the model also revealed that the intervention improved prosocial behavior among at-risk children (e.g., those with elevated symptoms of conduct problems at Time 1, n = 485). No intervention effects were unequivocally found in relation to disruptive behavior. These findings are discussed in relation to the extant literature, strengths and limitations are noted, and practical and methodological implications are highlighted.     

Empirical Bayes Derivative Estimates

Abstract

A dynamic system is a set of interacting elements characterized by changes occurring over time. The estimation of derivatives is a mainstay for exploring dynamics of constructs, particularly when the dynamics are complicated or unknown. The presence of measurement error in many social science constructs frequently results in poor estimates of derivatives, as even modest proportions of measurement error can compound when estimating derivatives. Given the overlap in the specification of latent differential equation models and latent growth curve models, and the equivalence of latent growth curve models and mixed models under some conditions, derivatives could be estimated from estimates of random effects. This article proposes a new method for estimating derivatives based on calculating the Empirical Bayes estimates of derivatives from a mixed model. Two simulations compare four derivative estimation methods: Generalized Local Linear Approximation, Generalized Orthogonal Derivative Estimates, Functional Data Analysis, and the proposed Empirical Bayes Derivative Estimates. The simulations consider two data collection scenarios: short time series (≤10 observations) from many individuals or occasions, and long individual time series (25–500 observations). A substantive example visualizing the dynamics of intraindividual positive affect time series is also presented.