Generalized Linear Mixed-Effects Modeling Programs in R for Binary Outcomes

We review, examine the performance, and discuss the relative strengths and weaknesses of various R functions for the estimation of generalized linear mixed-effects models (GLMMs) for binary outcomes. The R functions reviewed include glmer in the package lme4, hglm2 in the package hglm, MCMCglmm in the package MCMCglmm, and inla in the package INLA. We illustrate the use of these functions through an empirical example and provide sample code.     

On the Estimation of Nonlinear Mixed-Effects Models and Latent Curve Models for Longitudinal Data

Nonlinear models are effective tools for the analysis of longitudinal data. These models provide a flexible means for describing data that follow complex forms of change. Exponential and logistic functions that include a parameter to represent an asymptote, for instance, are useful for describing responses that tend to level off with time. There are forms of nonlinear latent curve models and nonlinear mixed-effects model that are equivalent, and so given the same set of data, growth function, distributional assumptions, and method of estimation, the 2 models yield equivalent results. There are also forms that are strikingly different and can yield different interpretations for a given set of data. This article discusses cases in which nonlinear mixed-effects models and nonlinear latent curve models are equivalent and those in which they are different and clarifies the estimation needs of the different models. Examples based on empirical data help to illustrate these points.     

Estimation of Time-Unstructured Nonlinear Mixed-Effects Mixture Models

Change over time often takes on a nonlinear form. Furthermore, change patterns can be characterized by heterogeneity due to unobserved subpopulations. Nonlinear mixed-effects mixture models provide one way of addressing both of these issues. This study attempts to extend these models to accommodate time-unstructured data. We develop methods to fit these models in both the structural equation modeling framework as well as the Bayesian framework and evaluate their performance. Simulations show that the success of these methods is driven by the separation between latent classes. When classes are well separated, a sample of 200 is sufficient. Otherwise, a sample of 1,000 or more is required before parameters can be accurately recovered. Ignoring individually varying measurement occasions can also lead to substantial bias, particularly in the random-effects parameters. Finally, we demonstrate the application of these techniques to a data set involving the development of reading ability in children.     

Longitudinal analysis of the environmental attitudes of university students

This article addresses the important questions that higher education institutions ask concerning their impact on their students’ sustainability-related attributes ‘How do our students’ worldviews change as they experience higher education with us?’ The process of monitoring such a dynamic entity is fraught with statistical complexity but may not be impossible for an institution willing to ask whether or not its educational efforts in ‘education for sustainability’, ‘education for sustainable development’ or ‘environmental education’, and campus sustainability developments, are paralleled by changes in the attitudes of its students. We describe here a longitudinal survey process based on the revised New Ecological Paradigm scale, with two cohorts of students, in three programmes of study, operating over four years, with multiple survey inputs by each student. We implemented the longitudinal analysis using a linear mixed-effects model and describe here the development and testing of this model. We conclude that higher education institutions can benchmark the sustainability attributes of their students and monitor changes, if they are minded to. We invite higher education practitioners worldwide to join us in further developing suitable research instruments, processes and statistical models, and in further analysing the assumptions that link higher education to sustainability and to global citizenship.     

混合效应模型框架下反应时数据的分析：原理和实践

从分布形状､趋中度以及离散程度来看,反应时都具有区别于其他数据类型的非常鲜明的特点。 因此,反应时数据的统计分析处理往往也有不同的技术要求和门槛。基于R 语言的混合效应模型为反应时分布上的正偏斜､各数据点之间强关联以及异常值等问题提供了很好的解决方案。本文在回顾传统的反应时数据分析方法后,以一项具体的研究为实例介绍了使用“混合效应模型”来拟合反应时数据的基本原理､概念内涵以及如何拟合最佳模型等问题｡     

Multivariate Meta-Analysis as Structural Equation Models

Multivariate meta-analysis has become increasingly popular in the educational, social, and medical sciences. It is because the outcome measures in a meta-analysis can involve more than one effect size. This article proposes 2 mathematically equivalent models to implement multivariate meta-analysis in structural equation modeling (SEM). Specifically, this article shows how multivariate fixed-, random- and mixed-effects meta-analyses can be formulated as structural equation models. metaSEM (a free R package based on OpenMx) and Mplus are used to implement the proposed procedures. A real data set is used to illustrate the procedures. Formulating multivariate meta-analysis as structural equation models provides many new research opportunities for methodological development in both meta-analysis and SEM. Issues related to and extensions on the SEM-based meta-analysis are discussed.     

混合效应随机微分方程的贝叶斯分析(英文)

采用带有随机微分方程的非线性混合效应模型对群体药物代谢动力学数据建模,通过在状态方程中引入随机项,将常微分方程扩展到随机微分方程.和常微分方程相比,随机微分方程可解决群体药物代谢动力学模型中相关残差问题.利用贝叶斯估计对非线性混合效应随机微分方程模型参数进行估计,给出群体参数及个体参数的精确后验分布,将Gibbs和Metropolis-Hastings算法相结合,给出参数估计值.通过计算机模拟和实例分析验证了方法的可靠性,结果表明利用非线性混合效应随机微分方程模型及贝叶斯估计方法分析群体药物代谢动力学数据是可行的.     

基于相关数据下的纵向数据混合效应模型估计

本文基于NPME模型提出一个核线性混合效应模型(KLME)估计量。该方法是结合核方法与线性混合效应模型方法得到的。此方法中,组内相关被融合成一种"权",此估计量能够达到很好的渐进有效性,并且在有限样本时更加实用。     

Stability analysis of discrete-time BAM neural networks based on standard neural network models

To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.     

An Excel Solver Exercise to Introduce Nonlinear Regression

Business students taking business analytics courses that have significant predictive modeling components, such as marketing research, data mining, forecasting, and advanced financial modeling, are introduced to nonlinear regression using application software that is a “black box” to the students. Thus, although correct models are estimated, students often do not obtain a thorough understanding of the nonlinear estimation process. The exercise presented in this article was created to demonstrate to students the need for nonlinear regression estimation—rather than using linear transformations and Ordinary Least Squares (OLS) and subsequently demonstrate the nonlinear optimization process to estimate nonlinear regression models. Using the spreadsheet exercise, students can see effects on the fit of the model by changing the model parameters as they change the values of the decision variables. After applying the spreadsheet to further exercises, students have expressed a deep understanding of the linear regression software. This exercise is innovative because the active learning exercise requires the students to make the logical connections between the structure of the model, the model's parameters, and the objective function.     

技术创新、转化与商业化的非线性模型和政策启示

技术创新、转化与商业化的过程并不一定是依次递进的熊彼特主义技术推动的线性关系，这是近年来技术创新研究领域的新观点和新认识。事实证明，非线性模型更加贴近真实的创新发展过程。近年来世界各国的技术创新政策实践，都能找出基于线性或非线性理论认识的影子，而非线性的发展模式则是创新政策的潮流和趋势。这些理论认识和政策实践对我国的科技发展有重要的借鉴意义。     

Tracking vocabulary and reading growth in children from lower and higher socioeconomic backgrounds during the transition from primary to secondary education

We examined the relation between socioeconomic status (SES), vocabulary, and reading in middle childhood, during the transition from primary (elementary) to secondary (high) school. Children (N = 279, 163 girls) completed assessments of everyday and curriculum-related vocabulary, (non)word reading, and reading comprehension at five timepoints from age 10 to 13. Piecewise linear mixed-effects models showed significant growth in everyday vocabulary and word reading between every time point. Curriculum vocabulary and reading comprehension showed significant growth during the school year, but not during the summer holidays. There were significant effects of SES on all measures except word reading; yet, SES differences did not widen over time. Our findings motivate targeted reading and vocabulary support for secondary school students from lower SES backgrounds.     

Nonlinear Growth Mixture Models With Fractional Polynomials: An Illustration With Early Childhood Mathematics Ability

Applications of growth mixture modeling have become widespread in the fields of medicine, public health, and the social sciences for modeling linear and nonlinear patterns of change in longitudinal data with presumed heterogeneity with respect to latent group membership. However, in contrast to linear approaches, there has been relatively less focus on methods for modeling nonlinear change. We introduce a nonlinear mixture modeling approach for estimating change trajectories that rely on the use of fractional polynomials within a growth mixture modeling framework. Fractional polynomials allow for more parsimonious and flexible models in comparison to conventional polynomial models. The procedures are illustrated through the use of math ability scores obtained from 499 children over a period of 3 years, with 4 measurement occasions. Techniques for identifying the best empirically derived growth mixture model solution are also described and illustrated by way of substantive example and a simulation.     

一类非线性不确定时滞系统的鲁棒性

利用LMI求解了一类非线性不确定时滞系统的鲁棒性．在非线性不确定性满足增益有界条件下，讨论了自由系统的稳定性问题，构造了无记忆状态反馈控制器来镇定系统并且使系统具有一定的鲁棒性．     

Implementing Restricted Maximum Likelihood Estimation in Structural Equation Models

Structural equation modeling (SEM) is now a generic modeling framework for many multivariate techniques applied in the social and behavioral sciences. Many statistical models can be considered either as special cases of SEM or as part of the latent variable modeling framework. One popular extension is the use of SEM to conduct linear mixed-effects modeling (LMM) such as cross-sectional multilevel modeling and latent growth modeling. It is well known that LMM can be formulated as structural equation models. However, one main difference between the implementations in SEM and LMM is that maximum likelihood (ML) estimation is usually used in SEM, whereas restricted (or residual) maximum likelihood (REML) estimation is the default method in most LMM packages. This article shows how REML estimation can be implemented in SEM. Two empirical examples on latent growth model and meta-analysis are used to illustrate the procedures implemented in OpenMx. Issues related to implementing REML in SEM are discussed.     

A Second-Order Conditionally Linear Mixed Effects Model With Observed and Latent Variable Covariates

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a nonlinear manner are common to all subjects. In this article we describe how a variant of the Michaelis-Menten (M-M) function can be fit within this modeling framework using Mplus 6.0. We demonstrate how observed and latent covariates can be incorporated to help explain individual differences in growth characteristics. Features of the model including an explication of key analytic decision points are illustrated using longitudinal reading data. To aid in making this class of models accessible, annotated Mplus code is provided.     

The merits of representational pictures in educational assessment: Evidence for cognitive and motivational effects in a time-on-task analysis

Adding representational pictures (RPs) to text-based items has been shown to improve students’ test performance. Focusing on potential explanations for this multimedia effect in testing, we propose two functions of RPs in testing, namely, (1) a cognitive facilitation function and (2) a motivational function. We found empirical support for both functions in this computer-based classroom experiment with N = 410 fifth and sixth graders. All students answered 36 manipulated science items that either contained (text-picture) or did not contain (text-only) an RP that visualized the text information in the item stem. Each student worked on both item types, following a rotated within-subject design. We measured students’ (a) solution success, (b) time on task (TOT), and identified (c) rapid-guessing behavior (RGB). We used generalized and linear mixed-effects models to investigate RPs’ impact on these outcome parameters and considered students’ level of test engagement and item positions as covariates. The results indicate that (1) RPs improved all students’ performance across item positions in a comparable manner (multimedia effect in testing). (2) RPs have the potential to accelerate item processing (cognitive facilitation function). (3) The presence of RPs reduced students’ RGB rates to a meaningful extent (motivational function). Overall, our data indicate that RPs may promote more reliable test scores, supporting a more valid interpretation of students’ achievement levels.     

Integrated statistical and engineering process control based on smooth transition autoregressive model

Traditional studies on integrated statistical process control and engineering process control (SPC-EPC) are based on linear autoregressive integrated moving average (ARIMA) time series models to describe the dynamic noise of the system.However,linear models sometimes are unable to model complex nonlinear autocorrelation.To solve this problem,this paper presents an integrated SPC-EPC method based on smooth transition autoregressive (STAR) time series model,and builds a minimum mean squared error (MMSE) controller as well as an integrated SPC-EPC control system.The performance of this method for checking the trend and sustained shift is analyzed.The simulation results indicate that this integrated SPC-EPC control method based on STAR model is effective in controlling complex nonlinear systems.     

A Second-Order Conditionally Linear Mixed Effects Model With Observed and Latent Variable Covariates

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a nonlinear manner are common to all subjects. In this article we describe how a variant of the Michaelis–Menten (M–M) function can be fit within this modeling framework using Mplus 6.0. We demonstrate how observed and latent covariates can be incorporated to help explain individual differences in growth characteristics. Features of the model including an explication of key analytic decision points are illustrated using longitudinal reading data. To aid in making this class of models accessible, annotated Mplus code is provided.     

Regime Switching Modeling of Substance Use: Time-Varying and Second-Order Markov Models and Individual Probability Plots

A linear latent growth curve mixture model with regime switching is extended in 2 ways. Previously, the matrix of first-order Markov switching probabilities was specified to be time-invariant, regardless of the pair of occasions being considered. The first extension, time-varying transitions, specifies different Markov transition matrices between each pair of occasions. The second extension is second-order time-invariant Markov transition probabilities, such that the probability of switching depends on the states at the 2 previous occasions. The models are implemented using the R package OpenMx, which facilitates data handling, parallel computation, and further model development. It also enables the extraction and display of relative likelihoods for every individual in the sample. The models are illustrated with previously published data on alcohol use observed on 4 occasions as part of the National Longitudinal Survey of Youth, and demonstrate improved fit to the data.