Recursive Partitioning to Identify Potential Causes of Differential Item Functioning in Cross-National Data

Differential item functioning (DIF) assessment is key in score validation. When DIF is present scores may not accurately reflect the construct of interest for some groups of examinees, leading to incorrect conclusions from the scores. Given rising immigration, and the increased reliance of educational policymakers on cross-national assessments such as Programme for International Student Assessment, Trends in International Mathematics and Science Study, and Progress in International Reading Literacy Study (PIRLS), DIF with regard to native language is of particular interest in this context. However, given differences in language and cultures, assuming similar cross-national DIF may lead to mistaken assumptions about the impact of immigration status, and native language on test performance. The purpose of this study was to use model-based recursive partitioning (MBRP) to investigate uniform DIF in PIRLS items across European nations. Results demonstrated that DIF based on mother's language was present for several items on a PIRLS assessment, but that the patterns of DIF were not the same across all nations.     

A Note on Recurring Misconceptions When Fitting Nonlinear Mixed Models

Nonlinear mixed-effects (NLME) models are used when analyzing continuous repeated measures data taken on each of a number of individuals where the focus is on characteristics of complex, nonlinear individual change. Challenges with fitting NLME models and interpreting analytic results have been well documented in the statistical literature. However, parameter estimates as well as fitted functions from NLME analyses in recent articles have been misinterpreted, suggesting the need for clarification of these issues before these misconceptions become fact. These misconceptions arise from the choice of popular estimation algorithms, namely, the first-order linearization method (FO) and Gaussian-Hermite quadrature (GHQ) methods, and how these choices necessarily lead to population-average (PA) or subject-specific (SS) interpretations of model parameters, respectively. These estimation approaches also affect the fitted function for the typical individual, the lack-of-fit of individuals’ predicted trajectories, and vice versa.     

An Examination of a Functional Mixed-Effects Modeling Approach to the Analysis of Longitudinal Data

Growth curve modeling is one of the main analytical approaches to study change over time. Growth curve models are commonly estimated in the linear and nonlinear mixed-effects modeling framework in which both the mean and person-specific curves are modeled parametrically with functions of time such as the linear, quadratic, and exponential. However, when more complex nonlinear trajectories need to be estimated and researchers do not have a priori knowledge of an appropriate functional form of growth, parametric models may be too restrictive. This paper reviews functional mixed-effects models, a nonparametric extension of mixed-effects models that permit both the mean and person-specific curves to be estimated without assuming a prespecified functional form of growth. Details of the model are presented along with results from a simulation study and an empirical example. The simulation study showed functional mixed-effects models performed reasonably well under various conditions commonly associated with longitudinal panel data, such as few time points per person, irregularly spaced time points across persons, missingness, and nonlinear trajectories. The usefulness of functional mixed-effects models is illustrated by analyzing empirical data from the Early Childhood Longitudinal Study – Kindergarten Class of 1998–1999.     

Estimating Age-Based Developmental Trajectories Using Latent Change Score Models Based on Measurement Occasion

Abstract

Accelerated longitudinal designs (ALDs) are designs in which participants from different cohorts provide repeated measures covering a fraction of the time range of the study. ALDs allow researchers to study developmental processes spanning long periods within a relatively shorter time framework. The common trajectory is studied by aggregating the information provided by the different cohorts. Latent change score (LCS) models provide a powerful analytical framework to analyze data from ALDs. With developmental data, LCS models can be specified using measurement occasion as the time metric. This provides a number of benefits, but has an important limitation: It makes it not possible to characterize the longitudinal changes as a function of a developmental process such as age or biological maturation. To overcome this limitation, we propose an extension of an occasion-based LCS model that includes age differences at the first measurement occasion. We conducted a Monte Carlo study and compared the results of including different transformations of the age variable. Our results indicate that some of the proposed transformations resulted in accurate expectations for the studied process across all the ages in the study, and excellent model fit. We discuss these results and provide the R code for our analysis.     

Misspecification in Latent Change Score Models: Consequences for Parameter Estimation,Model Evaluation,and Predicting Change

Latent change score models (LCS) are conceptually powerful tools for analyzing longitudinal data (McArdle & Hamagami, 2001). However, applications of these models typically include constraints on key parameters over time. Although practically useful, strict invariance over time in these parameters is unlikely in real data. This study investigates the robustness of LCS when invariance over time is incorrectly imposed on key change-related parameters. Monte Carlo simulation methods were used to explore the impact of misspecification on parameter estimation, predicted trajectories of change, and model fit in the dual change score model, the foundational LCS. When constraints were incorrectly applied, several parameters, most notably the slope (i.e., constant change) factor mean and autoproportion coefficient, were severely and consistently biased, as were regression paths to the slope factor when external predictors of change were included. Standard fit indices indicated that the misspecified models fit well, partly because mean level trajectories over time were accurately captured. Loosening constraint improved the accuracy of parameter estimates, but estimates were more unstable, and models frequently failed to converge. Results suggest that potentially common sources of misspecification in LCS can produce distorted impressions of developmental processes, and that identifying and rectifying the situation is a challenge.     

Model-based recursive partitioning of extended redundancy analysis with an application to nicotine dependence among US adults

Extended redundancy analysis (ERA) is used to reduce multiple sets of predictors to a smaller number of components and examine the effects of these components on a response variable. In various social and behavioural studies, auxiliary covariates (e.g., gender, ethnicity) can often lead to heterogeneous subgroups of observations, each of which involves distinctive relationships between predictor and response variables. ERA is currently unable to consider such covariate-dependent heterogeneity to examine whether the model parameters vary across subgroups differentiated by covariates. To address this issue, we combine ERA with model-based recursive partitioning in a single framework. This combined method, MOB-ERA, aims to partition observations into heterogeneous subgroups recursively based on a set of covariates while fitting a specified ERA model to data. Upon the completion of the partitioning procedure, one can easily examine the difference in the estimated ERA parameters across covariate-dependent subgroups. Moreover, it produces a tree diagram that aids in visualizing a hierarchy of partitioning covariates, as well as interpreting their interactions. In the analysis of public data concerning nicotine dependence among US adults, the method uncovered heterogeneous subgroups characterized by several sociodemographic covariates, each of which yielded different directional relationships between three predictor sets and nicotine dependence.     

Regularized Finite Mixture Models for Probability Trajectories

Finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time. In practice, trajectories are usually modeled as polynomials, which may fail to capture important features of the longitudinal pattern. Focusing on dichotomous response measures, we propose a likelihood penalization approach for parameter estimation that is able to capture a variety of nonlinear class mean trajectory shapes with higher precision than maximum likelihood estimates. We show how parameter estimation and inference for whether trajectories are time-invariant, linear time-varying, or nonlinear time-varying can be carried out for such models. To illustrate the method, we use simulation studies and data from a long-term longitudinal study of children at high risk for substance abuse. This work was supported in part by NIAAA grants R37 AA07065 and R01 AA12217 to RAZ.     

Estimation of nonlinear mixed-effects continuous-time models using the continuous-discrete extended Kalman filter

Many intensive longitudinal measurements are collected at irregularly spaced time intervals, and involve complex, possibly nonlinear and heterogeneous patterns of change. Effective modelling of such change processes requires continuous-time differential equation models that may be nonlinear and include mixed effects in the parameters. One approach of fitting such models is to define random effect variables as additional latent variables in a stochastic differential equation (SDE) model of choice, and use estimation algorithms designed for fitting SDE models, such as the continuous-discrete extended Kalman filter (CDEKF) approach implemented in the dynr R package, to estimate the random effect variables as latent variables. However, this approach's efficacy and identification constraints in handling mixed-effects SDE models have not been investigated. In the current study, we analytically inspect the identification constraints of using the CDEKF approach to fit nonlinear mixed-effects SDE models; extend a published model of emotions to a nonlinear mixed-effects SDE model as an example, and fit it to a set of irregularly spaced ecological momentary assessment data; and evaluate the feasibility of the proposed approach to fit the model through a Monte Carlo simulation study. Results show that the proposed approach produces reasonable parameter and standard error estimates when some identification constraint is met. We address the effects of sample size, process noise variance, and data spacing conditions on estimation results.     

Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis–Hastings algorithm is used to produce the joint Bayesian estimates of structural parameters, latent variables, parameters in the nonignorable missing model, as well as their standard errors estimates. A goodness-of-fit statistic for assessing the plausibility of the posited nonlinear structural equation model is introduced, and a procedure for computing the Bayes factor for model comparison is developed via path sampling. Results obtained with respect to different missing data models, and different prior inputs are compared via simulation studies. In particular, it is shown that in the presence of nonignorable missing data, results obtained by the proposed method with a nonignorable missing data model are significantly better than those that are obtained under the missing at random assumption. A real example is presented to illustrate the newly developed Bayesian methodologies. This research is fully supported by a grant (CUHK 4243/03H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are thankful to the editor and reviewers for valuable comments for improving the paper, and also to ICPSR and the relevant funding agency for allowing the use of the data. Requests for reprints should be sent to Professor S.Y. Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.     

Estimating Independent Locally Shifted Random Utility Models for Ranking Data

We present a mixed-effects location scale model (MELSM) for examining the daily dynamics of affect in dyads. The MELSM includes person and time-varying variables to predict the location, or individual means, and the scale, or within-person variances. It also incorporates a submodel to account for between-person variances. The dyadic specification can accommodate individual and partner effects in both the location and the scale components, and allows random effects for all location and scale parameters. All covariances among the random effects, within and across the location and the scale are also estimated. These covariances offer new insights into the interplay of individual mean structures, intra-individual variability, and the influence of partner effects on such factors. To illustrate the model, we use data from 274 couples who provided daily ratings on their positive and negative emotions toward their relationship – up to 90 consecutive days. The model is fit using Hamiltonian Monte Carlo methods, and includes subsets of predictors in order to demonstrate the flexibility of this approach. We conclude with a discussion on the usefulness and the limitations of the MELSM for dyadic research.     

A multivariate reduced-rank growth curve model with unbalanced data

A multivariate reduced-rank growth curve model is proposed that extends the univariate reducedrank growth curve model to the multivariate case, in which several response variables are measured over multiple time points. The proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way than the traditional growth curve model. In addition, the method is more flexible than the traditional growth curve model. For example, response variables do not have to be measured at the same time points, nor the same number of time points. It is also possible to apply various kinds of basis function matrices with different ranks across response variables. It is not necessary to specify an entire set of basis functions in advance. Examples are given for illustration.The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author. We thank Jennifer Stephan for her helpful comments on an earlier version of this paper. We also thank Patrick Curran and Terry Duncan for kindly letting us use the NLSY and substance use data, respectively. The substance use data were provided by Grant DA09548 from the National Institute on Drug Abuse.     

Testing Process Factor Analysis Models Using the Parametric Bootstrap

Process factor analysis (PFA) is a latent variable model for intensive longitudinal data. It combines P-technique factor analysis and time series analysis. The goodness-of-fit test in PFA is currently unavailable. In the paper, we propose a parametric bootstrap method for assessing model fit in PFA. We illustrate the test with an empirical data set in which 22 participants rated their effects everyday over a period of 90 days. We also explore Type I error and power of the parametric bootstrap test with simulated data.     

Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution then requires an integral equation that is of dimension equal to the number of nonlinear terms. For nonlinear functions that have linear coefficients, the improvement in computational speed and accuracy using the new algorithm can be dramatic. An illustration of the method with repeated measures data from a learning experiment is presented.     

航空决策模型及其影响因素分析

航空决策指在航空飞行驾驶过程中,飞行员面对特定情境做出最佳决策时的心理过程。情景评估和风险评估是航空决策模型中最重要的两个阶段。个体认知因素、疲劳和动机因素以及知识经验的限制会导致不良航空决策,组织压力和社会因素则通过混淆飞行员对飞行安全的看法间接影响航空决策。在未来的研究中,研究者应当重视构建更合理的航空决策模型,从辩证的角度全面看待知识经验与飞行安全的关系,加强对动机因素和环境因素的调查分析和实验性研究。     

A Comparison of Multilevel Imputation Schemes for Random Coefficient Models: Fully Conditional Specification and Joint Model Imputation with Random Covariance Matrices

Abstract

Literature addressing missing data handling for random coefficient models is particularly scant, and the few studies to date have focused on the fully conditional specification framework and “reverse random coefficient” imputation. Although it has not received much attention in the literature, a joint modeling strategy that uses random within-cluster covariance matrices to preserve cluster-specific associations is a promising alternative for random coefficient analyses. This study is apparently the first to directly compare these procedures. Analytic results suggest that both imputation procedures can introduce bias-inducing incompatibilities with a random coefficient analysis model. Problems with fully conditional specification result from an incorrect distributional assumption, whereas joint imputation uses an underparameterized model that assumes uncorrelated intercepts and slopes. Monte Carlo simulations suggest that biases from these issues are tolerable if the missing data rate is 10% or lower and the sample is composed of at least 30 clusters with 15 observations per group. Furthermore, fully conditional specification tends to be superior with intraclass correlations that are typical of crosssectional data (e.g., ICC?=?.10), whereas the joint model is preferable with high values typical of longitudinal designs (e.g., ICC?=?.50).     

面向“为学习而测评”的纵向认知诊断模型

基于“为学习而测评”的理念,以促进学生学习为目的,客观量化学习现状并提供诊断反馈的测评模式日益受到重视。相比于横断认识诊断测评,纵向认知诊断测评更有利于实现促进学生发展的目标。为使国内学者系统性地了解纵向认知诊断模型,首先,依据建模逻辑将已有纵向认知诊断模型划分为基于潜在转换分析的和基于高阶潜在结构模型的两类,并逐一介绍和说明两类模型的理论基础和应用情景;然后,通过模拟研究为读者呈现如何使用纵向认知诊断模型进行数据分析及如何解读相应的诊断结果。最后,提炼出四个可进一步研究的议题。     

Estimation of Controlled Direct Effects in Longitudinal Mediation Analyses with Latent Variables in Randomized Studies

Abstract

In a randomized study with longitudinal data on a mediator and outcome, estimating the direct effect of treatment on the outcome at a particular time requires adjusting for confounding of the association between the outcome and all preceding instances of the mediator. When the confounders are themselves affected by treatment, standard regression adjustment is prone to severe bias. In contrast, G-estimation requires less stringent assumptions than path analysis using SEM to unbiasedly estimate the direct effect even in linear settings. In this article, we propose a G-estimation method to estimate the controlled direct effect of treatment on the outcome, by adapting existing G-estimation methods for time-varying treatments without mediators. The proposed method can accommodate continuous and noncontinuous mediators, and requires no models for the confounders. Unbiased estimation only requires correctly specifying a mean model for either the mediator or the outcome. The method is further extended to settings where the mediator or outcome, or both, are latent, and generalizes existing methods for single measurement occasions of the mediator and outcome to longitudinal data on the mediator and outcome. The methods are utilized to assess the effects of an intervention on physical activity that is possibly mediated by motivation to exercise in a randomized study.     

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects

Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay &; Silverman, 2005 Ramsay, J. O., &; Silverman, B. W. (2005). Functional data analysis (2nd ed.). New York, NY: Springer-Verlag. [Google Scholar]), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, &; Peel, 2010 Boker, S. M., Deboeck, P. R., Edler, C., &; Peel, P. K. (2010). Generalized local linear approximation of derivatives from time series. In S. Chow, E. Ferrer, &; F. Hsieh (Eds.), Statistical methods for modeling human dynamics: An interdisciplinary dialogue (pp. 161–178). New York, NY: Taylor &; Francis. [Google Scholar]), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 Deboeck, P. R. (2010). Estimating dynamical systms: Derivative estimation hints from Sir Ronald A. Fisher. Multivariate Behavioral Research, 45, 725–745. doi:10.1080/00273171.2010.498294[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children’s self-regulation.