Bias in longitudinal data analysis with missing data using typical linear mixed‐effects modelling and pattern‐mixture approach: An analytical illustration

We analytically derive the fixed‐effects estimates in unconditional linear growth curve models by typical linear mixed‐effects modelling (TLME) and by a pattern‐mixture (PM) approach with random‐slope‐dependent two‐missing‐pattern missing not at random (MNAR) longitudinal data. Results showed that when the missingness mechanism is random‐slope‐dependent MNAR, TLME estimates of both the mean intercept and mean slope are biased because of incorrect weights used in the estimation. More specifically, the estimate of the mean slope is biased towards the mean slope for completers, whereas the estimate of the mean intercept is biased towards the opposite direction as compared to the estimate of the mean slope. We also discuss why the PM approach can provide unbiased fixed‐effects estimates for random‐coefficients‐dependent MNAR data but does not work well for missing at random or outcome‐dependent MNAR data. A small simulation study was conducted to illustrate the results and to compare results from TLME and PM. Results from an empirical data analysis showed that the conceptual finding can be generalized to other real conditions even when some assumptions for the analytical derivation cannot be met. Implications from the analytical and empirical results were discussed and sensitivity analysis was suggested for longitudinal data analysis with missing data.     

Missing not at random models for latent growth curve analyses

The past decade has seen a noticeable shift in missing data handling techniques that assume a missing at random (MAR) mechanism, where the propensity for missing data on an outcome is related to other analysis variables. Although MAR is often reasonable, there are situations where this assumption is unlikely to hold, leading to biased parameter estimates. One such example is a longitudinal study of substance use where participants with the highest frequency of use also have the highest likelihood of attrition, even after controlling for other correlates of missingness. There is a large body of literature on missing not at random (MNAR) analysis models for longitudinal data, particularly in the field of biostatistics. Because these methods allow for a relationship between the outcome variable and the propensity for missing data, they require a weaker assumption about the missing data mechanism. This article describes 2 classic MNAR modeling approaches for longitudinal data: the selection model and the pattern mixture model. To date, these models have been slow to migrate to the social sciences, in part because they required complicated custom computer programs. These models are now quite easy to estimate in popular structural equation modeling programs, particularly Mplus. The purpose of this article is to describe these MNAR modeling frameworks and to illustrate their application on a real data set. Despite their potential advantages, MNAR-based analyses are not without problems and also rely on untestable assumptions. This article offers practical advice for implementing and choosing among different longitudinal models.     

Neuropsychological changes in children with cancer: The treatment of missing data in longitudinal studies

Researchers conducting longitudinal studies with children or adults are inevitably confronted with problems of attrition and missing data. Missing data in longitudinal studies is frequently handled by excluding from analyses those cases for whom data are incomplete. This approach to missing data is not optimal. On the one hand, if data are missing at random, then dropping incomplete cases ignores information collected on those cases that could be used to improve estimates of population parameters (e.g., means, variances, covariances, and growth rates) and improve the power of significance tests of statistical hypotheses. On the other hand, if data are not missing at random, then dropping incomplete cases leads to biased parameter estimates and hypothesis tests that may be internally and externally invalid. This study uses three years of follow-up data from a longitudinal investigation of neuropsychological outcomes of cancer in children to demonstrate the problems presented by missing data in repeated measures designs and some solutions. In evaluating potential biasing effects of attrition, the study extends previous research on neuropsychological outcomes in pediatric cancer by inclusion of patients whose disease had relapsed, and by comparison of surviving and nonsurviving patients. Although the data presented have specific relevance to the study of neuropsychological outcome in pediatric cancer, the problems of missing data and the solutions presented are relevant to a wide variety of diseases and conditions of interest to researchers in child and adult neuropsychology.     

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).     

A Class of Distribution-Free Models for Longitudinal Mediation Analysis

Mediation analysis constitutes an important part of treatment study to identify the mechanisms by which an intervention achieves its effect. Structural equation model (SEM) is a popular framework for modeling such causal relationship. However, current methods impose various restrictions on the study designs and data distributions, limiting the utility of the information they provide in real study applications. In particular, in longitudinal studies missing data is commonly addressed under the assumption of missing at random (MAR), where current methods are unable to handle such missing data if parametric assumptions are violated. In this paper, we propose a new, robust approach to address the limitations of current SEM within the context of longitudinal mediation analysis by utilizing a class of functional response models (FRM). Being distribution-free, the FRM-based approach does not impose any parametric assumption on data distributions. In addition, by extending the inverse probability weighted (IPW) estimates to the current context, the FRM-based SEM provides valid inference for longitudinal mediation analysis under the two most popular missing data mechanisms; missing completely at random (MCAR) and missing at random (MAR). We illustrate the approach with both real and simulated data.     

基于增长模型的非随机缺失数据处理:选择模型和极大似然方法

对含有非随机缺失数据的潜变量增长模型,为了考察基于不同假设的缺失数据处理方法:极大似然(ML)方法与DiggleKenward选择模型的优劣,通过Monte Carlo模拟研究,比较两种方法对模型中增长参数估计精度及其标准误估计的差异,并考虑样本量、非随机缺失比例和随机缺失比例的影响。结果表明,符合前提假设的Diggle-Kenward选择模型的参数估计精度普遍高于ML方法;对于标准误估计值,ML方法存在一定程度的低估,得到的置信区间覆盖比率也明显低于Diggle-Kenward选择模型。     

Bayesian analysis of mixtures in structural equation models with non‐ignorable missing data

Structural equation models (SEMs) have become widely used to determine the interrelationships between latent and observed variables in social, psychological, and behavioural sciences. As heterogeneous data are very common in practical research in these fields, the analysis of mixture models has received a lot of attention in the literature. An important issue in the analysis of mixture SEMs is the presence of missing data, in particular of data missing with a non‐ignorable mechanism. However, only a limited amount of work has been done in analysing mixture SEMs with non‐ignorable missing data. The main objective of this paper is to develop a Bayesian approach for analysing mixture SEMs with an unknown number of components and non‐ignorable missing data. A simulation study shows that Bayesian estimates obtained by the proposed Markov chain Monte Carlo methods are accurate and the Bayes factor computed via a path sampling procedure is useful for identifying the correct number of components, selecting an appropriate missingness mechanism, and investigating various effects of latent variables in the mixture SEMs. A real data set on a study of job satisfaction is used to demonstrate the methodology.     

认知诊断缺失数据处理方法的比较：零替换、多重插补与极大似然估计法

数据缺失在测验中经常发生, 认知诊断评估也不例外, 数据缺失会导致诊断结果的偏差。首先, 通过模拟研究在多种实验条件下比较了常用的缺失数据处理方法。结果表明：(1)缺失数据导致估计精确性下降, 随着人数与题目数量减少、缺失率增大、题目质量降低, 所有方法的PCCR均下降, Bias绝对值和RMSE均上升。(2)估计题目参数时, EM法表现最好, 其次是MI, FIML和ZR法表现不稳定。(3)估计被试知识状态时, EM和FIML表现最好, MI和ZR表现不稳定。其次, 在PISA2015实证数据中进一步探索了不同方法的表现。综合模拟和实证研究结果, 推荐选用EM或FIML法进行缺失数据处理。     

错失焦虑与大学生被动性社交网站使用的交叉滞后分析

为探讨大学生错失焦虑与被动性社交网站使用间的准因果关系,采用错失焦虑量表和被动性社交网站使用量表对403名大学生进行间隔8个月的两阶段追踪调查。结果发现：(1)错失焦虑和被动性社交网站使用的自回归路径系数显著,存在风险累积效应。(2)错失焦虑与被动性社交网站使用在8个月内能够互相预测,存在强化螺旋效应。(3)错失焦虑与被动性社交网站使用的交叉滞后效应性别差异不显著,存在跨性别趋同效应。结果支持了强化螺旋模型,表明错失焦虑与大学生被动性社交网站使用能够交互影响。     

Postmodeling Sensitivity Analysis to Detect the Effect of Missing Data Mechanisms

Incomplete or missing data is a common problem in almost all areas of empirical research. It is well known that simple and ad hoc methods such as complete case analysis or mean imputation can lead to biased and/or inefficient estimates. The method of maximum likelihood works well; however, when the missing data mechanism is not one of missing completely at random (MCAR) or missing at random (MAR), it too can result in incorrect inference. Statistical tests for MCAR have been proposed, but these are restricted to a certain class of problems. The idea of sensitivity analysis as a means to detect the missing data mechanism has been proposed in the statistics literature in conjunction with selection models where conjointly the data and missing data mechanism are modeled. Our approach is different here in that we do not model the missing data mechanism but use the data at hand to examine the sensitivity of a given model to the missing data mechanism. Our methodology is meant to raise a flag for researchers when the assumptions of MCAR (or MAR) do not hold. To our knowledge, no specific proposal for sensitivity analysis has been set forth in the area of structural equation models (SEM). This article gives a specific method for performing postmodeling sensitivity analysis using a statistical test and graphs. A simulation study is performed to assess the methodology in the context of structural equation models. This study shows success of the method, especially when the sample size is 300 or more and the percentage of missing data is 20% or more. The method is also used to study a set of real data measuring physical and social self-concepts in 463 Nigerian adolescents using a factor analysis model.     

Cross-Sectional versus Longitudinal Age Gradients of Tower of Hanoi Performance: The Role of Practice Effects and Cohort Differences in Education

ABSTRACT

We examined 5-year longitudinal changes in Tower of Hanoi (TOH) performance in a population-based sample of adults (35–85 years initially; n?=?1480). An age-matched sample (n?=?433) was included to estimate practice effects. The longitudinal age gradients differed substantially from the cross-sectional age gradients. This was the case even when practice effects, that were substantial in magnitude across the young/middle-aged groups, were controlled for. Instead of a continuous age-related deficit in performance from 35 and onwards, longitudinal data showed slowing of performance and increases of illegal moves past age 65. Cohort-related differences in educational attainment did not account for this discrepancy. Further analyses revealed a positive relation between practice-related gains and explicit memory of having performed the task at the first test occasion and a positive association between latent changes in TOH and Block Design, in line with cross-sectional findings. In conclusion, the results demonstrate a pattern of age-related changes indicating a late-onset decline of TOH performance and underscore the need to control for retest effects in longitudinal aging research.     

追踪研究中缺失数据处理方法及应用现状分析

追踪研究中普遍存在缺失数据, 缺失数据处理方法的选择影响统计推断的精度及研究结果的有效性。首先, 阐述缺失机制及判断方法, 比较追踪研究中主要的缺失数据处理方法的特点、及实际应用中的缺失处理方法的选择和软件实现。其次, 对国内心理学中92篇追踪研究文献进行分析, 发现有59篇(64.13%)报告不同程度缺失, 其中仅39篇报告了处理方法且均为删除法。未来研究应深入探讨现有缺失数据处理方法的有效性, 进一步规范应用研究中缺失数据的处理。     

Dual imputation model for incomplete longitudinal data

Missing values are a practical issue in the analysis of longitudinal data. Multiple imputation (MI) is a well‐known likelihood‐based method that has optimal properties in terms of efficiency and consistency if the imputation model is correctly specified. Doubly robust (DR) weighing‐based methods protect against misspecification bias if one of the models, but not necessarily both, for the data or the mechanism leading to missing data is correct. We propose a new imputation method that captures the simplicity of MI and protection from the DR method. This method integrates MI and DR to protect against misspecification of the imputation model under a missing at random assumption. Our method avoids analytical complications of missing data particularly in multivariate settings, and is easy to implement in standard statistical packages. Moreover, the proposed method works very well with an intermittent pattern of missingness when other DR methods can not be used. Simulation experiments show that the proposed approach achieves improved performance when one of the models is correct. The method is applied to data from the fireworks disaster study, a randomized clinical trial comparing therapies in disaster‐exposed children. We conclude that the new method increases the robustness of imputations.     

Asymptotic bias of normal-distribution-based maximum likelihood estimates of moderation effects with data missing at random

Moderation analysis is useful for addressing interesting research questions in social sciences and behavioural research. In practice, moderated multiple regression (MMR) models have been most widely used. However, missing data pose a challenge, mainly because the interaction term is a product of two or more variables and thus is a non-linear function of the involved variables. Normal-distribution-based maximum likelihood (NML) has been proposed and applied for estimating MMR models with incomplete data. When data are missing completely at random, moderation effect estimates are consistent. However, simulation results have found that when data in the predictor are missing at random (MAR), NML can yield inaccurate estimates of moderation effects when the moderation effects are non-null. Simulation studies are subject to the limitation of confounding systematic bias with sampling errors. Thus, the purpose of this paper is to analytically derive asymptotic bias of NML estimates of moderation effects with MAR data. Results show that when the moderation effect is zero, there is no asymptotic bias in moderation effect estimates with either normal or non-normal data. When the moderation effect is non-zero, however, asymptotic bias may exist and is determined by factors such as the moderation effect size, missing-data proportion, and type of missingness dependence. Our analytical results suggest that researchers should apply NML to MMR models with caution when missing data exist. Suggestions are given regarding moderation analysis with missing data.     

错失恐惧对亲社会行为的影响

网络信息的纷繁复杂,让人们担忧因错失信息而导致自身的利益受损,本研究探讨这种现象的加剧对个体的亲社会行为的影响。本研究分别使用问卷法（研究1）和实验法（研究2）,探究错失恐惧对亲社会行为的影响以及在其过程中人际安全感的中介作用和基本心理需要满足的调节作用。结果发现：（1）个体的错失恐惧程度负向预测了其亲社会行为;（2）人际安全感在错失恐惧对亲社会行为的影响中起中介作用,高的错失恐惧水平会降低个体的人际安全感,从而减少个体的亲社会行为;（3）基本心理需要满足在错失恐惧对亲社会行为的负向预测作用中起调节作用,当个体的基本心理需要满足程度低的时候,错失恐惧对亲社会行为的消极影响显著增强。     

计划缺失设计——通过有意缺失让研究更高效

缺失值是社会科学研究中非常普遍的现象。全息极大似然估计和多重插补是目前处理缺失值最有效的方法。计划缺失设计利用特殊的实验设计有意产生缺失值, 再用现代的缺失值处理方法来完成统计分析, 获得无偏的统计结果。计划缺失设计可用于横断面调查减少(或增加)问卷长度和纵向调查减少测量次数, 也可用于提高测量有效性。常用的计划缺失设计有三式设计和两种方法测量。     

追踪研究方法在国内心理研究中的应用述评

以1982~2012年中国期刊网收录的88例追踪研究为对象,从应用现状、设计特征、数据处理三方面分析和评估追踪研究方法在国内心理研究的应用情况及存在的问题。结果显示,2005年之前追踪研究方法应用增长缓慢,2005年开始呈显著增长趋势,研究对象以未成年及成年早期群体为主。主要采用固定样本追踪设计,大部分研究测量2-3次、样本量在10~300之间、持续时间在3年内。61例有缺失的研究中,38例用删除法处理缺失;主要运用 HLM、方差分析、t检验和SEM分析追踪数据。相当部分研究存在测量次数少、样本量较小、持续时间短、被试缺失严重及数据处理方法相对陈旧问题。追踪研究方法的应用应注意,根据理论模型和研究有效性要求确定设计类型和设计特征,根据数据特征选择缺失处理方法和追踪数据分析方法。     

Bayesian Diagnostics of Hidden Markov Structural Equation Models with Missing Data

Cocaine is a type of drug that functions to increase the availability of the neurotransmitter dopamine in the brain. However, cocaine dependence or abuse is highly related to an increased risk of psychiatric disorders and deficits in cognitive performance, attention, and decision-making abilities. Given the chronic and persistent features of drug addiction, the progression of abstaining from cocaine often evolves across several states, such as addiction to, moderate dependence on, and swearing off cocaine. Hidden Markov models (HMMs) are well suited to the characterization of longitudinal data in terms of a set of unobservable states, and have increasingly been used to uncover the dynamic heterogeneity in progressive diseases or activities. However, the existence of outliers or influential points may misidentify the hidden states and distort the associated inference. In this study, we develop a Bayesian local influence procedure for HMMs with latent variables in the presence of missing data. The proposed model enables us to investigate the dynamic heterogeneity of multivariate longitudinal data, reveal how the interrelationships among latent variables change from one state to another, and simultaneously conduct statistical diagnosis for the given data, model assumptions, and prior inputs. We apply the proposed procedure to analyze a dataset collected by the UCLA center for advancing longitudinal drug abuse research. Several outliers or influential points that seriously influence estimation results are identified and removed. The proposed procedure also discovers the effects of treatment and individuals’ psychological problems on cocaine use behavior and delineates their dynamic changes across the cocaine-addiction states.     

On structural equation modeling with data that are not missing completely at random

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.The research of the first author was supported by grant No. SES-8312583 from the National Science Foundation and by a Spencer Foundation grant. We wish to thank Chuen-Rong Chan for drawing the path diagram.     

加速追踪设计的方法和应用

加速追踪设计(ALD)是一种选择相邻多个群组同时进行短期追踪研究, 获得在测量上有重叠的多个群组追踪数据, 对多个群组数据进行合并建构一条在时间跨度上较长的发展趋势或增长曲线的方法。ALD结合真追踪和横断设计的特征, 既保持真追踪设计的大部分优点, 克服真追踪研究中由于重测效应和被试缺失导致的问题, 又尝试分离年龄、群组和历史时间效应, 在发展心理研究有重要应用。已有研究探讨ALD的数据分析方法、ALD的有效性及设计特征。未来研究应关注拓展设计条件下ALD的适应性, 探索非线性假设或群组效应显著时的数据分析方法和ALD中缺失数据处理问题。