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。     

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。     

Sensitive Topics,Missing Data,and Refusal in Social Network Studies: An Ethical Examination

We describe our ethics‐driven process of addressing missing data within a social network study about accountability for racism, classism, sexism, heterosexism, cis‐sexism, ableism, and other forms of oppression among social justice union organizers. During data collection, some would‐be participants did not return emails and others explicitly refused to engage in the research. All refusals came from women of color. We faced an ethical dilemma: Should we continue to seek participation from those who had not yet responded, with the hopes of recruiting more women of color from within the network so their perspectives would not be tokenized? Or, should we stop asking those who had been contacted multiple times, which would compromise the social network data and analysis? We delineate ways in which current discussions of the ethics of social network studies fell short, given our framework and our community psychology (CP ) values. We outline literature that was helpful in thinking through this challenge; we looked outside of CP to the decolonization literature on refusal. Lessons learned include listening for the possible meanings of refusals and considering the level of engagement and the labor required of participants when designing research studies.     

Estimating Incremental Validity Under Missing Data

A common form of missing data is caused by selection on an observed variable (e.g., Z). If the selection variable was measured and is available, the data are regarded as missing at random (MAR). Selection biases correlation, reliability, and effect size estimates when these estimates are computed on listwise deleted (LD) data sets. On the other hand, maximum likelihood (ML) estimates are generally unbiased and outperform LD in most situations, at least when the data are MAR. The exception is when we estimate the partial correlation. In this situation, LD estimates are unbiased when the cause of missingness is partialled out. In other words, there is no advantage of ML estimates over LD estimates in this situation. We demonstrate that under a MAR condition, even ML estimates may become biased, depending on how partial correlations are computed. Finally, we conclude with recommendations about how future researchers might estimate partial correlations even when the cause of missingness is unknown and, perhaps, unknowable.     

Measuring Creativity with Planned Missing Data

This paper introduces a method for the assessment of creativity that relies on creativity tasks, a subjective evaluation procedure, and a planned missing data design that offers a drastic reduction in the overall implementation costs (administration time and scoring procedure). This method was tested on a sample of 149 people, using three creativity tasks as a basis. Participants were instructed to produce several ideas in each task and then to select what they considered to be their best two ideas (i.e., “Top 2” procedure; Silvia, Winterstein, Willse, Barona, et al., Psychology of Aesthetics, Creativity, and the Arts, 2 , 2008 and 68). These ideas were then evaluated by a panel of peers and experts. Creativity ratings were analyzed with structural equations; measurement models were estimated for each task and correlations between factor-scores across the three tasks were investigated. Further insights regarding validity are provided through systematic investigation of the relationship between fluency scores, creativity ratings, intelligence tasks, self-reported idea generation abilities, and creative activities and achievements. Overall, the results support the viability of this new approach, providing evidence of convergent and discriminant validity. They are discussed in relation to past research and avenues for further extension are proposed.     

Methods for Mediation Analysis with Missing Data

Despite wide applications of both mediation models and missing data techniques, formal discussion of mediation analysis with missing data is still rare. We introduce and compare four approaches to dealing with missing data in mediation analysis including listwise deletion, pairwise deletion, multiple imputation (MI), and a two-stage maximum likelihood (TS-ML) method. An R package bmem is developed to implement the four methods for mediation analysis with missing data in the structural equation modeling framework, and two real examples are used to illustrate the application of the four methods. The four methods are evaluated and compared under MCAR, MAR, and MNAR missing data mechanisms through simulation studies. Both MI and TS-ML perform well for MCAR and MAR data regardless of the inclusion of auxiliary variables and for AV-MNAR data with auxiliary variables. Although listwise deletion and pairwise deletion have low power and large parameter estimation bias in many studied conditions, they may provide useful information for exploring missing mechanisms.     

Planned Missing Data Designs for Research in Cognitive Development

Data collection can be the most time- and cost-intensive part of developmental research. This article describes some long-proposed but little-used research designs that have the potential to maximize data quality (reliability and validity) while minimizing research cost. In planned missing data designs, missing data are used strategically to improve the validity of data collection in one of two ways. Multiform designs allow one to increase the number of measures assessed on each participant without increasing each participant's burden. Two-method measurement designs allow one to reap the benefits of a cost-intensive gold-standard measure, using a larger sample size made possible by a rougher, cheaper measure. We explain each method using examples relevant to cognitive development research. With the use of analysis methods that produce unbiased results, planned missing data designs are an efficient way to manage cost, improve data quality, and reduce participant fatigue and practice effects.     

Using Principal Components as Auxiliary Variables in Missing Data Estimation

To deal with missing data that arise due to participant nonresponse or attrition, methodologists have recommended an “inclusive” strategy where a large set of auxiliary variables are used to inform the missing data process. In practice, the set of possible auxiliary variables is often too large. We propose using principal components analysis (PCA) to reduce the number of possible auxiliary variables to a manageable number. A series of Monte Carlo simulations compared the performance of the inclusive strategy with eight auxiliary variables (inclusive approach) to the PCA strategy using just one principal component derived from the eight original variables (PCA approach). We examined the influence of four independent variables: magnitude of correlations, rate of missing data, missing data mechanism, and sample size on parameter bias, root mean squared error, and confidence interval coverage. Results indicate that the PCA approach results in unbiased parameter estimates and potentially more accuracy than the inclusive approach. We conclude that using the PCA strategy to reduce the number of auxiliary variables is an effective and practical way to reap the benefits of the inclusive strategy in the presence of many possible auxiliary variables.     

Treatment of Missing Data: Beyond Ends and Means

The ethical decision making process behind the treatment of missing data has yet to be examined in the research literature in any discipline. The purpose of the current paper is to begin to discuss this decision-making process in view of a Foucauldian framework. The paper suggests how the ethical treatment of missing data should be considered from the adoption of this theoretical framework.     

Identifying Variables Responsible for Data not Missing at Random

When data are not missing at random (NMAR), maximum likelihood (ML) procedure will not generate consistent parameter estimates unless the missing data mechanism is correctly modeled. Understanding NMAR mechanism in a data set would allow one to better use the ML methodology. A survey or questionnaire may contain many items; certain items may be responsible for NMAR values in other items. The paper develops statistical procedures to identify the responsible items. By comparing ML estimates (MLE), statistics are developed to test whether the MLEs are changed when excluding items. The items that cause a significant change of the MLEs are responsible for the NMAR mechanism. Normal distribution is used for obtaining the MLEs; a sandwich-type covariance matrix is used to account for distribution violations. The class of nonnormal distributions within which the procedure is valid is provided. Both saturated and structural models are considered. Effect sizes are also defined and studied. The results indicate that more missing data in a sample does not necessarily imply more significant test statistics due to smaller effect sizes. Knowing the true population means and covariances or the parameter values in structural equation models may not make things easier either. The research was supported by NSF grant DMS04-37167, the James McKeen Cattell Fund.     

Examining Nonnormal Latent Variable Distributions for Non-Ignorable Missing Data

Missing not at random (MNAR) modeling for non-ignorable missing responses usually assumes that the latent variable distribution is a bivariate normal distribution. Such an assumption is rarely verified and often employed as a standard in practice. Recent studies for “complete” item responses (i.e., no missing data) have shown that ignoring the nonnormal distribution of a unidimensional latent variable, especially skewed or bimodal, can yield biased estimates and misleading conclusion. However, dealing with the bivariate nonnormal latent variable distribution with present MNAR data has not been looked into. This article proposes to extend unidimensional empirical histogram and Davidian curve methods to simultaneously deal with nonnormal latent variable distribution and MNAR data. A simulation study is carried out to demonstrate the consequence of ignoring bivariate nonnormal distribution on parameter estimates, followed by an empirical analysis of “don’t know” item responses. The results presented in this article show that examining the assumption of bivariate nonnormal latent variable distribution should be considered as a routine for MNAR data to minimize the impact of nonnormality on parameter estimates.     

Exploratory Factor Analysis With Small Samples and Missing Data

Exploratory factor analysis (EFA) is an extremely popular method for determining the underlying factor structure for a set of variables. Due to its exploratory nature, EFA is notorious for being conducted with small sample sizes, and recent reviews of psychological research have reported that between 40% and 60% of applied studies have 200 or fewer observations. Recent methodological studies have addressed small size requirements for EFA models; however, these models have only considered complete data, which are the exception rather than the rule in psychology. Furthermore, the extant literature on missing data techniques with small samples is scant, and nearly all existing studies focus on topics that are not of primary interest to EFA models. Therefore, this article presents a simulation to assess the performance of various missing data techniques for EFA models with both small samples and missing data. Results show that deletion methods do not extract the proper number of factors and estimate the factor loadings with severe bias, even when data are missing completely at random. Predictive mean matching is the best method overall when considering extracting the correct number of factors and estimating factor loadings without bias, although 2-stage estimation was a close second.     

概化理论缺失数据方差分量估计

各种心理调查、心理实验中, 数据的缺失随处可见。由于数据缺失, 给概化理论分析非平衡数据的方差分量带来一系列问题。基于概化理论框架下, 运用Matlab 7.0软件, 自编程序模拟产生随机双面交叉设计p×i×r缺失数据, 比较和探讨公式法、REML法、拆分法和MCMC法在估计各个方差分量上的性能优劣。结果表明：(1) MCMC方法估计随机双面交叉设计p×i×r缺失数据方差分量, 较其它3种方法表现出更强的优势; (2) 题目和评分者是缺失数据方差分量估计重要的影响因素。     

Robust Structural Equation Modeling with Missing Data and Auxiliary Variables

The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package rsem to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables are then fitted to the structural model in the second stage. A sandwich-type covariance matrix is used to obtain consistent standard errors (SE) of the structural parameter estimates. Rescaled, adjusted as well as corrected and F-statistics are proposed for overall model evaluation. Using R and EQS, the R package rsem combines the two stages and generates all the test statistics and consistent SEs. Following the robust analysis, multiple model fit indices and standardized solutions are provided in the corresponding output of EQS. An example with open/closed book examination data illustrates the proper use of the package. The method is further applied to the analysis of a data set from the National Longitudinal Survey of Youth 1997 cohort, and results show that the developed procedure not only gives a better endorsement of the substantive models but also yields estimates with uniformly smaller standard errors than the normal-distribution-based maximum likelihood.     

A Bayesian Approach for Estimating Mediation Effects With Missing Data

Methodologists have developed mediation analysis techniques for a broad range of substantive applications, yet methods for estimating mediating mechanisms with missing data have been understudied. This study outlined a general Bayesian missing data handling approach that can accommodate mediation analyses with any number of manifest variables. Computer simulation studies showed that the Bayesian approach produced frequentist coverage rates and power estimates that were comparable to those of maximum likelihood with the bias-corrected bootstrap. We share an SAS macro that implements Bayesian estimation and use 2 data analysis examples to demonstrate its use.     

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.