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.     

Multiple Imputation of Item Scores in Test and Questionnaire Data,and Influence on Psychometric Results

The performance of five simple multiple imputation methods for dealing with missing data were compared. In addition, random imputation and multivariate normal imputation were used as lower and upper benchmark, respectively. Test data were simulated and item scores were deleted such that they were either missing completely at random, missing at random, or not missing at random. Cronbach's alpha, Loevinger's scalability coefficient H, and the item cluster solution from Mokken scale analysis of the complete data were compared with the corresponding results based on the data including imputed scores. The multiple-imputation methods, two-way with normally distributed errors, corrected item-mean substitution with normally distributed errors, and response function, produced discrepancies in Cronbach's coefficient alpha, Loevinger's coefficient H, and the cluster solution from Mokken scale analysis, that were smaller than the discrepancies in upper benchmark multivariate normal imputation.     

Multiple Imputation for Multivariate Missing-Data Problems: A Data Analyst's Perspective

Analyses of multivariate data are frequently hampered by missing values. Until recently, the only missing-data methods available to most data analysts have been relatively ad1 hoc practices such as listwise deletion. Recent dramatic advances in theoretical and computational statistics, however, have produced anew generation of flexible procedures with a sound statistical basis. These procedures involve multiple imputation (Rubin, 1987), a simulation technique that replaces each missing datum with a set of m > 1 plausible values. The rn versions of the complete data are analyzed by standard complete-data methods, and the results are combined using simple rules to yield estimates, standard errors, and p-values that formally incorporate missing-data uncertainty. New computational algorithms and software described in a recent book (Schafer, 1997a) allow us to create proper multiple imputations in complex multivariate settings. This article reviews the key ideas of multiple imputation, discusses the software programs currently available, and demonstrates their use on data from the Adolescent Alcohol Prevention Trial (Hansen & Graham, 199 I).     

A Bayesian Nonparametric Approach to Test Equating

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are compared through the analysis of data sets famous in the equating literature. Also, the classical percentile-rank, linear, and mean equating models are each proven to be a special case of a Bayesian model under a highly-informative choice of prior distribution.     

Abstract: Evaluation of Test Statistics for Robust Structural Equation Modeling With Nonnormal Missing Data

Traditional structural equation modeling (SEM) techniques have trouble dealing with incomplete and/or nonnormal data that are often encountered in practice. Yuan and Zhang (2011a) developed a two-stage procedure for SEM to handle nonnormal missing data and proposed four test statistics for overall model evaluation. Although these statistics have been shown to work well with complete data, their performance for incomplete data has not been investigated in the context of robust statistics.

Focusing on a linear growth curve model, a systematic simulation study is conducted to evaluate the accuracy of the parameter estimates and the performance of five test statistics including the naive statistic derived from normal distribution based maximum likelihood (ML), the Satorra-Bentler scaled chi-square statistic (RML), the mean- and variance-adjusted chi-square statistic (AML), Yuan-Bentler residual-based test statistic (CRADF), and Yuan-Bentler residual-based F statistic (RF). Data are generated and analyzed in R using the package rsem (Yuan & Zhang, 2011b).

Based on the simulation study, we can observe the following: (a) The traditional normal distribution-based method cannot yield accurate parameter estimates for nonnormal data, whereas the robust method obtains much more accurate model parameter estimates for nonnormal data and performs almost as well as the normal distribution based method for normal distributed data. (b) With the increase of sample size, or the decrease of missing rate or the number of outliers, the parameter estimates are less biased and the empirical distributions of test statistics are closer to their nominal distributions. (c) The ML test statistic does not work well for nonnormal or missing data. (d) For nonnormal complete data, CRADF and RF work relatively better than RML and AML. (e) For missing completely at random (MCAR) missing data, in almost all the cases, RML and AML work better than CRADF and RF. (f) For nonnormal missing at random (MAR) missing data, CRADF and RF work better than AML. (g) The performance of the robust method does not seem to be influenced by the symmetry of outliers.     

On the Model-Based Bootstrap With Missing Data: Obtaining a P-Value for a Test of Exact Fit

Evaluating the fit of a structural equation model via bootstrap requires a transformation of the data so that the null hypothesis holds exactly in the sample. For complete data, such a transformation was proposed by Beran and Srivastava (1985) Beran, R. and Srivastava, M. S. 1985. Bootstrap tests and confidence regions for functions of a covariance matrix. The Annals of Statistics, 13: 95–115. [Crossref], [Web of Science ®] , [Google Scholar] for general covariance structure models and applied to structural equation modeling by Bollen and Stine (1992) Bollen, K. A. and Stine, R. A. 1992. Bootstrapping goodness-of-fit measures in structural equation models. Sociological Methods and Research, 21: 205–229. [Crossref], [Web of Science ®] , [Google Scholar]. An extension of this transformation to missing data was presented by Enders (2002) Enders, C. K. 2002. Applying the Bollen-Stine bootstrap for goodness-of-fit measures to structural equation models with missing data. Multivariate Behavioral Research, 37: 359–377. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], but it is an approximate and not an exact solution, with the degree of approximation unknown. In this article, we provide several approaches to obtaining an exact solution. First, an explicit solution for the special case when the sample covariance matrix within each missing data pattern is invertible is given. Second, 2 iterative algorithms are described for obtaining an exact solution in the general case. We evaluate the rejection rates of the bootstrapped likelihood ratio statistic obtained via the new procedures in a Monte Carlo study. Our main finding is that model-based bootstrap with incomplete data performs quite well across a variety of distributional conditions, missing data mechanisms, and proportions of missing data. We illustrate our new procedures using empirical data on 26 cognitive ability measures in junior high students, published in Holzinger and Swineford (1939) Holzinger, K. J. and Swineford, F. 1939. A study in factor analysis: The stability of a bi-factor solution. Supplementary Educational Monographs, 48: 1–91.  [Google Scholar].     

The Performance of Methods to Test Upper-Level Mediation in the Presence of Nonnormal Data

A Monte Carlo study compared the statistical performance of standard and robust multilevel mediation analysis methods to test indirect effects for a cluster randomized experimental design under various departures from normality. The performance of these methods was examined for an upper-level mediation process, where the indirect effect is a fixed effect and a group-implemented treatment is hypothesized to impact a person-level outcome via a person-level mediator. Two methods—the bias-corrected parametric percentile bootstrap and the empirical-M test—had the best overall performance. Methods designed for nonnormal score distributions exhibited elevated Type I error rates and poorer confidence interval coverage under some conditions. Although preliminary, the findings suggest that new mediation analysis methods may provide for robust tests of indirect effects.     

A Procedure for Dimensionality Analyses of Response Data from Various Test Designs

In some popular test designs (including computerized adaptive testing and multistage testing), many item pairs are not administered to any test takers, which may result in some complications during dimensionality analyses. In this paper, a modified DETECT index is proposed in order to perform dimensionality analyses for response data from such designs. It is proven in this paper that under certain conditions, the modified DETECT can successfully find the dimensionality-based partition of items. Furthermore, the modified DETECT index is decomposed into two parts, which can serve as indices of the reliability of results from the DETECT procedure when response data are judged to be multidimensional. A simulation study shows that the modified DETECT can successfully recover the dimensional structure of response data under reasonable specifications. Finally, the modified DETECT procedure is applied to real response data from two-stage tests to demonstrate how to utilize these indices and interpret their values in dimensionality analyses.     

A Test of Order-Constrained Hypotheses for Circular Data With Applications to Human Movement Science

Researchers studying the movements of the human body often encounter data measured in angles (e.g., angular displacements of joints). The evaluation of these circular data requires special statistical methods. The authors introduce a new test for the analysis of order-constrained hypotheses for circular data. Through this test, researchers can evaluate their expectations regarding the outcome of an experiment directly by representing their ideas in the form of a hypothesis containing inequality constraints. The resulting data analysis is generally more powerful than one using standard null hypothesis testing. Two examples of circular data from human movement science are presented to illustrate the use of the test. Results from a simulation study show that the test performs well.     

应用计算机技术实现精确测试双手协调性的方法

双手协调性测试是测量个体注意分配经常使用的方法。在同一时间内,把注意分配到两种或两种以上不同的对象与活动上,叫做注意分配。注意的分配品质是完成复杂工作的重要条件。如果一个汽车司机不能同时把注意分配在不同的活动之上,就不能成为一个合格的司机。对于其它许多的职业,注意分配都是一个很重要的个性心理品质。准确地获得个体的个性心理品质特点对于个体选择职业以及在岗位上的贡献都很重要。     

Nonlinear Predictive Models for Multiple Mediation Analysis: With an Application to Explore Ethnic Disparities in Anxiety and Depression Among Cancer Survivors

Mediation analysis allows the examination of effects of a third variable (mediator/confounder) in the causal pathway between an exposure and an outcome. The general multiple mediation analysis method (MMA), proposed by Yu et al., improves traditional methods (e.g., estimation of natural and controlled direct effects) to enable consideration of multiple mediators/confounders simultaneously and the use of linear and nonlinear predictive models for estimating mediation/confounding effects. Previous studies find that compared with non-Hispanic cancer survivors, Hispanic survivors are more likely to endure anxiety and depression after cancer diagnoses. In this paper, we applied MMA on MY-Health study to identify mediators/confounders and quantify the indirect effect of each identified mediator/confounder in explaining ethnic disparities in anxiety and depression among cancer survivors who enrolled in the study. We considered a number of socio-demographic variables, tumor characteristics, and treatment factors as potential mediators/confounders and found that most of the ethnic differences in anxiety or depression between Hispanic and non-Hispanic white cancer survivors were explained by younger diagnosis age, lower education level, lower proportions of employment, less likely of being born in the USA, less insurance, and less social support among Hispanic patients.     

Self-efficacy and Endurance Performance: A Longitudinal Field Test of Cognitive Mediation Theory

On demanda à 123 étudiants de cours de perfectionnement, désignés au hasard, de réaliser de leur mieux une tâche très difficile, au but presqu' impossible à atteindre, après cinq semaines d'entraînement à effectuer une tâche spécifique en trois minutes. Une période-test de quatre semaines suivit au cours de laquelle les buts des táches que devaient réaliser les sujets et leur confiance en leur efficacité furent mesurés une fois par semaine avant chaque évaluation de performance. Construit d'après une théorie de médiation cognitive (Garland, 1985), un modèle causal fut utilisé dans lequel des buts de tâches individuelles furent soumis aux effets de la performance, notamment sur l'efficacité des sujets. L'analyse des résultats à partir des quatre tests hebdomadaires confirma les propositions du modèle.
One hundred and twenty-three students in a fitness training course were assigned at random to a do your best, very hard, or highly improbable goal condition after five weeks of baseline training on a three-minute sit-up task. A four-week test period followed in which subjects' task goals and efficacy expectations were measured once each week prior to an assessment of their performance. Based on cognitive mediation theory (Garland, 1985), a causal model was presented in which individual task goals are proposed to influence performance through their influence on self-efficacy. Path analyses on the data over each of the four test weeks provided support for the proposed model.     

Addressing Item-Level Missing Data: A Comparison of Proration and Full Information Maximum Likelihood Estimation

Often when participants have missing scores on one or more of the items comprising a scale, researchers compute prorated scale scores by averaging the available items. Methodologists have cautioned that proration may make strict assumptions about the mean and covariance structures of the items comprising the scale (Schafer &; Graham, 2002 Schafer, J.L., &; Graham, J.W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147–177.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Graham, 2009 Graham, J.W. (2009). Missing data analysis: Making it work in the real world. Annual Review of Psychology, 60, 549–576.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Enders, 2010 Enders, C.K. (2010). Applied missing data analysis. New York, NY: Guilford Press. [Google Scholar]). We investigated proration empirically and found that it resulted in bias even under a missing completely at random (MCAR) mechanism. To encourage researchers to forgo proration, we describe a full information maximum likelihood (FIML) approach to item-level missing data handling that mitigates the loss in power due to missing scale scores and utilizes the available item-level data without altering the substantive analysis. Specifically, we propose treating the scale score as missing whenever one or more of the items are missing and incorporating items as auxiliary variables. Our simulations suggest that item-level missing data handling drastically increases power relative to scale-level missing data handling. These results have important practical implications, especially when recruiting more participants is prohibitively difficult or expensive. Finally, we illustrate the proposed method with data from an online chronic pain management program.     

Regime Switching State-Space Models Applied to Psychological Processes: Handling Missing Data and Making Inferences

Many psychological processes are characterized by recurrent shifts between distinct regimes or states. Examples that are considered in this paper are the switches between different states associated with premenstrual syndrome, hourly fluctuations in affect during a major depressive episode, and shifts between a “hot hand” and a “cold hand” in a top athlete. We model these processes with the regime switching state-space model proposed by Kim (J. Econom. 60:1–22, 1994), which results in both maximum likelihood estimates for the model parameters and estimates of the latent variables and the discrete states of the process. However, the current algorithm cannot handle missing data, which limits its applicability to psychological data. Moreover, the performance of standard errors for the purpose of making inferences about the parameter estimates is yet unknown. In this paper we modify Kim’s algorithm so it can handle missing data and we perform a simulation study to investigate its performance in (relatively) short time series in cases of different kinds of missing data and in case of complete data. Finally, we apply the regime switching state-space model to the three empirical data sets described above.     

A New Variable Weighting and Selection Procedure for K-means Cluster Analysis

A variance-to-range ratio variable weighting procedure is proposed. We show how this weighting method is theoretically grounded in the inherent variability found in data exhibiting cluster structure. In addition, a variable selection procedure is proposed to operate in conjunction with the variable weighting technique. The performances of these procedures are demonstrated in a simulation study, showing favorable results when compared with existing standardization methods. A detailed demonstration of the weighting and selection procedure is provided for the well-known Fisher Iris data and several synthetic data sets.     

The Effects of Piece-Rate Underpayment and Overpayment on Job Performance: A Test of Equity Theory with a New Induction Procedure1

An experiment was designed to test the following hypotheses derived from Equity Theory: (I) Underpaid pieceworkers will produce more work of lower quality than equitably paid pieceworkers and (II) Overpaid pieceworkers will produce less work of higher quality than equitably paid pieceworkcrs. Thirty-six males and 36 females were hired for a 1-hour proofreading job. Subjects were assigned randomly to receive 15, 30, or 60 cents per page. All subjects met another worker (really a confederate) who revealed that he was receiving 30 cents per page. This produced three experimental conditions: underpayment, equity, and overpayment. The principal dependent variables were number of pages read and proportion of errors detected by subjects. In general, the results provide strong support for Equity Theory. Males and females both performed in a manner consistent with the hypotheses, although females did tend to react less intensely than did males when overpaid.     

Mediation in discrimination transfers: A reply to Cole and Medin

In replying to Cole and Medin we agree with their main point that a demonstration of the existence of mediation in young children no longer constitutes an important theoretical contribution. However, we emphasize the features of the Brown and Scott study which we believe make it more than an existence demonstration. Furthermore, we have some quarrels with Cole and Medin's general assessment of the problems in the area and wish to raise a further question: Do the shift paradigms thus far employed deal with mediated learning or mediated transfer?     

Disclosure of Tests and Raw Test Data to the Courts: A Need for Reform

Psychologists' current practices with respect to the disclosure of tests and raw test data to courts are damaging their reputations as scientists, undermining their credibility as honest professionals acting in good faith, and contrary to the best interests of consumers. The profession is conducting itself in a contradictory fashion that deserves reform. There is need for an interdisciplinary panel drawn from the American Psychological Association and American Bar Association to develop reasonable procedures for disclosure of tests and test data in legal proceedings. These procedures should be developed with input from experienced psychological expert witnesses, attorneys, and judges from a variety of state and federal jurisdictions, diverse geographical areas, and different types of legal proceedings. This expert panel should also address the issue of attorney coaching of clients in preparation for assessment by psychologists.