RMediation: An R package for mediation analysis confidence intervals

This article describes the RMediation package,which offers various methods for building confidence intervals (CIs) for mediated effects. The mediated effect is the product of two regression coefficients. The distribution-of-the-product method has the best statistical performance of existing methods for building CIs for the mediated effect. RMediation produces CIs using methods based on the distribution of product, Monte Carlo simulations, and an asymptotic normal distribution. Furthermore, RMediation generates percentiles, quantiles, and the plot of the distribution and CI for the mediated effect. An existing program, called PRODCLIN, published in Behavior Research Methods, has been widely cited and used by researchers to build accurate CIs. PRODCLIN has several limitations: The program is somewhat cumbersome to access and yields no result for several cases. RMediation described herein is based on the widely available R software, includes several capabilities not available in PRODCLIN, and provides accurate results that PRODCLIN could not.     

The Distribution of the Product Explains Normal Theory Mediation Confidence Interval Estimation

The distribution of the product has several useful applications. One of these applications is its use to form confidence intervals for the indirect effect as the product of 2 regression coefficients. The purpose of this article is to investigate how the moments of the distribution of the product explain normal theory mediation confidence interval coverage and imbalance. Values of the critical ratio for each random variable are used to demonstrate how the moments of the distribution of the product change across values of the critical ratio observed in research studies. Results of the simulation study showed that as skewness in absolute value increases, coverage decreases. And as skewness in absolute value and kurtosis increases, imbalance increases. The difference between testing the significance of the indirect effect using the normal theory versus the asymmetric distribution of the product is further illustrated with a real data example. This article is the first study to show the direct link between the distribution of the product and indirect effect confidence intervals and clarifies the results of previous simulation studies by showing why normal theory confidence intervals for indirect effects are often less accurate than those obtained from the asymmetric distribution of the product or from resampling methods.     

Comparison of methods for constructing confidence intervals of standardized indirect effects

Mediation models are often used as a means to explain the psychological mechanisms between an independent and a dependent variable in the behavioral and social sciences. A major limitation of the unstandardized indirect effect calculated from raw scores is that it cannot be interpreted as an effect-size measure. In contrast, the standardized indirect effect calculated from standardized scores can be a good candidate as a measure of effect size because it is scale invariant. In the present article, 11 methods for constructing the confidence intervals (CIs) of the standardized indirect effects were evaluated via a computer simulation. These included six Wald CIs, three bootstrap CIs, one likelihood-based CI, and the PRODCLIN CI. The results consistently showed that the percentile bootstrap, the bias-corrected bootstrap, and the likelihood-based approaches had the best coverage probability. Mplus, LISREL, and Mx syntax were included to facilitate the use of these preferred methods in applied settings. Future issues on the use of the standardized indirect effects are discussed.     

Exploring the mediating role of integrative self-knowledge in the relationship between mindfulness and well-being in the context of a mindfulness-based stress reduction program

Mindfulness-based stress reduction (MBSR) is an effective program for improving well-being. A growing body of studies is exploring the mechanisms mediating its beneficial effects. Integrative self-knowledge (ISK) is the construct of focus in this study. The primary goal of the current study was to investigate the mediating role of ISK in the relationship between improved mindful observing (MO), non-judging inner experience (NJ), and well-being following an MBSR program with an Iranian sample. Participants (n = 118) enrolled in MBSR and completed depression, anxiety, stress (DASS), Bartone Symptoms Checklist (BSC), Five-Facet Mindfulness Questionnaire, and ISK scale before and after the program. Results showed significant reductions in BSC, DASS, and improvements in MO, NJ, and ISK at the end of the program. Mediation analyses revealed that changes in ISK significantly mediated the relationship between changes in MO and NJ and symptoms (MO indirect effect on DASS: β = 0.11, confidence interval [CI] [0.003, 0.29]; NJ indirect effect on DASS: β = 0.12, CI [−0.16, 0.45]; MO indirect effect on BSC: β = 0.08, CI [0.001, 0.27]; NJ indirect effect on BSC: β = 0.09, CI [0.01, 0.22]). Improvements in MO and NJ may provide a pathway to cultivating ISK in MBSR, which may lead to enhanced well-being.     

非正态分布下概化理论方差分量变异量估计

方差分量估计是概化理论的必用技术,但受限于抽样,需要对其变异量进行探讨。采用Monte Carlo数据模拟技术,探讨非正态数据分布对四种方法估计概化理论方差分量变异量的影响。结果表明：（1）不同非正态数据分布下,各种估计方法的“性能”表现出差异性;（2）数据分布对方差分量变异量估计有影响,适合于非正态分布数据的方差分量变异量估计方法不一定适合于正态分布数据。     

基于概化理论的方差分量变异量估计

概化理论广泛应用于心理与教育测量实践中, 方差分量估计是进行概化理论分析的关键。方差分量估计受限于抽样, 需要对其变异量进行探讨。采用蒙特卡洛(Monte Carlo)数据模拟技术, 在正态分布下讨论不同方法对基于概化理论的方差分量变异量估计的影响。结果表明: Jackknife方法在方差分量变异量估计上不足取; 不采取Bootstrap方法的“分而治之”策略, 从总体上看, Traditional方法和有先验信息的MCMC方法在标准误及置信区间这两个变异量估计上优势明显。     

Problematic standard errors and confidence intervals for skewness and kurtosis

Many statistics packages print skewness and kurtosis statistics with estimates of their standard errors. The function most often used for the standard errors (e.g., in SPSS) assumes that the data are drawn from a normal distribution, an unlikely situation. Some textbooks suggest that if the statistic is more than about 2 standard errors from the hypothesized value (i.e., an approximate value for the critical value from the t distribution for moderate or large sample sizes when α = 5%), the hypothesized value can be rejected. This is an inappropriate practice unless the standard error estimate is accurate and the sampling distribution is approximately normal. We show distributions where the traditional standard errors provided by the function underestimate the actual values, often being 5 times too small, and distributions where the function overestimates the true values. Bootstrap standard errors and confidence intervals are more accurate than the traditional approach, although still imperfect. The reasons for this are discussed. We recommend that if you are using skewness and kurtosis statistics based on the 3^rd and 4^th moments, bootstrapping should be used to calculate standard errors and confidence intervals, rather than using the traditional standard. Software in the freeware R for this article provides these estimates.     

Some supplementary methods for the analysis of the Delis-Kaplan Executive Function System

Supplementary methods for the analysis of the Delis-Kaplan Executive Function System (Delis, Kaplan, & Kramer, 2001) are made available, including (a) quantifying the number of abnormally low achievement scores exhibited by an individual and accompanying this with an estimate of the percentage of the normative population expected to exhibit at least this number of low scores; (b) estimating the overall abnormality of an individual's achievement score profile with the Mahalanobis distance index; (c) calculating a composite executive function index score for an individual and providing accompanying confidence limits; and (d) providing the percentile ranks for an individual's achievement scores and executive index score (in the latter case, confidence limits on scores are also expressed as percentile ranks). With the exception of the Mahalanobis distance index, all the methods can be obtained with the equations and tables provided in this article. However, for the convenience of clinicians and to reduce the possibility of clerical error, the methods have also been implemented in a computer program. More important, the program allows the methods to be applied when only a subset of scores is available. The program can be downloaded (as a zip file) from this article's supplemental materials or from www.abdn.ac.uk/~psy086/dept/DKEFS_Supplementary_Analysis.htm.     

Exact distributions of intraclass correlation and Cronbach's alpha with Gaussian data and general covariance

Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions. New exact results allow calculating the exact distribution function and other properties of intraclass correlation and Cronbach's alpha, for Gaussian data with any covariance pattern, not just compound symmetry. Probabilities are computed in terms of the distribution function of a weighted sum of independent chi-square random variables. NewF approximations for the distribution functions of intraclass correlation and Cronbach's alpha are much simpler and faster to compute than the exact forms. Assuming the covariance matrix is known, the approximations typically provide sufficient accuracy, even with as few as ten observations. Either the exact or approximate distributions may be used to create confidence intervals around an estimate of reliability. Monte Carlo simulations led to a number of conclusions. Correctly assuming that the covariance matrix is compound symmetric leads to accurate confidence intervals, as was expected from previously known results. However, assuming and estimating a general covariance matrix produces somewhat optimistically narrow confidence intervals with 10 observations. Increasing sample size to 100 gives essentially unbiased coverage. Incorrectly assuming compound symmetry leads to pessimistically large confidence intervals, with pessimism increasing with sample size. In contrast, incorrectly assuming general covariance introduces only a modest optimistic bias in small samples. Hence the new methods seem preferable for creating confidence intervals, except when compound symmetry definitely holds. An earlier version of this paper was submitted in partial fulfillment of the requirements for the M.S. in Biostatistics, and also summarized in a presentation at the meetings of the Eastern North American Region of the International Biometric Society in March, 2001. Kistner's work was supported in part by NIEHS training grant ES07018-24 and NCI program project grant P01 CA47 982-04. She gratefully acknowledges the inspiration of A. Calandra's “Scoring formulas and probability considerations” (Psychometrika, 6, 1–9). Muller's work supported in part by NCI program project grant P01 CA47 982-04.     

Order effects and memory for evidence in individual versus group decision making in auditing

Sequential processing of evidence may lead to recency effect, a potential bias in judgment. The present research seeks to extend the literature on recency effects by assessing the potential moderating influence of team work: whether group decision making moderates the severity of recency effects predicted by Hogarth and Einhorn (1992), and whether group processing influences the accuracy of, and confidence in memory for evidence. Experienced auditors from a Big‐6 accounting firm made audit judgments, either individually or as groups. They were randomly assigned to one of two levels of evidence presentation order. After performing the judgment task, participants completed two evidence recognition tests. Consistent with prior findings, recency effects on judgments were observed, but only for individuals. Group judgments or audit reports were not affected by recency. Order effects, however, did not translate into different choices of audit reports, and did not persist in memories of either individuals or groups. As expected, group memory was more accurate than individual memory and groups were more confident than individuals. Overall, confidence in accurate memories was greater than in inaccurate ones. Copyright © 1999 John Wiley & Sons, Ltd.     

基于结构方程模型的多重中介效应分析

多重中介模型是指存在多个中介变量的模型。多重中介模型可以分析特定中介效应、总的中介效应和对比中介效应。指出了目前多重中介模型分析普遍存在的问题,包括分析不完整、使用Sobel检验带来的局限。建议通过增加辅助变量的方法进行完整的多重中介效应分析,使用偏差校正的Bootstrap方法进行中介检验。总结出一个多重中介SEM分析流程,并有示例和相应的MPLUS程序。随后展望了辅助变量和中介效应检验方法的发展方向。     

Memory conformity affects inaccurate memories more than accurate memories

After controlling for initial confidence, inaccurate memories were shown to be more easily distorted than accurate memories. In two experiments groups of participants viewed 50 stimuli and were then presented with these stimuli plus 50 fillers. During this test phase participants reported their confidence that each stimulus was originally shown. This was followed by computer-generated responses from a bogus participant. After being exposed to this response participants again rated the confidence of their memory. The computer-generated responses systematically distorted participants’ responses. Memory distortion depended on initial memory confidence, with uncertain memories being more malleable than confident memories. This effect was moderated by whether the participant's memory was initially accurate or inaccurate. Inaccurate memories were more malleable than accurate memories. The data were consistent with a model describing two types of memory (i.e., recollective and non-recollective memories), which differ in how susceptible these memories are to memory distortion.     

Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis

When bivariate normality is violated, the default confidence interval of the Pearson correlation can be inaccurate. Two new methods were developed based on the asymptotic sampling distribution of Fisher's z′ under the general case where bivariate normality need not be assumed. In Monte Carlo simulations, the most successful of these methods relied on the (Vale & Maurelli, 1983, Psychometrika, 48, 465) family to approximate a distribution via the marginal skewness and kurtosis of the sample data. In Simulation 1, this method provided more accurate confidence intervals of the correlation in non-normal data, at least as compared to no adjustment of the Fisher z′ interval, or to adjustment via the sample joint moments. In Simulation 2, this approximate distribution method performed favourably relative to common non-parametric bootstrap methods, but its performance was mixed relative to an observed imposed bootstrap and two other robust methods (PM1 and HC4). No method was completely satisfactory. An advantage of the approximate distribution method, though, is that it can be implemented even without access to raw data if sample skewness and kurtosis are reported, making the method particularly useful for meta-analysis. Supporting information includes R code.     

Attachment Representations and Maternal Confidence: The Mediating Role of Postnatal Depressive Symptoms and Negative Thoughts

Attachment security can act as an inner resource to promote women’s adjustment to motherhood. However, the mechanisms explaining the relationship between attachment representations and maternal adaptation outcomes are not well understood. This study aimed to examine the direct and indirect effects of attachment representations on maternal confidence, through postpartum negative automatic thoughts and depressive symptoms. The sample consisted of 387 postpartum women who completed a cross-sectional online survey including measures of attachment representations, depressive symptoms, postpartum negative automatic thoughts and maternal confidence. Our results showed a significant relationship between more insecure attachment representations and higher depressive symptoms (p?<?.001), but also with more frequent postpartum negative automatic thoughts (p?<?.001); depressive symptoms and postpartum negative automatic thoughts were also inversely associated with women’s maternal confidence (p?<?.001). Moreover, indirect effects of attachment representations on maternal confidence were found, but only through postpartum negative thoughts [attachment-related anxiety: 95% CI?=??0.03/?0.01; attachment-related avoidance: 95% CI?=??0.05/?0.01]. The results of the present study emphasize the important role of the cognitive component of depressive symptomatology (postpartum negative automatic thoughts) in the relationship between attachment representations and maternal confidence, allowing to draw specific implications. We highlight the implications for clinical practice during the perinatal period to address both negative thoughts and women’s maternal confidence.     

Memory conformity affects inaccurate memories more than accurate memories

After controlling for initial confidence, inaccurate memories were shown to be more easily distorted than accurate memories. In two experiments groups of participants viewed 50 stimuli and were then presented with these stimuli plus 50 fillers. During this test phase participants reported their confidence that each stimulus was originally shown. This was followed by computer-generated responses from a bogus participant. After being exposed to this response participants again rated the confidence of their memory. The computer-generated responses systematically distorted participants' responses. Memory distortion depended on initial memory confidence, with uncertain memories being more malleable than confident memories. This effect was moderated by whether the participant's memory was initially accurate or inaccurate. Inaccurate memories were more malleable than accurate memories. The data were consistent with a model describing two types of memory (i.e., recollective and non-recollective memories), which differ in how susceptible these memories are to memory distortion.     

Two sides of the career resources coin: Career adaptability resources and the impostor phenomenon

Considering the impostor phenomenon (IP) as an important psychological construct in the context of career development requires a theoretical grounding. Using the career construction model of adaptation as a guiding framework, we investigated how the IP is related to adaptive readiness (represented by core self-evaluations), career adaptability resources, and adapting responses, namely, career planning, career decision-making difficulties, career exploration, and occupational self-efficacy. We used parallel multiple mediation modeling to investigate specific indirect effects through concern, control, curiosity, confidence, and the IP. We conducted an online study with 289 university students. Results indicated a positive effect of core self-evaluations on career planning, career exploration, and occupational self-efficacy and a negative effect on career decision-making difficulties through adaptability resources. The IP emerged as a “maladaptability” resource: That is, it might be a hindrance to adaptive coping and behavior and consequently promote maladaptive coping and behavior by decreasing career planning and occupational self-efficacy and increasing career decision-making difficulties. Supplementary negative effects of the IP on adaptability resources are discussed.     

Target detection and localization in visual search: a dual systems perspective

The dual visual systems framework (Milner & Goodale, 1995) was used to explore target detection and localization in visual search. Observers searched for a small patch of tilted bars against a dense background of upright bars. Target detection was performed along with two different localization tasks: direct pointing, designed to engage the dorsal stream, and indirect pointing, designed to engage the ventral stream. The results indicated that (1) target detection was influenced more by orientation differences in 3-D space than by 2-D pictorial differences, (2) target localization was more accurate for direct than for indirect pointing, and (3) there were performance costs for indirect localization when it followed target detection, but not for direct localization. This is consistent with direct localization's having greater dependence on the dorsal visual system than either target detection or indirect localization.