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1.  The Distribution of the Product Explains Normal Theory Mediation Confidence Interval Estimation 
Multivariate behavioral research  2014;49(3):261-268.
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.
PMCID: PMC4280020  PMID: 25554711
2.  Prenatal Stress, Partner Support, and Infant Cortisol Reactivity in Low-Income Mexican American Families 
Psychoneuroendocrinology  2013;38(12):10.1016/j.psyneuen.2013.09.006.
Maternal exposure to significant prenatal stress can negatively affect infant neurobiological development and increase the risk for developmental and health disturbances. These effects may be pronounced in low SES and ethnic minority families. We explored prenatal partner support as a buffer of the impact of prenatal stress on cortisol reactivity of infants born to low-income Mexican American women. Women (N=220; age 18–42; 84% Spanish-speaking; 89% foreign born; modal family income $10,000–$15,000) reported on economic stress and satisfaction with spousal/partner support during the prenatal period (26–38 weeks gestation), and infant salivary cortisol reactivity to mildly challenging mother-infant interaction tasks was assessed at women’s homes at six weeks postpartum. Multilevel models estimated the interactive effect of prenatal stress and partner support on cortisol reactivity, controlling for covariates and potential confounds. Infants born to mothers who reported high prenatal stress and low partner support exhibited higher cortisol reactivity relative to those whose mothers reported high support or low stress. The effects did not appear to operate through birth outcomes. For low-income Mexican American women, partner support may buffer the impact of prenatal stress on infant cortisol reactivity, potentially promoting more adaptive infant health and development.
PMCID: PMC3844006  PMID: 24090585
prenatal stress; infant cortisol; partner support
3.  A commentary on current practice in mediating variable analyses in behavioural nutrition and physical activity 
Public health nutrition  2008;12(8):1182-1188.
To critique current practice in, and provide recommendations for, mediating variable analyses (MVA) of nutrition and physical activity behaviour change.
Theory-based behavioural nutrition and physical activity interventions aim at changing mediating variables that are hypothesized to be responsible for changes in the outcome of interest. MVA are useful because they help to identify the most promising theoretical approaches, mediators and intervention components for behaviour change. However, the current literature suggests that MVA are often inappropriately conducted, poorly understood and inadequately presented. Main problems encountered in the published literature are explained and suggestions for overcoming weaknesses of current practice are proposed.
The use of the most appropriate, currently available methods of MVA, and a correct, comprehensive presentation and interpretation of their findings, is of paramount importance for understanding how obesity can be treated and prevented.
PMCID: PMC4207270  PMID: 18778534
Mediation models; Logistic regression; Behaviour change
4.  Sensitivity Plots for Confounder Bias in the Single Mediator Model 
Evaluation review  2014;37(5):405-431.
Causal inference continues to be a critical aspect of evaluation research. Recent research in causal inference for statistical mediation has focused on addressing the sequential ignorability assumption; specifically, that there is no confounding between the mediator and the outcome variable.
This article compares and contrasts three different methods for assessing sensitivity to confounding and describes the graphical depiction of these methods.
Two types of data were used to fully examine the plots for sensitivity analysis. The first type was generated data from a single mediator model with a confounder influencing both the mediator and the outcome variable. The second was data from an actual intervention study. With both types of data, situations are examined where confounding has a large effect and a small effect.
The nonsimulated data were from a large intervention study to decrease intentions to use steroids among high school football players. We demonstrate one situation where confounding is likely and another situation where confounding is unlikely.
We discuss how these methods could be implemented in future mediation studies as well as the limitations and future directions for these methods.
PMCID: PMC4207278  PMID: 24681690
mediation; indirect effects; causal inference; confounder bias; sensitivity analysis
5.  Guidelines for the Investigation of Mediating Variables in Business Research 
Business theories often specify the mediating mechanisms by which a predictor variable affects an outcome variable. In the last 30 years, investigations of mediating processes have become more widespread with corresponding developments in statistical methods to conduct these tests. The purpose of this article is to provide guidelines for mediation studies by focusing on decisions made prior to the research study that affect the clarity of conclusions from a mediation study, the statistical models for mediation analysis, and methods to improve interpretation of mediation results after the research study. Throughout this article, the importance of a program of experimental and observational research for investigating mediating mechanisms is emphasized.
PMCID: PMC4165346  PMID: 25237213
Mediation; Moderation; Indirect effects; Causal inference; Longitudinal models; Significance testing; Confidence intervals
6.  Sweetened Drink and Snacking Cues in Adolescents: A Study Using Ecological Momentary Assessment 
Appetite  2013;67:61-73.
The objective of this study was to identify physical, social, and intrapersonal cues that were associated with the consumption of sweetened beverages and sweet and salty snacks among adolescents from lower SES neighborhoods. Students were recruited from high schools with a minimum level of 25% free or reduced cost lunches. Using Ecological Momentary Assessment, participants (N=158) were trained to answer brief questionnaires on handheld PDA devices: (a) each time they ate or drank, (b) when prompted randomly, and (c) once each evening. Data were collected over 7 days for each participant. Participants reported their location (e.g., school grounds, home), mood, social environment, activities (e.g., watching TV, texting), cravings, food cues (e.g., saw a snack), and food choices. Results showed that having unhealthy snacks or sweet drinks among adolescents was associated with being at school, being with friends, feeling lonely or bored, craving a drink or snack, and being exposed to food cues. Surprisingly, sweet drink consumption was associated with exercising. Watching TV was associated with consuming sweet snacks but not with salty snacks or sweet drinks. These findings identify important environmental and intrapersonal cues to poor snacking choices that may be applied to interventions designed to disrupt these food-related, cue-behavior linked habits.
PMCID: PMC3677830  PMID: 23583312
adolescents; diet; food habits; cues; Ecological Momentary Assessment
7.  The Safety and Health Improvement: Enhancing Law Enforcement Departments Study: Feasibility and Findings 
This randomized prospective trial aimed to assess the feasibility and efficacy of a team-based worksite health and safety intervention for law enforcement personnel. Four-hundred and eight subjects were enrolled and half were randomized to meet for weekly, peer-led sessions delivered from a scripted team-based health and safety curriculum. Curriculum addressed: exercise, nutrition, stress, sleep, body weight, injury, and other unhealthy lifestyle behaviors such as smoking and heavy alcohol use. Health and safety questionnaires administered before and after the intervention found significant improvements for increased fruit and vegetable consumption, overall healthy eating, increased sleep quantity and sleep quality, and reduced personal stress.
PMCID: PMC4021110  PMID: 24847475
health promotion; safety; law enforcement; occupational health; team-based
8.  Body Mass Index is a Predictor of Fire Fighter Injury and Worker Compensation Claims 
To determine the relationship between lifestyle variables including body mass index (BMI) and filing a worker’s compensation claim due to firefighter injury.
A cross-sectional evaluation of firefighter injury related worker compensation claims occurring 5 years after the original PHLAME study intervention.
Logistic regression analysis for variables predicting filing a worker’s compensation claim due to an injury were performed. with a total of 433 participants. The odds of filing a compensation claim were almost three times higher for firefighters with a BMI >30 compared to firefighters with normal BMI (odds ratio=2.89, p<.05).
This study addresses a high priority area of reducing firefighter injuries and worker’s compensation claims. Maintaining a healthy body weight is important to reduce injury and worker’s compensation claims among firefighters.
PMCID: PMC3349447  PMID: 22569476
9.  Some Methodological Considerations in Theory-Based Health Behavior Research 
As this special issue shows, much research in social and personality psychology is directly relevant to health psychology. In this brief commentary, we discuss three topics in research methodology that may be of interest to investigators involved in health-related psychological research. The first topic is statistical analysis of mediated and moderated effects. The second is measurement of latent constructs. The third is the Multiphase Optimization Strategy, a framework for translation of innovations from social and personality psychology into behavioral interventions.
PMCID: PMC3832141  PMID: 23646842
mediation analysis; psychological measurement; Multiphase Optimization Strategy
11.  Cognitive Mediation of Cognitive-Behavioural Therapy Outcomes for Anxiety-Based School Refusal 
Cognitive-behavioural therapy (CBT) has proven to be effective for anxiety-based school refusal, but it is still unknown how CBT for school refusal works, or through which mechanisms.
Innovative statistical approaches for analyzing small uncontrolled samples were used to investigate the role of self-efficacy in mediating CBT outcomes for anxiety-based school refusal.
Participants were 19 adolescents (12 to 17 years) who completed a manual-based cognitive-behavioural treatment. Primary outcomes (school attendance; school-related fear; anxiety) and secondary outcomes (depression; internalizing problems) were assessed at post-treatment and 2-month follow-up.
Post-treatment increases in school attendance and decreases in fear about attending school the next day were found to be mediated by self-efficacy. Mediating effects were not observed at 2-month follow-up.
These findings provide partial support for the role of self-efficacy in mediating the outcome of CBT for school refusal. They contribute to a small body of literature suggesting that cognitive change enhances CBT outcomes for young people with internalizing problems. Regarding methodology, the product of coefficient test appears to be a valuable way to study mediation in outcome studies involving small samples.
PMCID: PMC3772992  PMID: 23017774
CBT; mediators; school refusal; anxiety; self-efficacy
12.  Statistical analysis for identifying mediating variables in public health dentistry interventions 
Journal of Public Health Dentistry  2011;71(Suppl 1):S37-S46.
This article provides an overview of statistical mediation analysis methods in the evaluation of public health dentistry interventions.
Methods and Results
First, reasons for conducting mediation analysis are outlined, followed by a discussion of the link between the mediation model and theoretical bases of interventions. Second, the basic statistical procedures in mediation analysis are presented. An example application to data from a hypothetical intervention is provided in Appendix A. Third, interpretation of the results from statistical mediation analysis is described along with additional information pertinent to identifying true mediation relations.
Guidelines for describing mediation analyses in research articles related to public health dentistry intervention studies are outlined.
PMCID: PMC3366631  PMID: 21656950
mediation; prevention; statistical analysis
13.  Integrating Mediators and Moderators in Research Design 
Research on social work practice  2011;21(6):675-681.
The purpose of this article is to describe mediating variables and moderating variables and provide reasons for integrating them in outcome studies. Separate sections describe examples of moderating and mediating variables and the simplest statistical model for investigating each variable. The strengths and limitations of incorporating mediating and moderating variables in a research study are discussed as well as approaches to routinely including these variables in outcome research. The routine inclusion of mediating and moderating variables holds the promise of increasing the amount of information from outcome studies by generating practical information about interventions as well as testing theory. The primary focus is on mediating and moderating variables for intervention research but many issues apply to nonintervention research as well.
PMCID: PMC3366634  PMID: 22675239
methodology; methodological article; intervention; outcome
14.  Explanation of Two Anomalous Results in Statistical Mediation Analysis 
Previous studies of different methods of testing mediation models have consistently found two anomalous results. The first result is elevated Type I error rates for the bias-corrected and accelerated bias-corrected bootstrap tests not found in nonresampling tests or in resampling tests that did not include a bias correction. This is of special concern as the bias-corrected bootstrap is often recommended and used due to its higher statistical power compared with other tests. The second result is statistical power reaching an asymptote far below 1.0 and in some conditions even declining slightly as the size of the relationship between X and M, a, increased. Two computer simulations were conducted to examine these findings in greater detail. Results from the first simulation found that the increased Type I error rates for the bias-corrected and accelerated bias-corrected bootstrap are a function of an interaction between the size of the individual paths making up the mediated effect and the sample size, such that elevated Type I error rates occur when the sample size is small and the effect size of the nonzero path is medium or larger. Results from the second simulation found that stagnation and decreases in statistical power as a function of the effect size of the a path occurred primarily when the path between M and Y, b, was small. Two empirical mediation examples are provided using data from a steroid prevention and health promotion program aimed at high school football players (Athletes Training and Learning to Avoid Steroids; Goldberg et al., 1996), one to illustrate a possible Type I error for the bias-corrected bootstrap test and a second to illustrate a loss in power related to the size of a. Implications of these findings are discussed.
PMCID: PMC3773882  PMID: 24049213
15.  A Bayesian Approach for Estimating Mediation Effects with Missing Data 
Multivariate behavioral research  2013;48(3):340-369.
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 a SAS macro that implements Bayesian estimation and use two data analysis examples to demonstrate its use.
PMCID: PMC3769802  PMID: 24039298
Mediation; indirect effects; missing data; Bayesian estimation; bias corrected bootstrap; Sobel test
16.  Understanding the Durability of a Fire Department Wellness Program 
To understand the influences associated with durability and diffusion of benefits of a fire service wellness program.
Qualitative assessment of group interviews.
Five years following a controlled worksite wellness trial, behavioral improvements were durable and had diffused to control participants. These findings were associated with firefighters’ team orientation, enacted healthy norms and competitiveness regarding the results of annual health assessments. The original intervention trial appeared to initiate individual change that coalesced into group effects. Secondary influences included increasing public awareness about health, newly hired younger firefighters, and a modicum of administrative support. Culture shift was achieved at the workplace.
Although the fire service is a unique occupation, these findings suggest general strategies to achieve durable positive health change in other occupational settings.
PMCID: PMC3761399  PMID: 23985292
worksite; dietary behaviors; physical activity; qualitative
Applied researchers often include mediation effects in applications of advanced methods such as latent variable models and linear growth curve models. Guidance on how to estimate statistical power to detect mediation for these models has not yet been addressed in the literature. We describe a general framework for power analyses for complex mediational models. The approach is based on the well known technique of generating a large number of samples in a Monte Carlo study, and estimating power as the percentage of cases in which an estimate of interest is significantly different from zero. Examples of power calculation for commonly used mediational models are provided. Power analyses for the single mediator, multiple mediators, three-path mediation, mediation with latent variables, moderated mediation, and mediation in longitudinal designs are described. Annotated sample syntax for Mplus is appended and tabled values of required sample sizes are shown for some models.
PMCID: PMC3737006  PMID: 23935262
Mediation; Statistical Power; Monte Carlo; Mplus
18.  Do Cognitive Attributions for Smoking Predict Subsequent Smoking Development? 
Addictive Behaviors  2011;37(3):273-279.
To develop more effective anti-smoking programs, it is important to understand the factors that influence people to smoke. Guided by attribution theory, a longitudinal study was conducted to investigate how individuals’ cognitive attributions for smoking were associated with subsequent smoking development and through which pathways.
Middle and high school students in seven large cities in China (N=12,382; 48.5% boys and 51.5% girls) completed two annual surveys. Associations between cognitive attributions for smoking and subsequent smoking initiation and progression were tested with multilevel analysis, taking into account plausible moderation effects of gender and baseline smoking status. Mediation effects of susceptibility to smoking were investigated using statistical mediation analysis (MacKinnon, 2008).
Six out of eight tested themes of cognitive attributions were associated with subsequent smoking development. Curiosity (β=0.11, p<0.001) and autonomy (β=0.08, p=0.019) were associated with smoking initiation among baseline non-smokers. Coping (β=0.07, p<0.001) and social image (β=0.10, p=<.0001) were associated with smoking progression among baseline lifetime smokers. Social image (β=0.05, p=0.043), engagement (β=0.07, p=0.003), and mental enhancement (β=0.15, p<0.001) were associated with smoking progression among baseline past 30-day smokers. More attributions were associated with smoking development among males than among females. Susceptibility to smoking partially mediated most of the associations, with the proportion of mediated effects ranging from 4.3% to 30.8%.
This study identifies the roles that cognitive attributions for smoking play in subsequent smoking development. These attributions could be addressed in smoking prevention programs.
PMCID: PMC3286308  PMID: 22112425
Attributions; Smoking; Attribution Theory; Adolescents; China
19.  A Mediation Analysis of the ATHENA Intervention for Female Athletes: Prevention of Athletic-Enhancing Substance Use and Unhealthy Weight Loss Behaviors 
Journal of Pediatric Psychology  2009;34(10):1069-1083.
Objective To explain, through mediation analyses, the mechanisms by which ATHENA (Athletes Targeting Healthy Exercise and Nutrition Alternatives), a primary prevention and health promotion intervention designed to deter unhealthy body shaping behaviors among female high school athletes, produced immediate changes in intentions for unhealthy weight loss and steroid/creatine use, and to examine the link to long-term follow-up intentions and behaviors. Methods In a randomized trial of 1668 athletes, intervention participants completed coach-led peer-facilitated sessions during their sport season. Participants provided pre-test, immediate post-test, and 9-month follow-up assessments. Results ATHENA decreased intentions for steroid/creatine use and intentions for unhealthy weight loss behaviors at post-test. These effects were most strongly mediated by social norms and self-efficacy for healthy eating. Low post-test intentions were maintained 9 months later and predicted subsequent behavior. Conclusions ATHENA successfully modified mediators that in turn related to athletic-enhancing substance use and unhealthy weight loss practices. Mediation analyses aid in the understanding of health promotion interventions and inform program development.
PMCID: PMC2782253  PMID: 19386771
adolescents; educational interventions; health promotion and prevention; lLongitudinal research; peers; mediation analysis.
20.  Advances in Statistical Methods for Substance Abuse Prevention Research 
The paper describes advances in statistical methods for prevention research with a particular focus on substance abuse prevention. Standard analysis methods are extended to the typical research designs and characteristics of the data collected in prevention research. Prevention research often includes longitudinal measurement, clustering of data in units such as schools or clinics, missing data, and categorical as well as continuous outcome variables. Statistical methods to handle these features of prevention data are outlined. Developments in mediation, moderation, and implementation analysis allow for the extraction of more detailed information from a prevention study. Advancements in the interpretation of prevention research results include more widespread calculation of effect size and statistical power, the use of confidence intervals as well as hypothesis testing, detailed causal analysis of research findings, and meta-analysis. The increased availability of statistical software has contributed greatly to the use of new methods in prevention research. It is likely that the Internet will continue to stimulate the development and application of new methods.
PMCID: PMC2843515  PMID: 12940467
prevention; statistical methods; substance abuse
22.  Confidence Limits for the Indirect Effect: Distribution of the Product and Resampling Methods 
The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on critical values from the standard normal distribution. This article uses a simulation study to demonstrate that confidence limits are imbalanced because the distribution of the indirect effect is normal only in special cases. Two alternatives for improving the performance of confidence limits for the indirect effect are evaluated: (a) a method based on the distribution of the product of two normal random variables, and (b) resampling methods. In Study 1, confidence limits based on the distribution of the product are more accurate than methods based on an assumed normal distribution but confidence limits are still imbalanced. Study 2 demonstrates that more accurate confidence limits are obtained using resampling methods, with the bias-corrected bootstrap the best method overall.
PMCID: PMC2821115  PMID: 20157642
23.  Investigation of Mediational Processes Using Parallel Process Latent Growth Curve Modeling 
This study investigated a method to evaluate mediational processes using latent growth curve modeling. The mediator and the outcome measured across multiple time points were viewed as 2 separate parallel processes. The mediational process was defined as the independent variable influencing the growth of the mediator, which, in turn, affected the growth of the outcome. To illustrate modeling procedures, empirical data from a longitudinal drug prevention program, Adolescents Training and Learning to Avoid Steroids, were used. The program effects on the growth of the mediator and the growth of the outcome were examined first in a 2-group structural equation model. The mediational process was then modeled and tested in a parallel process latent growth curve model by relating the prevention program condition, the growth rate factor of the mediator, and the growth rate factor of the outcome.
PMCID: PMC2821108  PMID: 20157639
24.  Current Directions in Mediation Analysis 
Mediating variables continue to play an important role in psychological theory and research. A mediating variable transmits the effect of an antecedent variable on to a dependent variable, thereby providing more detailed understanding of relations among variables. Methods to assess mediation have been an active area of research for the last two decades. This paper describes the current state of methods to investigate mediating variables.
PMCID: PMC2821103  PMID: 20157637
mediation; indirect effect; statistical methods
25.  A Comparison of Methods to Test Mediation and Other Intervening Variable Effects 
Psychological methods  2002;7(1):83.
A Monte Carlo study compared 14 methods to test the statistical significance of the intervening variable effect. An intervening variable (mediator) transmits the effect of an independent variable to a dependent variable. The commonly used R. M. Baron and D. A. Kenny (1986) approach has low statistical power. Two methods based on the distribution of the product and 2 difference-in-coefficients methods have the most accurate Type I error rates and greatest statistical power except in 1 important case in which Type I error rates are too high. The best balance of Type I error and statistical power across all cases is the test of the joint significance of the two effects comprising the intervening variable effect.
PMCID: PMC2819363  PMID: 11928892

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