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Mediation as a novel method for increasing statistical power

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Including a covariate can increase power to detect an effect between two variables. Although previous research has studied power in mediation models, the extent to which the inclusion of a mediator will increase the power to detect a relation between

Including a covariate can increase power to detect an effect between two variables. Although previous research has studied power in mediation models, the extent to which the inclusion of a mediator will increase the power to detect a relation between two variables has not been investigated. The first study identified situations where empirical and analytical power of two tests of significance for a single mediator model was greater than power of a bivariate significance test. Results from the first study indicated that including a mediator increased statistical power in small samples with large effects and in large samples with small effects. Next, a study was conducted to assess when power was greater for a significance test for a two mediator model as compared with power of a bivariate significance test. Results indicated that including two mediators increased power in small samples when both specific mediated effects were large and in large samples when both specific mediated effects were small. Implications of the results and directions for future research are then discussed.

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Date Created
2013

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Propensity score estimation with random forests

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Random Forests is a statistical learning method which has been proposed for propensity score estimation models that involve complex interactions, nonlinear relationships, or both of the covariates. In this dissertation I conducted a simulation study to examine the effects of

Random Forests is a statistical learning method which has been proposed for propensity score estimation models that involve complex interactions, nonlinear relationships, or both of the covariates. In this dissertation I conducted a simulation study to examine the effects of three Random Forests model specifications in propensity score analysis. The results suggested that, depending on the nature of data, optimal specification of (1) decision rules to select the covariate and its split value in a Classification Tree, (2) the number of covariates randomly sampled for selection, and (3) methods of estimating Random Forests propensity scores could potentially produce an unbiased average treatment effect estimate after propensity scores weighting by the odds adjustment. Compared to the logistic regression estimation model using the true propensity score model, Random Forests had an additional advantage in producing unbiased estimated standard error and correct statistical inference of the average treatment effect. The relationship between the balance on the covariates' means and the bias of average treatment effect estimate was examined both within and between conditions of the simulation. Within conditions, across repeated samples there was no noticeable correlation between the covariates' mean differences and the magnitude of bias of average treatment effect estimate for the covariates that were imbalanced before adjustment. Between conditions, small mean differences of covariates after propensity score adjustment were not sensitive enough to identify the optimal Random Forests model specification for propensity score analysis.

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Agent

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Date Created
2013

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When resilience rides the cycle of fatigue: the role of interpersonal enjoyment on daily fatigue in women with fibromyalgia

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Fibromyalgia (FM) is a chronic pain condition characterized by debilitating fatigue. This study examined the dynamic relation between interpersonal enjoyment and fatigue in 102 partnered and 74 unpartnered women with FM. Participants provided three daily ratings for 21 days. They

Fibromyalgia (FM) is a chronic pain condition characterized by debilitating fatigue. This study examined the dynamic relation between interpersonal enjoyment and fatigue in 102 partnered and 74 unpartnered women with FM. Participants provided three daily ratings for 21 days. They rated their fatigue in late morning and at the end of the day. Both partnered and unpartnered participants reported their interpersonal enjoyment in the combined familial, friendship, and work domains (COMBINED domain) in the afternoon. Additionally, partnered participants reported their interpersonal enjoyment in the spousal domain. The study was guided by three hypotheses at the within-person level, based on daily diaries: (1) elevated late morning fatigue would predict diminished afternoon interpersonal enjoyment; (2) diminished interpersonal enjoyment would predict elevated end-of-day fatigue; (3) interpersonal enjoyment would mediate the late morning to end-of-day fatigue relationship. In cross-level models, the study explored whether individual differences (between-person) in late morning fatigue and afternoon interpersonal enjoyment would moderate within-person relations from late morning fatigue to afternoon interpersonal enjoyment, and from afternoon interpersonal enjoyment to end-of-day fatigue. Furthermore, it explored whether the hypothesized relationships at the within-person level would also emerge at the between-person level (between-person mediation models). Multilevel structural equation modeling and multilevel modeling were employed for model testing, separately for partnered and unpartnered participants. Within-person mediation models supported that on high fatigue mornings, afternoon interpersonal enjoyment was dampened in the spousal and combined domains in partnered and unpartnered samples. Moreover, low afternoon interpersonal enjoyment in both the spousal and combined domains predicted elevated end-of-day fatigue. Afternoon interpersonal enjoyment mediated the relationship of late morning to end-of-day fatigue in the combined domain but in not the spousal domain. Cross-level moderation analyses showed that individual differences in afternoon spousal enjoyment moderated the day-to-day relation between afternoon spousal enjoyment and end-of-day fatigue. Finally, the mediational chain was not observed at the between-person level. These findings suggest that preserving interpersonal enjoyment in non-spousal relations limits within-day increases in FM fatigue. They highlight the importance of examining domain-specificity in interpersonal enjoyment when studying fatigue, and suggest that targeting enjoyment in social relations may improve the efficacy of existing treatments.

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Agent

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Date Created
2013

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Regression analysis of grouped counts and frequencies using the generalized linear model

Description

Coarsely grouped counts or frequencies are commonly used in the behavioral sciences. Grouped count and grouped frequency (GCGF) that are used as outcome variables often violate the assumptions of linear regression as well as models designed for categorical outcomes; there

Coarsely grouped counts or frequencies are commonly used in the behavioral sciences. Grouped count and grouped frequency (GCGF) that are used as outcome variables often violate the assumptions of linear regression as well as models designed for categorical outcomes; there is no analytic model that is designed specifically to accommodate GCGF outcomes. The purpose of this dissertation was to compare the statistical performance of four regression models (linear regression, Poisson regression, ordinal logistic regression, and beta regression) that can be used when the outcome is a GCGF variable. A simulation study was used to determine the power, type I error, and confidence interval (CI) coverage rates for these models under different conditions. Mean structure, variance structure, effect size, continuous or binary predictor, and sample size were included in the factorial design. Mean structures reflected either a linear relationship or an exponential relationship between the predictor and the outcome. Variance structures reflected homoscedastic (as in linear regression), heteroscedastic (monotonically increasing) or heteroscedastic (increasing then decreasing) variance. Small to medium, large, and very large effect sizes were examined. Sample sizes were 100, 200, 500, and 1000. Results of the simulation study showed that ordinal logistic regression produced type I error, statistical power, and CI coverage rates that were consistently within acceptable limits. Linear regression produced type I error and statistical power that were within acceptable limits, but CI coverage was too low for several conditions important to the analysis of counts and frequencies. Poisson regression and beta regression displayed inflated type I error, low statistical power, and low CI coverage rates for nearly all conditions. All models produced unbiased estimates of the regression coefficient. Based on the statistical performance of the four models, ordinal logistic regression seems to be the preferred method for analyzing GCGF outcomes. Linear regression also performed well, but CI coverage was too low for conditions with an exponential mean structure and/or heteroscedastic variance. Some aspects of model prediction, such as model fit, were not assessed here; more research is necessary to determine which statistical model best captures the unique properties of GCGF outcomes.

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Agent

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Date Created
2012

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Multilevel mediation analysis: statistical assumptions and centering

Description

Mediation analysis is a statistical approach that examines the effect of a treatment (e.g., prevention program) on an outcome (e.g., substance use) achieved by targeting and changing one or more intervening variables (e.g., peer drug use norms). The increased use

Mediation analysis is a statistical approach that examines the effect of a treatment (e.g., prevention program) on an outcome (e.g., substance use) achieved by targeting and changing one or more intervening variables (e.g., peer drug use norms). The increased use of prevention intervention programs with outcomes measured at multiple time points following the intervention requires multilevel modeling techniques to account for clustering in the data. Estimating multilevel mediation models, in which all the variables are measured at individual level (Level 1), poses several challenges to researchers. The first challenge is to conceptualize a multilevel mediation model by clarifying the underlying statistical assumptions and implications of those assumptions on cluster-level (Level-2) covariance structure. A second challenge is that variables measured at Level 1 potentially contain both between- and within-cluster variation making interpretation of multilevel analysis difficult. As a result, multilevel mediation analyses may yield coefficient estimates that are composites of coefficient estimates at different levels if proper centering is not used. This dissertation addresses these two challenges. Study 1 discusses the concept of a correctly specified multilevel mediation model by examining the underlying statistical assumptions and implication of those assumptions on Level-2 covariance structure. Further, Study 1 presents analytical results showing algebraic relationships between the population parameters in a correctly specified multilevel mediation model. Study 2 extends previous work on centering in multilevel mediation analysis. First, different centering methods in multilevel analysis including centering within cluster with the cluster mean as a Level-2 predictor of intercept (CWC2) are discussed. Next, application of the CWC2 strategy to accommodate multilevel mediation models is explained. It is shown that the CWC2 centering strategy separates the between- and within-cluster mediated effects. Next, Study 2 discusses assumptions underlying a correctly specified CWC2 multilevel mediation model and defines between- and within-cluster mediated effects. In addition, analytical results for the algebraic relationships between the population parameters in a CWC2 multilevel mediation model are presented. Finally, Study 2 shows results of a simulation study conducted to verify derived algebraic relationships empirically.

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Agent

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Date Created
2010

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Planned missing data in mediation analysis

Description

This dissertation examines a planned missing data design in the context of mediational analysis. The study considered a scenario in which the high cost of an expensive mediator limited sample size, but in which less expensive mediators could be gathered

This dissertation examines a planned missing data design in the context of mediational analysis. The study considered a scenario in which the high cost of an expensive mediator limited sample size, but in which less expensive mediators could be gathered on a larger sample size. Simulated multivariate normal data were generated from a latent variable mediation model with three observed indicator variables, M1, M2, and M3. Planned missingness was implemented on M1 under the missing completely at random mechanism. Five analysis methods were employed: latent variable mediation model with all three mediators as indicators of a latent construct (Method 1), auxiliary variable model with M1 as the mediator and M2 and M3 as auxiliary variables (Method 2), auxiliary variable model with M1 as the mediator and M2 as a single auxiliary variable (Method 3), maximum likelihood estimation including all available data but incorporating only mediator M1 (Method 4), and listwise deletion (Method 5).

The main outcome of interest was empirical power to detect the mediated effect. The main effects of mediation effect size, sample size, and missing data rate performed as expected with power increasing for increasing mediation effect sizes, increasing sample sizes, and decreasing missing data rates. Consistent with expectations, power was the greatest for analysis methods that included all three mediators, and power decreased with analysis methods that included less information. Across all design cells relative to the complete data condition, Method 1 with 20% missingness on M1 produced only 2.06% loss in power for the mediated effect; with 50% missingness, 6.02% loss; and 80% missingess, only 11.86% loss. Method 2 exhibited 20.72% power loss at 80% missingness, even though the total amount of data utilized was the same as Method 1. Methods 3 – 5 exhibited greater power loss. Compared to an average power loss of 11.55% across all levels of missingness for Method 1, average power losses for Methods 3, 4, and 5 were 23.87%, 29.35%, and 32.40%, respectively. In conclusion, planned missingness in a multiple mediator design may permit higher quality characterization of the mediator construct at feasible cost.

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Date Created
2015