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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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Agent

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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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The sensitivity of confirmatory factor analytic fit indices to violations of factorial invariance across latent classes: a simulation study

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Although the issue of factorial invariance has received increasing attention in the literature, the focus is typically on differences in factor structure across groups that are directly observed, such as those denoted by sex or ethnicity. While establishing factorial invariance

Although the issue of factorial invariance has received increasing attention in the literature, the focus is typically on differences in factor structure across groups that are directly observed, such as those denoted by sex or ethnicity. While establishing factorial invariance across observed groups is a requisite step in making meaningful cross-group comparisons, failure to attend to possible sources of latent class heterogeneity in the form of class-based differences in factor structure has the potential to compromise conclusions with respect to observed groups and may result in misguided attempts at instrument development and theory refinement. The present studies examined the sensitivity of two widely used confirmatory factor analytic model fit indices, the chi-square test of model fit and RMSEA, to latent class differences in factor structure. Two primary questions were addressed. The first of these concerned the impact of latent class differences in factor loadings with respect to model fit in a single sample reflecting a mixture of classes. The second question concerned the impact of latent class differences in configural structure on tests of factorial invariance across observed groups. The results suggest that both indices are highly insensitive to class-based differences in factor loadings. Across sample size conditions, models with medium (0.2) sized loading differences were rejected by the chi-square test of model fit at rates just slightly higher than the nominal .05 rate of rejection that would be expected under a true null hypothesis. While rates of rejection increased somewhat when the magnitude of loading difference increased, even the largest sample size with equal class representation and the most extreme violations of loading invariance only had rejection rates of approximately 60%. RMSEA was also insensitive to class-based differences in factor loadings, with mean values across conditions suggesting a degree of fit that would generally be regarded as exceptionally good in practice. In contrast, both indices were sensitive to class-based differences in configural structure in the context of a multiple group analysis in which each observed group was a mixture of classes. However, preliminary evidence suggests that this sensitivity may contingent on the form of the cross-group model misspecification.

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Agent

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Date Created
2011

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

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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

Created

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

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Performance of contextual multilevel models for comparing between-person and within-person effects

Description

The comparison of between- versus within-person relations addresses a central issue in psychological research regarding whether group-level relations among variables generalize to individual group members. Between- and within-person effects may differ in magnitude as well as direction, and contextual multilevel

The comparison of between- versus within-person relations addresses a central issue in psychological research regarding whether group-level relations among variables generalize to individual group members. Between- and within-person effects may differ in magnitude as well as direction, and contextual multilevel models can accommodate this difference. Contextual multilevel models have been explicated mostly for cross-sectional data, but they can also be applied to longitudinal data where level-1 effects represent within-person relations and level-2 effects represent between-person relations. With longitudinal data, estimating the contextual effect allows direct evaluation of whether between-person and within-person effects differ. Furthermore, these models, unlike single-level models, permit individual differences by allowing within-person slopes to vary across individuals. This study examined the statistical performance of the contextual model with a random slope for longitudinal within-person fluctuation data.

A Monte Carlo simulation was used to generate data based on the contextual multilevel model, where sample size, effect size, and intraclass correlation (ICC) of the predictor variable were varied. The effects of simulation factors on parameter bias, parameter variability, and standard error accuracy were assessed. Parameter estimates were in general unbiased. Power to detect the slope variance and contextual effect was over 80% for most conditions, except some of the smaller sample size conditions. Type I error rates for the contextual effect were also high for some of the smaller sample size conditions. Conclusions and future directions are discussed.

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Agent

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Date Created
2016