Matching Items (5)
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- All Subjects: Mediation
- All Subjects: Multilevel models (Statistics)
- Creators: Grimm, Kevin J.
- Creators: Millsap, Roger
Description
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.
ContributorsO'Rourke, Holly Patricia (Author) / Mackinnon, David P (Thesis advisor) / Enders, Craig K. (Committee member) / Millsap, Roger (Committee member) / Arizona State University (Publisher)
Created2013
Description
Previous research has shown functional mixed-effects models and traditional mixed-effects models perform similarly when recovering mean and individual trajectories (Fine, Suk, & Grimm, 2019). However, Fine et al. (2019) showed traditional mixed-effects models were able to more accurately recover the underlying mean curves compared to functional mixed-effects models. That project generated data following a parametric structure. This paper extended previous work and aimed to compare nonlinear mixed-effects models and functional mixed-effects models on their ability to recover underlying trajectories which were generated from an inherently nonparametric process. This paper introduces readers to nonlinear mixed-effects models and functional mixed-effects models. A simulation study is then presented where the mean and random effects structure of the simulated data were generated using B-splines. The accuracy of recovered curves was examined under various conditions including sample size, number of time points per curve, and measurement design. Results showed the functional mixed-effects models recovered the underlying mean curve more accurately than the nonlinear mixed-effects models. In general, the functional mixed-effects models recovered the underlying individual curves more accurately than the nonlinear mixed-effects models. Progesterone cycle data from Brumback and Rice (1998) were then analyzed to demonstrate the utility of both models. Both models were shown to perform similarly when analyzing the progesterone data.
ContributorsFine, Kimberly L (Author) / Grimm, Kevin J. (Thesis advisor) / Edward, Mike (Committee member) / O'Rourke, Holly (Committee member) / McNeish, Dan (Committee member) / Arizona State University (Publisher)
Created2019
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 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.
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.
ContributorsWurpts, Ingrid Carlson (Author) / Mackinnon, David P (Thesis advisor) / West, Stephen G. (Committee member) / Grimm, Kevin J. (Committee member) / Suk, Hye Won (Committee member) / Arizona State University (Publisher)
Created2016
Description
In investigating mediating processes, researchers usually use randomized experiments and linear regression or structural equation modeling to determine if the treatment affects the hypothesized mediator and if the mediator affects the targeted outcome. However, randomizing the treatment will not yield accurate causal path estimates unless certain assumptions are satisfied. Since randomization of the mediator may not be plausible for most studies (i.e., the mediator status is not randomly assigned, but self-selected by participants), both the direct and indirect effects may be biased by confounding variables. The purpose of this dissertation is (1) to investigate the extent to which traditional mediation methods are affected by confounding variables and (2) to assess the statistical performance of several modern methods to address confounding variable effects in mediation analysis. This dissertation first reviewed the theoretical foundations of causal inference in statistical mediation analysis, modern statistical analysis for causal inference, and then described different methods to estimate causal direct and indirect effects in the presence of two post-treatment confounders. A large simulation study was designed to evaluate the extent to which ordinary regression and modern causal inference methods are able to obtain correct estimates of the direct and indirect effects when confounding variables that are present in the population are not included in the analysis. Five methods were compared in terms of bias, relative bias, mean square error, statistical power, Type I error rates, and confidence interval coverage to test how robust the methods are to the violation of the no unmeasured confounders assumption and confounder effect sizes. The methods explored were linear regression with adjustment, inverse propensity weighting, inverse propensity weighting with truncated weights, sequential g-estimation, and a doubly robust sequential g-estimation. Results showed that in estimating the direct and indirect effects, in general, sequential g-estimation performed the best in terms of bias, Type I error rates, power, and coverage across different confounder effect, direct effect, and sample sizes when all confounders were included in the estimation. When one of the two confounders were omitted from the estimation process, in general, none of the methods had acceptable relative bias in the simulation study. Omitting one of the confounders from estimation corresponded to the common case in mediation studies where no measure of a confounder is available but a confounder may affect the analysis. Failing to measure potential post-treatment confounder variables in a mediation model leads to biased estimates regardless of the analysis method used and emphasizes the importance of sensitivity analysis for causal mediation analysis.
ContributorsKisbu Sakarya, Yasemin (Author) / Mackinnon, David Peter (Thesis advisor) / Aiken, Leona (Committee member) / West, Stephen (Committee member) / Millsap, Roger (Committee member) / Arizona State University (Publisher)
Created2013
Description
Statistical inference from mediation analysis applies to populations, however, researchers and clinicians may be interested in making inference to individual clients or small, localized groups of people. Person-oriented approaches focus on the differences between people, or latent groups of people, to ask how individuals differ across variables, and can help researchers avoid ecological fallacies when making inferences about individuals. Traditional variable-oriented mediation assumes the population undergoes a homogenous reaction to the mediating process. However, mediation is also described as an intra-individual process where each person passes from a predictor, through a mediator, to an outcome (Collins, Graham, & Flaherty, 1998). Configural frequency mediation is a person-oriented analysis of contingency tables that has not been well-studied or implemented since its introduction in the literature (von Eye, Mair, & Mun, 2010; von Eye, Mun, & Mair, 2009). The purpose of this study is to describe CFM and investigate its statistical properties while comparing it to traditional and casual inference mediation methods. The results of this study show that joint significance mediation tests results in better Type I error rates but limit the person-oriented interpretations of CFM. Although the estimator for logistic regression and causal mediation are different, they both perform well in terms of Type I error and power, although the causal estimator had higher bias than expected, which is discussed in the limitations section.
ContributorsSmyth, Heather Lynn (Author) / Mackinnon, David P (Thesis advisor) / Grimm, Kevin J. (Committee member) / Edwards, Michael C (Committee member) / Arizona State University (Publisher)
Created2019