Matching Items (6)
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- All Subjects: Quantitative psychology
- All Subjects: Psychology--Statistical methods.
- Creators: Grimm, Kevin
Description
This paper investigates a relatively new analysis method for longitudinal data in the framework of functional data analysis. This approach treats longitudinal data as so-called sparse functional data. The first section of the paper introduces functional data and the general ideas of functional data analysis. The second section discusses the analysis of longitudinal data in the context of functional data analysis, while considering the unique characteristics of longitudinal data such, in particular sparseness and missing data. The third section introduces functional mixed-effects models that can handle these unique characteristics of sparseness and missingness. The next section discusses a preliminary simulation study conducted to examine the performance of a functional mixed-effects model under various conditions. An extended simulation study was carried out to evaluate the estimation accuracy of a functional mixed-effects model. Specifically, the accuracy of the estimated trajectories was examined under various conditions including different types of missing data and varying levels of sparseness.
ContributorsWard, Kimberly l (Author) / Suk, Hye Won (Thesis advisor) / Aiken, Leona (Committee member) / Grimm, Kevin (Committee member) / Arizona State University (Publisher)
Created2016
Description
The process of combining data is one in which information from disjoint datasets sharing at least a number of common variables is merged. This process is commonly referred to as data fusion, with the main objective of creating a new dataset permitting more flexible analyses than the separate analysis of each individual dataset. Many data fusion methods have been proposed in the literature, although most utilize the frequentist framework. This dissertation investigates a new approach called Bayesian Synthesis in which information obtained from one dataset acts as priors for the next analysis. This process continues sequentially until a single posterior distribution is created using all available data. These informative augmented data-dependent priors provide an extra source of information that may aid in the accuracy of estimation. To examine the performance of the proposed Bayesian Synthesis approach, first, results of simulated data with known population values under a variety of conditions were examined. Next, these results were compared to those from the traditional maximum likelihood approach to data fusion, as well as the data fusion approach analyzed via Bayes. The assessment of parameter recovery based on the proposed Bayesian Synthesis approach was evaluated using four criteria to reflect measures of raw bias, relative bias, accuracy, and efficiency. Subsequently, empirical analyses with real data were conducted. For this purpose, the fusion of real data from five longitudinal studies of mathematics ability varying in their assessment of ability and in the timing of measurement occasions was used. Results from the Bayesian Synthesis and data fusion approaches with combined data using Bayesian and maximum likelihood estimation methods were reported. The results illustrate that Bayesian Synthesis with data driven priors is a highly effective approach, provided that the sample sizes for the fused data are large enough to provide unbiased estimates. Bayesian Synthesis provides another beneficial approach to data fusion that can effectively be used to enhance the validity of conclusions obtained from the merging of data from different studies.
ContributorsMarcoulides, Katerina M (Author) / Grimm, Kevin (Thesis advisor) / Levy, Roy (Thesis advisor) / MacKinnon, David (Committee member) / Suk, Hye Won (Committee member) / Arizona State University (Publisher)
Created2017
Description
Statistical mediation analysis has been widely used in the social sciences in order to examine the indirect effects of an independent variable on a dependent variable. The statistical properties of the single mediator model with manifest and latent variables have been studied using simulation studies. However, the single mediator model with latent variables in the Bayesian framework with various accurate and inaccurate priors for structural and measurement model parameters has yet to be evaluated in a statistical simulation. This dissertation outlines the steps in the estimation of a single mediator model with latent variables as a Bayesian structural equation model (SEM). A Monte Carlo study is carried out in order to examine the statistical properties of point and interval summaries for the mediated effect in the Bayesian latent variable single mediator model with prior distributions with varying degrees of accuracy and informativeness. Bayesian methods with diffuse priors have equally good statistical properties as Maximum Likelihood (ML) and the distribution of the product. With accurate informative priors Bayesian methods can increase power up to 25% and decrease interval width up to 24%. With inaccurate informative priors the point summaries of the mediated effect are more biased than ML estimates, and the bias is higher if the inaccuracy occurs in priors for structural parameters than in priors for measurement model parameters. Findings from the Monte Carlo study are generalizable to Bayesian analyses with priors of the same distributional forms that have comparable amounts of (in)accuracy and informativeness to priors evaluated in the Monte Carlo study.
ContributorsMiočević, Milica (Author) / Mackinnon, David P. (Thesis advisor) / Levy, Roy (Thesis advisor) / Grimm, Kevin (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2017
Description
Guided by the Risky Families model and Daily Process methods, the present study examined how daily stressors are related to emotional well-being at the between- and within-person levels among adolescent grandchildren raised by grandmothers. This study also examined whether risk (i.e., adverse childhood experiences/ACES) and resilience (i.e., socio-emotional skills) factors were linked to differences in daily well-being, stressor exposure, and emotional reactivity, and evaluated the efficacy of an online social intelligence training (SIT) program on daily stressor-emotion dynamics. Data came from a subsample (n = 188) of custodial adolescents who participated in an attention-controlled randomized clinical trial and completed 14-day daily surveys prior to and following intervention. Analyses were conducted with dynamic structural equation modeling. Daily stressors, on average, and experiencing above average stressors, were associated with higher negative emotions and lower positive emotions and social connection. Those with more ACEs, on average, reported higher daily stressors and worse well-being, whereas those with higher socio-emotional skills, on average, reported lower daily stressors and better well-being. At the within-person level, more ACEs were associated with higher daily negative emotions. Nonverbal processing was linked to higher daily positive emotions and social connection. Conversational skills were associated with higher daily positive emotions and social connection, and lower, more inert daily negative emotions. Neither ACEs nor socio-emotional skills were associated with within-person reactivity to stressors. Also, the SIT program did not demonstrate efficacy for any outcome. My discussion focused on how findings extend the literature on custodial adolescents by showing that daily stressors impact well-being, offer knowledge of how ACEs and socio-emotional skills shape daily stressor-emotion dynamics, and considers reasons why the online, self-guided SIT program failed to show efficacy on key outcomes.
ContributorsCastro, Saul (Author) / Infurna, Frank (Thesis advisor) / Doane, Leah (Committee member) / Davis, Mary (Committee member) / Grimm, Kevin (Committee member) / Arizona State University (Publisher)
Created2023
Description
Mediation analysis is integral to psychology, investigating human behavior’s causal mechanisms. The diversity of explanations for human behavior has implications for the estimation and interpretation of statistical mediation models. Individuals can have similar observed outcomes while undergoing different causal processes or different observed outcomes while receiving the same treatment. Researchers can employ diverse strategies when studying individual differences in multiple mediation pathways, including individual fit measures and analysis of residuals. This dissertation investigates the use of individual residuals and fit measures to identify individual differences in multiple mediation pathways. More specifically, this study focuses on mediation model residuals in a heterogeneous population in which some people experience indirect effects through one mediator and others experience indirect effects through a different mediator. A simulation study investigates 162 conditions defined by effect size and sample size for three proposed methods: residual differences, delta z, and generalized Cook’s distance. Results indicate that analogs of Type 1 error rates are generally acceptable for the method of residual differences, but statistical power is limited. Likewise, neither delta z nor gCd could reliably distinguish between contrasts that had true effects and those that did not. The outcomes of this study reveal the potential for statistical measures of individual mediation. However, limitations related to unequal subpopulation variances, multiple dependent variables, the inherent relationship between direct effects and unestimated indirect effects, and minimal contrast effects require more research to develop a simple method that researchers can use on single data sets.
ContributorsSmyth, Heather Lynn (Author) / MacKinnon, David (Thesis advisor) / Tein, Jenn-Yun (Committee member) / McNeish, Daniel (Committee member) / Grimm, Kevin (Committee member) / Arizona State University (Publisher)
Created2022
Description
Longitudinal recursive partitioning (LRP) is a tree-based method for longitudinal data. It takes a sample of individuals that were each measured repeatedly across time, and it splits them based on a set of covariates such that individuals with similar trajectories become grouped together into nodes. LRP does this by fitting a mixed-effects model to each node every time that it becomes partitioned and extracting the deviance, which is the measure of node purity. LRP is implemented using the classification and regression tree algorithm, which suffers from a variable selection bias and does not guarantee reaching a global optimum. Additionally, fitting mixed-effects models to each potential split only to extract the deviance and discard the rest of the information is a computationally intensive procedure. Therefore, in this dissertation, I address the high computational demand, variable selection bias, and local optimum solution. I propose three approximation methods that reduce the computational demand of LRP, and at the same time, allow for a straightforward extension to recursive partitioning algorithms that do not have a variable selection bias and can reach the global optimum solution. In the three proposed approximations, a mixed-effects model is fit to the full data, and the growth curve coefficients for each individual are extracted. Then, (1) a principal component analysis is fit to the set of coefficients and the principal component score is extracted for each individual, (2) a one-factor model is fit to the coefficients and the factor score is extracted, or (3) the coefficients are summed. The three methods result in each individual having a single score that represents the growth curve trajectory. Therefore, now that the outcome is a single score for each individual, any tree-based method may be used for partitioning the data and group the individuals together. Once the individuals are assigned to their final nodes, a mixed-effects model is fit to each terminal node with the individuals belonging to it.
I conduct a simulation study, where I show that the approximation methods achieve the goals proposed while maintaining a similar level of out-of-sample prediction accuracy as LRP. I then illustrate and compare the methods using an applied data.
I conduct a simulation study, where I show that the approximation methods achieve the goals proposed while maintaining a similar level of out-of-sample prediction accuracy as LRP. I then illustrate and compare the methods using an applied data.
ContributorsStegmann, Gabriela (Author) / Grimm, Kevin (Thesis advisor) / Edwards, Michael (Committee member) / MacKinnon, David (Committee member) / McNeish, Daniel (Committee member) / Arizona State University (Publisher)
Created2019