Matching Items (6)
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- All Subjects: Psychology--Statistical methods.
- Creators: Grimm, Kevin
- Creators: Grimm, Kevin J.
- Member of: ASU Electronic Theses and Dissertations
Description
Researchers who conduct longitudinal studies are inherently interested in studying individual and population changes over time (e.g., mathematics achievement, subjective well-being). To answer such research questions, models of change (e.g., growth models) make the assumption of longitudinal measurement invariance. In many applied situations, key constructs are measured by a collection of ordered-categorical indicators (e.g., Likert scale items). To evaluate longitudinal measurement invariance with ordered-categorical indicators, a set of hierarchical models can be sequentially tested and compared. If the statistical tests of measurement invariance fail to be supported for one of the models, it is useful to have a method with which to gauge the practical significance of the differences in measurement model parameters over time. Drawing on studies of latent growth models and second-order latent growth models with continuous indicators (e.g., Kim & Willson, 2014a; 2014b; Leite, 2007; Wirth, 2008), this study examined the performance of a potential sensitivity analysis to gauge the practical significance of violations of longitudinal measurement invariance for ordered-categorical indicators using second-order latent growth models. The change in the estimate of the second-order growth parameters following the addition of an incorrect level of measurement invariance constraints at the first-order level was used as an effect size for measurement non-invariance. This study investigated how sensitive the proposed sensitivity analysis was to different locations of non-invariance (i.e., non-invariance in the factor loadings, the thresholds, and the unique factor variances) given a sufficient sample size. This study also examined whether the sensitivity of the proposed sensitivity analysis depended on a number of other factors including the magnitude of non-invariance, the number of non-invariant indicators, the number of non-invariant occasions, and the number of response categories in the indicators.
ContributorsLiu, Yu, Ph.D (Author) / West, Stephen G. (Thesis advisor) / Tein, Jenn-Yun (Thesis advisor) / Green, Samuel (Committee member) / Grimm, Kevin J. (Committee member) / Arizona State University (Publisher)
Created2016
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
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
Measurement invariance exists when a scale functions equivalently across people and is therefore essential for making meaningful group comparisons. Often, measurement invariance is examined with independent and identically distributed data; however, there are times when the participants are clustered within units, creating dependency in the data. Researchers have taken different approaches to address this dependency when studying measurement invariance (e.g., Kim, Kwok, & Yoon, 2012; Ryu, 2014; Kim, Yoon, Wen, Luo, & Kwok, 2015), but there are no comparisons of the various approaches. The purpose of this master's thesis was to investigate measurement invariance in multilevel data when the grouping variable was a level-1 variable using five different approaches. Publicly available data from the Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K) was used as an illustrative example. The construct of early behavior, which was made up of four teacher-rated behavior scales, was evaluated for measurement invariance in relation to gender. In the specific case of this illustrative example, the statistical conclusions of the five approaches were in agreement (i.e., the loading of the externalizing item and the intercept of the approaches to learning item were not invariant). Simulation work should be done to investigate in which situations the conclusions of these approaches diverge.
ContributorsGunn, Heather (Author) / Grimm, Kevin J. (Thesis advisor) / Aiken, Leona S. (Committee member) / Suk, Hye Won (Committee member) / Arizona State University (Publisher)
Created2016