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- All Subjects: Quantitative psychology
- Creators: Levy, Roy
- Creators: Amazeen, Polemnia
- Resource Type: Text
Description
Dynamic Bayesian networks (DBNs; Reye, 2004) are a promising tool for modeling student proficiency under rich measurement scenarios (Reichenberg, in press). These scenarios often present assessment conditions far more complex than what is seen with more traditional assessments and require assessment arguments and psychometric models capable of integrating those complexities. Unfortunately, DBNs remain understudied and their psychometric properties relatively unknown. If the apparent strengths of DBNs are to be leveraged, then the body of literature surrounding their properties and use needs to be expanded upon. To this end, the current work aimed at exploring the properties of DBNs under a variety of realistic psychometric conditions. A two-phase Monte Carlo simulation study was conducted in order to evaluate parameter recovery for DBNs using maximum likelihood estimation with the Netica software package. Phase 1 included a limited number of conditions and was exploratory in nature while Phase 2 included a larger and more targeted complement of conditions. Manipulated factors included sample size, measurement quality, test length, the number of measurement occasions. Results suggested that measurement quality has the most prominent impact on estimation quality with more distinct performance categories yielding better estimation. While increasing sample size tended to improve estimation, there were a limited number of conditions under which greater samples size led to more estimation bias. An exploration of this phenomenon is included. From a practical perspective, parameter recovery appeared to be sufficient with samples as low as N = 400 as long as measurement quality was not poor and at least three items were present at each measurement occasion. Tests consisting of only a single item required exceptional measurement quality in order to adequately recover model parameters. The study was somewhat limited due to potentially software-specific issues as well as a non-comprehensive collection of experimental conditions. Further research should replicate and, potentially expand the current work using other software packages including exploring alternate estimation methods (e.g., Markov chain Monte Carlo).
ContributorsReichenberg, Raymond E (Author) / Levy, Roy (Thesis advisor) / Eggum-Wilkens, Natalie (Thesis advisor) / Iida, Masumi (Committee member) / DeLay, Dawn (Committee member) / Arizona State University (Publisher)
Created2018
Description
Investigation of measurement invariance (MI) commonly assumes correct specification of dimensionality across multiple groups. Although research shows that violation of the dimensionality assumption can cause bias in model parameter estimation for single-group analyses, little research on this issue has been conducted for multiple-group analyses. This study explored the effects of mismatch in dimensionality between data and analysis models with multiple-group analyses at the population and sample levels. Datasets were generated using a bifactor model with different factor structures and were analyzed with bifactor and single-factor models to assess misspecification effects on assessments of MI and latent mean differences. As baseline models, the bifactor models fit data well and had minimal bias in latent mean estimation. However, the low convergence rates of fitting bifactor models to data with complex structures and small sample sizes caused concern. On the other hand, effects of fitting the misspecified single-factor models on the assessments of MI and latent means differed by the bifactor structures underlying data. For data following one general factor and one group factor affecting a small set of indicators, the effects of ignoring the group factor in analysis models on the tests of MI and latent mean differences were mild. In contrast, for data following one general factor and several group factors, oversimplifications of analysis models can lead to inaccurate conclusions regarding MI assessment and latent mean estimation.
ContributorsXu, Yuning (Author) / Green, Samuel (Thesis advisor) / Levy, Roy (Committee member) / Thompson, Marilyn (Committee member) / Arizona State University (Publisher)
Created2018
Description
With improvements in technology, intensive longitudinal studies that permit the investigation of daily and weekly cycles in behavior have increased exponentially over the past few decades. Traditionally, when data have been collected on two variables over time, multivariate time series approaches that remove trends, cycles, and serial dependency have been used. These analyses permit the study of the relationship between random shocks (perturbations) in the presumed causal series and changes in the outcome series, but do not permit the study of the relationships between cycles. Liu and West (2016) proposed a multilevel approach that permitted the study of potential between subject relationships between features of the cycles in two series (e.g., amplitude). However, I show that the application of the Liu and West approach is restricted to a small set of features and types of relationships between the series. Several authors (e.g., Boker & Graham, 1998) proposed a connected mass-spring model that appears to permit modeling of more general cyclic relationships. I showed that the undamped connected mass-spring model is also limited and may be unidentified. To test the severity of the restrictions of the motion trajectories producible by the undamped connected mass-spring model I mathematically derived their connection to the force equations of the undamped connected mass-spring system. The mathematical solution describes the domain of the trajectory pairs that are producible by the undamped connected mass-spring model. The set of producible trajectory pairs is highly restricted, and this restriction sets major limitations on the application of the connected mass-spring model to psychological data. I used a simulation to demonstrate that even if a pair of psychological time-varying variables behaved exactly like two masses in an undamped connected mass-spring system, the connected mass-spring model would not yield adequate parameter estimates. My simulation probed the performance of the connected mass-spring model as a function of several aspects of data quality including number of subjects, series length, sampling rate relative to the cycle, and measurement error in the data. The findings can be extended to damped and nonlinear connected mass-spring systems.
ContributorsMartynova, Elena (M.A.) (Author) / West, Stephen G. (Thesis advisor) / Amazeen, Polemnia (Committee member) / Tein, Jenn-Yun (Committee member) / Arizona State University (Publisher)
Created2019
Description
The action of running is difficult to measure, but well worth it to receive valuable information about one of our most basic evolutionary functions. In the context of modern day, recreational runners typically listen to music while running, and so the purpose of this experiment is to analyze the influence of music on running from a more dynamical approach. The first experiment was a running task involving running without a metronome and running with one while setting one's own preferred running tempo. The second experiment sought to manipulate the participant's preferred running tempo by having them listen to the metronome set at their preferred tempo, 20% above their preferred tempo, or 20% below. The purpose of this study is to analyze whether or not rhythmic perturbations different to one's preferred running tempo would interfere with one's preferred running tempo and cause a change in the variability of one's running patterns as well as a change in one's running performance along the measures of step rate, stride length, and stride pace. The evidence suggests that participants naturally entrained to the metronome tempo which influenced them to run faster or slower as a function of metronome tempo. However, this change was also accompanied by a shift in the variability of one's step rate and stride length.
ContributorsZavala, Andrew Geovanni (Author) / Amazeen, Eric (Thesis director) / Amazeen, Polemnia (Committee member) / Vedeler, Dankert (Committee member) / Department of Psychology (Contributor) / W. P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Although models for describing longitudinal data have become increasingly sophisticated, the criticism of even foundational growth curve models remains challenging. The challenge arises from the need to disentangle data-model misfit at multiple and interrelated levels of analysis. Using posterior predictive model checking (PPMC)—a popular Bayesian framework for model criticism—the performance of several discrepancy functions was investigated in a Monte Carlo simulation study. The discrepancy functions of interest included two types of conditional concordance correlation (CCC) functions, two types of R2 functions, two types of standardized generalized dimensionality discrepancy (SGDDM) functions, the likelihood ratio (LR), and the likelihood ratio difference test (LRT). Key outcomes included effect sizes of the design factors on the realized values of discrepancy functions, distributions of posterior predictive p-values (PPP-values), and the proportion of extreme PPP-values.
In terms of the realized values, the behavior of the CCC and R2 functions were generally consistent with prior research. However, as diagnostics, these functions were extremely conservative even when some aspect of the data was unaccounted for. In contrast, the conditional SGDDM (SGDDMC), LR, and LRT were generally sensitive to the underspecifications investigated in this work on all outcomes considered. Although the proportions of extreme PPP-values for these functions tended to increase in null situations for non-normal data, this behavior may have reflected the true misfit that resulted from the specification of normal prior distributions. Importantly, the LR and the SGDDMC to a greater extent exhibited some potential for untangling the sources of data-model misfit. Owing to connections of growth curve models to the more fundamental frameworks of multilevel modeling, structural equation models with a mean structure, and Bayesian hierarchical models, the results of the current work may have broader implications that warrant further research.
In terms of the realized values, the behavior of the CCC and R2 functions were generally consistent with prior research. However, as diagnostics, these functions were extremely conservative even when some aspect of the data was unaccounted for. In contrast, the conditional SGDDM (SGDDMC), LR, and LRT were generally sensitive to the underspecifications investigated in this work on all outcomes considered. Although the proportions of extreme PPP-values for these functions tended to increase in null situations for non-normal data, this behavior may have reflected the true misfit that resulted from the specification of normal prior distributions. Importantly, the LR and the SGDDMC to a greater extent exhibited some potential for untangling the sources of data-model misfit. Owing to connections of growth curve models to the more fundamental frameworks of multilevel modeling, structural equation models with a mean structure, and Bayesian hierarchical models, the results of the current work may have broader implications that warrant further research.
ContributorsFay, Derek (Author) / Levy, Roy (Thesis advisor) / Thompson, Marilyn (Committee member) / Enders, Craig (Committee member) / Arizona State University (Publisher)
Created2015
Description
Through a two study simulation design with different design conditions (sample size at level 1 (L1) was set to 3, level 2 (L2) sample size ranged from 10 to 75, level 3 (L3) sample size ranged from 30 to 150, intraclass correlation (ICC) ranging from 0.10 to 0.50, model complexity ranging from one predictor to three predictors), this study intends to provide general guidelines about adequate sample sizes at three levels under varying ICC conditions for a viable three level HLM analysis (e.g., reasonably unbiased and accurate parameter estimates). In this study, the data generating parameters for the were obtained using a large-scale longitudinal data set from North Carolina, provided by the National Center on Assessment and Accountability for Special Education (NCAASE). I discuss ranges of sample sizes that are inadequate or adequate for convergence, absolute bias, relative bias, root mean squared error (RMSE), and coverage of individual parameter estimates. The current study, with the help of a detailed two-part simulation design for various sample sizes, model complexity and ICCs, provides various options of adequate sample sizes under different conditions. This study emphasizes that adequate sample sizes at either L1, L2, and L3 can be adjusted according to different interests in parameter estimates, different ranges of acceptable absolute bias, relative bias, root mean squared error, and coverage. Under different model complexity and varying ICC conditions, this study aims to help researchers identify L1, L2, and L3 sample size or both as the source of variation in absolute bias, relative bias, RMSE, or coverage proportions for a certain parameter estimate. This assists researchers in making better decisions for selecting adequate sample sizes in a three-level HLM analysis. A limitation of the study was the use of only a single distribution for the dependent and explanatory variables, different types of distributions and their effects might result in different sample size recommendations.
ContributorsYel, Nedim (Author) / Levy, Roy (Thesis advisor) / Elliott, Stephen N. (Thesis advisor) / Schulte, Ann C (Committee member) / Iida, Masumi (Committee member) / Arizona State University (Publisher)
Created2016
Description
Accurate data analysis and interpretation of results may be influenced by many potential factors. The factors of interest in the current work are the chosen analysis model(s), the presence of missing data, and the type(s) of data collected. If analysis models are used which a) do not accurately capture the structure of relationships in the data such as clustered/hierarchical data, b) do not allow or control for missing values present in the data, or c) do not accurately compensate for different data types such as categorical data, then the assumptions associated with the model have not been met and the results of the analysis may be inaccurate. In the presence of clustered
ested data, hierarchical linear modeling or multilevel modeling (MLM; Raudenbush & Bryk, 2002) has the ability to predict outcomes for each level of analysis and across multiple levels (accounting for relationships between levels) providing a significant advantage over single-level analyses. When multilevel data contain missingness, multilevel multiple imputation (MLMI) techniques may be used to model both the missingness and the clustered nature of the data. With categorical multilevel data with missingness, categorical MLMI must be used. Two such routines for MLMI with continuous and categorical data were explored with missing at random (MAR) data: a formal Bayesian imputation and analysis routine in JAGS (R/JAGS) and a common MLM procedure of imputation via Bayesian estimation in BLImP with frequentist analysis of the multilevel model in Mplus (BLImP/Mplus). Manipulated variables included interclass correlations, number of clusters, and the rate of missingness. Results showed that with continuous data, R/JAGS returned more accurate parameter estimates than BLImP/Mplus for almost all parameters of interest across levels of the manipulated variables. Both R/JAGS and BLImP/Mplus encountered convergence issues and returned inaccurate parameter estimates when imputing and analyzing dichotomous data. Follow-up studies showed that JAGS and BLImP returned similar imputed datasets but the choice of analysis software for MLM impacted the recovery of accurate parameter estimates. Implications of these findings and recommendations for further research will be discussed.
ested data, hierarchical linear modeling or multilevel modeling (MLM; Raudenbush & Bryk, 2002) has the ability to predict outcomes for each level of analysis and across multiple levels (accounting for relationships between levels) providing a significant advantage over single-level analyses. When multilevel data contain missingness, multilevel multiple imputation (MLMI) techniques may be used to model both the missingness and the clustered nature of the data. With categorical multilevel data with missingness, categorical MLMI must be used. Two such routines for MLMI with continuous and categorical data were explored with missing at random (MAR) data: a formal Bayesian imputation and analysis routine in JAGS (R/JAGS) and a common MLM procedure of imputation via Bayesian estimation in BLImP with frequentist analysis of the multilevel model in Mplus (BLImP/Mplus). Manipulated variables included interclass correlations, number of clusters, and the rate of missingness. Results showed that with continuous data, R/JAGS returned more accurate parameter estimates than BLImP/Mplus for almost all parameters of interest across levels of the manipulated variables. Both R/JAGS and BLImP/Mplus encountered convergence issues and returned inaccurate parameter estimates when imputing and analyzing dichotomous data. Follow-up studies showed that JAGS and BLImP returned similar imputed datasets but the choice of analysis software for MLM impacted the recovery of accurate parameter estimates. Implications of these findings and recommendations for further research will be discussed.
ContributorsKunze, Katie L (Author) / Levy, Roy (Thesis advisor) / Enders, Craig K. (Committee member) / Thompson, Marilyn S (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
The proliferation of intensive longitudinal datasets has necessitated the development of analytical techniques that are flexible and accessible to researchers collecting dyadic or individual data. Dynamic structural equation models (DSEMs), as implemented in Mplus, provides the flexibility researchers require by combining components from multilevel modeling, structural equation modeling, and time series analyses. This dissertation project presents a simulation study that evaluates the performance of categorical DSEM using a probit link function across different numbers of clusters (N = 50 or 200), timepoints (T = 14, 28, or 56), categories on the outcome (2, 3, or 5), and distribution of responses on the outcome (symmetric/approximate normal, skewed, or uniform) for both univariate and multivariate models (representing individual data and dyadic longitudinal Actor-Partner Interdependence Model data, respectively). The 3- and 5-category model conditions were also evaluated as continuous DSEMs across the same cluster, timepoint, and distribution conditions to evaluate to what extent ignoring the categorical nature of the outcome impacted model performance. Results indicated that previously-suggested minimums for number of clusters and timepoints from studies evaluating continuous DSEM performance with continuous outcomes are not large enough to produce unbiased and adequately powered models in categorical DSEM. The distribution of responses on the outcome did not have a noticeable impact in model performance for categorical DSEM, but did affect model performance when fitting a continuous DSEM to the same datasets. Ignoring the categorical nature of the outcome lead to underestimated effects across parameters and conditions, and showed large Type-I error rates in the N = 200 cluster conditions.
ContributorsSavord, Andrea (Author) / McNeish, Daniel (Thesis advisor) / Grimm, Kevin J (Committee member) / Iida, Masumi (Committee member) / Levy, Roy (Committee member) / Arizona State University (Publisher)
Created2023