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- All Subjects: Quantitative psychology
- Creators: Levy, Roy
- Creators: Mackinnon, David P
Description
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.
ContributorsCham, Hei Ning (Author) / Tein, Jenn-Yun (Thesis advisor) / Enders, Stephen G (Thesis advisor) / Enders, Craig K. (Committee member) / Mackinnon, David P (Committee member) / Arizona State University (Publisher)
Created2013
Description
Understanding how adherence affects outcomes is crucial when developing and assigning interventions. However, interventions are often evaluated by conducting randomized experiments and estimating intent-to-treat effects, which ignore actual treatment received. Dose-response effects can supplement intent-to-treat effects when participants are offered the full dose but many only receive a partial dose due to nonadherence. Using these data, we can estimate the magnitude of the treatment effect at different levels of adherence, which serve as a proxy for different levels of treatment. In this dissertation, I conducted Monte Carlo simulations to evaluate when linear dose-response effects can be accurately and precisely estimated in randomized experiments comparing a no-treatment control condition to a treatment condition with partial adherence. Specifically, I evaluated the performance of confounder adjustment and instrumental variable methods when their assumptions were met (Study 1) and when their assumptions were violated (Study 2). In Study 1, the confounder adjustment and instrumental variable methods provided unbiased estimates of the dose-response effect across sample sizes (200, 500, 2,000) and adherence distributions (uniform, right skewed, left skewed). The adherence distribution affected power for the instrumental variable method. In Study 2, the confounder adjustment method provided unbiased or minimally biased estimates of the dose-response effect under no or weak (but not moderate or strong) unobserved confounding. The instrumental variable method provided extremely biased estimates of the dose-response effect under violations of the exclusion restriction (no direct effect of treatment assignment on the outcome), though less severe violations of the exclusion restriction should be investigated.
ContributorsMazza, Gina L (Author) / Grimm, Kevin J. (Thesis advisor) / West, Stephen G. (Thesis advisor) / Mackinnon, David P (Committee member) / Tein, Jenn-Yun (Committee member) / Arizona State University (Publisher)
Created2018
Description
The goal of diagnostic assessment is to discriminate between groups. In many cases, a binary decision is made conditional on a cut score from a continuous scale. Psychometric methods can improve assessment by modeling a latent variable using item response theory (IRT), and IRT scores can subsequently be used to determine a cut score using receiver operating characteristic (ROC) curves. Psychometric methods provide reliable and interpretable scores, but the prediction of the diagnosis is not the primary product of the measurement process. In contrast, machine learning methods, such as regularization or binary recursive partitioning, can build a model from the assessment items to predict the probability of diagnosis. Machine learning predicts the diagnosis directly, but does not provide an inferential framework to explain why item responses are related to the diagnosis. It remains unclear whether psychometric and machine learning methods have comparable accuracy or if one method is preferable in some situations. In this study, Monte Carlo simulation methods were used to compare psychometric and machine learning methods on diagnostic classification accuracy. Results suggest that classification accuracy of psychometric models depends on the diagnostic-test correlation and prevalence of diagnosis. Also, machine learning methods that reduce prediction error have inflated specificity and very low sensitivity compared to the data-generating model, especially when prevalence is low. Finally, machine learning methods that use ROC curves to determine probability thresholds have comparable classification accuracy to the psychometric models as sample size, number of items, and number of item categories increase. Therefore, results suggest that machine learning models could provide a viable alternative for classification in diagnostic assessments. Strengths and limitations for each of the methods are discussed, and future directions are considered.
ContributorsGonzález, Oscar (Author) / Mackinnon, David P (Thesis advisor) / Edwards, Michael C (Thesis advisor) / Grimm, Kevin J. (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2018
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
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
Time metric is an important consideration for all longitudinal models because it can influence the interpretation of estimates, parameter estimate accuracy, and model convergence in longitudinal models with latent variables. Currently, the literature on latent difference score (LDS) models does not discuss the importance of time metric. Furthermore, there is little research using simulations to investigate LDS models. This study examined the influence of time metric on model estimation, interpretation, parameter estimate accuracy, and convergence in LDS models using empirical simulations. Results indicated that for a time structure with a true time metric where participants had different starting points and unequally spaced intervals, LDS models fit with a restructured and less informative time metric resulted in biased parameter estimates. However, models examined using the true time metric were less likely to converge than models using the restructured time metric, likely due to missing data. Where participants had different starting points but equally spaced intervals, LDS models fit with a restructured time metric resulted in biased estimates of intercept means, but all other parameter estimates were unbiased, and models examined using the true time metric had less convergence than the restructured time metric as well due to missing data. The findings of this study support prior research on time metric in longitudinal models, and further research should examine these findings under alternative conditions. The importance of these findings for substantive researchers is discussed.
ContributorsO'Rourke, Holly P (Author) / Grimm, Kevin J. (Thesis advisor) / Mackinnon, David P (Thesis advisor) / Chassin, Laurie (Committee member) / Aiken, Leona S. (Committee member) / Arizona State University (Publisher)
Created2016
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