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- All Subjects: Psychology--Statistical methods.
- Genre: Academic theses
- Creators: Enders, Craig
- Creators: Millsap, Roger E
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
Methods to test hypotheses of mediated effects in the pretest-posttest control group design are understudied in the behavioral sciences (MacKinnon, 2008). Because many studies aim to answer questions about mediating processes in the pretest-posttest control group design, there is a need to determine which model is most appropriate to test hypotheses about mediating processes and what happens to estimates of the mediated effect when model assumptions are violated in this design. The goal of this project was to outline estimator characteristics of four longitudinal mediation models and the cross-sectional mediation model. Models were compared on type 1 error rates, statistical power, accuracy of confidence interval coverage, and bias of parameter estimates. Four traditional longitudinal models and the cross-sectional model were assessed. The four longitudinal models were analysis of covariance (ANCOVA) using pretest scores as a covariate, path analysis, difference scores, and residualized change scores. A Monte Carlo simulation study was conducted to evaluate the different models across a wide range of sample sizes and effect sizes. All models performed well in terms of type 1 error rates and the ANCOVA and path analysis models performed best in terms of bias and empirical power. The difference score, residualized change score, and cross-sectional models all performed well given certain conditions held about the pretest measures. These conditions and future directions are discussed.
ContributorsValente, Matthew John (Author) / MacKinnon, David (Thesis advisor) / West, Stephen (Committee member) / Aiken, Leona (Committee member) / Enders, Craig (Committee member) / Arizona State University (Publisher)
Created2015
Description
Research methods based on the frequentist philosophy use prior information in a priori power calculations and when determining the necessary sample size for the detection of an effect, but not in statistical analyses. Bayesian methods incorporate prior knowledge into the statistical analysis in the form of a prior distribution. When prior information about a relationship is available, the estimates obtained could differ drastically depending on the choice of Bayesian or frequentist method. Study 1 in this project compared the performance of five methods for obtaining interval estimates of the mediated effect in terms of coverage, Type I error rate, empirical power, interval imbalance, and interval width at N = 20, 40, 60, 100 and 500. In Study 1, Bayesian methods with informative prior distributions performed almost identically to Bayesian methods with diffuse prior distributions, and had more power than normal theory confidence limits, lower Type I error rates than the percentile bootstrap, and coverage, interval width, and imbalance comparable to normal theory, percentile bootstrap, and the bias-corrected bootstrap confidence limits. Study 2 evaluated if a Bayesian method with true parameter values as prior information outperforms the other methods. The findings indicate that with true values of parameters as the prior information, Bayesian credibility intervals with informative prior distributions have more power, less imbalance, and narrower intervals than Bayesian credibility intervals with diffuse prior distributions, normal theory, percentile bootstrap, and bias-corrected bootstrap confidence limits. Study 3 examined how much power increases when increasing the precision of the prior distribution by a factor of ten for either the action or the conceptual path in mediation analysis. Power generally increases with increases in precision but there are many sample size and parameter value combinations where precision increases by a factor of 10 do not lead to substantial increases in power.
ContributorsMiocevic, Milica (Author) / Mackinnon, David P. (Thesis advisor) / Levy, Roy (Committee member) / West, Stephen G. (Committee member) / Enders, Craig (Committee member) / Arizona State University (Publisher)
Created2014
Description
Although the issue of factorial invariance has received increasing attention in the literature, the focus is typically on differences in factor structure across groups that are directly observed, such as those denoted by sex or ethnicity. While establishing factorial invariance across observed groups is a requisite step in making meaningful cross-group comparisons, failure to attend to possible sources of latent class heterogeneity in the form of class-based differences in factor structure has the potential to compromise conclusions with respect to observed groups and may result in misguided attempts at instrument development and theory refinement. The present studies examined the sensitivity of two widely used confirmatory factor analytic model fit indices, the chi-square test of model fit and RMSEA, to latent class differences in factor structure. Two primary questions were addressed. The first of these concerned the impact of latent class differences in factor loadings with respect to model fit in a single sample reflecting a mixture of classes. The second question concerned the impact of latent class differences in configural structure on tests of factorial invariance across observed groups. The results suggest that both indices are highly insensitive to class-based differences in factor loadings. Across sample size conditions, models with medium (0.2) sized loading differences were rejected by the chi-square test of model fit at rates just slightly higher than the nominal .05 rate of rejection that would be expected under a true null hypothesis. While rates of rejection increased somewhat when the magnitude of loading difference increased, even the largest sample size with equal class representation and the most extreme violations of loading invariance only had rejection rates of approximately 60%. RMSEA was also insensitive to class-based differences in factor loadings, with mean values across conditions suggesting a degree of fit that would generally be regarded as exceptionally good in practice. In contrast, both indices were sensitive to class-based differences in configural structure in the context of a multiple group analysis in which each observed group was a mixture of classes. However, preliminary evidence suggests that this sensitivity may contingent on the form of the cross-group model misspecification.
ContributorsBlackwell, Kimberly Carol (Author) / Millsap, Roger E (Thesis advisor) / Aiken, Leona S. (Committee member) / Enders, Craig K. (Committee member) / Mackinnon, David P (Committee member) / Arizona State University (Publisher)
Created2011
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
Mediation analysis is a statistical approach that examines the effect of a treatment (e.g., prevention program) on an outcome (e.g., substance use) achieved by targeting and changing one or more intervening variables (e.g., peer drug use norms). The increased use of prevention intervention programs with outcomes measured at multiple time points following the intervention requires multilevel modeling techniques to account for clustering in the data. Estimating multilevel mediation models, in which all the variables are measured at individual level (Level 1), poses several challenges to researchers. The first challenge is to conceptualize a multilevel mediation model by clarifying the underlying statistical assumptions and implications of those assumptions on cluster-level (Level-2) covariance structure. A second challenge is that variables measured at Level 1 potentially contain both between- and within-cluster variation making interpretation of multilevel analysis difficult. As a result, multilevel mediation analyses may yield coefficient estimates that are composites of coefficient estimates at different levels if proper centering is not used. This dissertation addresses these two challenges. Study 1 discusses the concept of a correctly specified multilevel mediation model by examining the underlying statistical assumptions and implication of those assumptions on Level-2 covariance structure. Further, Study 1 presents analytical results showing algebraic relationships between the population parameters in a correctly specified multilevel mediation model. Study 2 extends previous work on centering in multilevel mediation analysis. First, different centering methods in multilevel analysis including centering within cluster with the cluster mean as a Level-2 predictor of intercept (CWC2) are discussed. Next, application of the CWC2 strategy to accommodate multilevel mediation models is explained. It is shown that the CWC2 centering strategy separates the between- and within-cluster mediated effects. Next, Study 2 discusses assumptions underlying a correctly specified CWC2 multilevel mediation model and defines between- and within-cluster mediated effects. In addition, analytical results for the algebraic relationships between the population parameters in a CWC2 multilevel mediation model are presented. Finally, Study 2 shows results of a simulation study conducted to verify derived algebraic relationships empirically.
ContributorsTofighi, Davood (Author) / West, Stephen G. (Thesis advisor) / Mackinnon, David P (Thesis advisor) / Enders, Craig C (Committee member) / Millsap, Roger E (Committee member) / Arizona State University (Publisher)
Created2010