Matching Items (10)
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- All Subjects: Quantitative Psychology and Psychometrics
- All Subjects: Multilevel Modeling
- Creators: West, Stephen G.
- Member of: ASU Electronic Theses and Dissertations
Description
In order to analyze data from an instrument administered at multiple time points it is a common practice to form composites of the items at each wave and to fit a longitudinal model to the composites. The advantage of using composites of items is that smaller sample sizes are required in contrast to second order models that include the measurement and the structural relationships among the variables. However, the use of composites assumes that longitudinal measurement invariance holds; that is, it is assumed that that the relationships among the items and the latent variables remain constant over time. Previous studies conducted on latent growth models (LGM) have shown that when longitudinal metric invariance is violated, the parameter estimates are biased and that mistaken conclusions about growth can be made. The purpose of the current study was to examine the impact of non-invariant loadings and non-invariant intercepts on two longitudinal models: the LGM and the autoregressive quasi-simplex model (AR quasi-simplex). A second purpose was to determine if there are conditions in which researchers can reach adequate conclusions about stability and growth even in the presence of violations of invariance. A Monte Carlo simulation study was conducted to achieve the purposes. The method consisted of generating items under a linear curve of factors model (COFM) or under the AR quasi-simplex. Composites of the items were formed at each time point and analyzed with a linear LGM or an AR quasi-simplex model. The results showed that AR quasi-simplex model yielded biased path coefficients only in the conditions with large violations of invariance. The fit of the AR quasi-simplex was not affected by violations of invariance. In general, the growth parameter estimates of the LGM were biased under violations of invariance. Further, in the presence of non-invariant loadings the rejection rates of the hypothesis of linear growth increased as the proportion of non-invariant items and as the magnitude of violations of invariance increased. A discussion of the results and limitations of the study are provided as well as general recommendations.
ContributorsOlivera-Aguilar, Margarita (Author) / Millsap, Roger E. (Thesis advisor) / Levy, Roy (Committee member) / MacKinnon, David (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2013
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
Daily dairies and other intensive measurement methods are increasingly used to study the relationships between two time varying variables X and Y. These data are commonly analyzed using longitudinal multilevel or bivariate growth curve models that allow for random effects of intercept (and sometimes also slope) but which do not address the effects of weekly cycles in the data. Three Monte Carlo studies investigated the impact of omitting the weekly cycles in daily dairy data under the multilevel model framework. In cases where cycles existed in both the time-varying predictor series (X) and the time-varying outcome series (Y) but were ignored, the effects of the within- and between-person components of X on Y tended to be biased, as were their corresponding standard errors. The direction and magnitude of the bias depended on the phase difference between the cycles in the two series. In cases where cycles existed in only one series but were ignored, the standard errors of the regression coefficients for the within- and between-person components of X tended to be biased, and the direction and magnitude of bias depended on which series contained cyclical components.
ContributorsLiu, Yu (Author) / West, Stephen G. (Thesis advisor) / Enders, Craig K. (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2013
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
Missing data are common in psychology research and can lead to bias and reduced power if not properly handled. Multiple imputation is a state-of-the-art missing data method recommended by methodologists. Multiple imputation methods can generally be divided into two broad categories: joint model (JM) imputation and fully conditional specification (FCS) imputation. JM draws missing values simultaneously for all incomplete variables using a multivariate distribution (e.g., multivariate normal). FCS, on the other hand, imputes variables one at a time, drawing missing values from a series of univariate distributions. In the single-level context, these two approaches have been shown to be equivalent with multivariate normal data. However, less is known about the similarities and differences of these two approaches with multilevel data, and the methodological literature provides no insight into the situations under which the approaches would produce identical results. This document examined five multilevel multiple imputation approaches (three JM methods and two FCS methods) that have been proposed in the literature. An analytic section shows that only two of the methods (one JM method and one FCS method) used imputation models equivalent to a two-level joint population model that contained random intercepts and different associations across levels. The other three methods employed imputation models that differed from the population model primarily in their ability to preserve distinct level-1 and level-2 covariances. I verified the analytic work with computer simulations, and the simulation results also showed that imputation models that failed to preserve level-specific covariances produced biased estimates. The studies also highlighted conditions that exacerbated the amount of bias produced (e.g., bias was greater for conditions with small cluster sizes). The analytic work and simulations lead to a number of practical recommendations for researchers.
ContributorsMistler, Stephen (Author) / Enders, Craig K. (Thesis advisor) / Aiken, Leona (Committee member) / Levy, Roy (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2015
Description
Coarsely grouped counts or frequencies are commonly used in the behavioral sciences. Grouped count and grouped frequency (GCGF) that are used as outcome variables often violate the assumptions of linear regression as well as models designed for categorical outcomes; there is no analytic model that is designed specifically to accommodate GCGF outcomes. The purpose of this dissertation was to compare the statistical performance of four regression models (linear regression, Poisson regression, ordinal logistic regression, and beta regression) that can be used when the outcome is a GCGF variable. A simulation study was used to determine the power, type I error, and confidence interval (CI) coverage rates for these models under different conditions. Mean structure, variance structure, effect size, continuous or binary predictor, and sample size were included in the factorial design. Mean structures reflected either a linear relationship or an exponential relationship between the predictor and the outcome. Variance structures reflected homoscedastic (as in linear regression), heteroscedastic (monotonically increasing) or heteroscedastic (increasing then decreasing) variance. Small to medium, large, and very large effect sizes were examined. Sample sizes were 100, 200, 500, and 1000. Results of the simulation study showed that ordinal logistic regression produced type I error, statistical power, and CI coverage rates that were consistently within acceptable limits. Linear regression produced type I error and statistical power that were within acceptable limits, but CI coverage was too low for several conditions important to the analysis of counts and frequencies. Poisson regression and beta regression displayed inflated type I error, low statistical power, and low CI coverage rates for nearly all conditions. All models produced unbiased estimates of the regression coefficient. Based on the statistical performance of the four models, ordinal logistic regression seems to be the preferred method for analyzing GCGF outcomes. Linear regression also performed well, but CI coverage was too low for conditions with an exponential mean structure and/or heteroscedastic variance. Some aspects of model prediction, such as model fit, were not assessed here; more research is necessary to determine which statistical model best captures the unique properties of GCGF outcomes.
ContributorsCoxe, Stefany (Author) / Aiken, Leona S. (Thesis advisor) / West, Stephen G. (Thesis advisor) / Mackinnon, David P (Committee member) / Reiser, Mark R. (Committee member) / Arizona State University (Publisher)
Created2012
Description
Researchers are often interested in estimating interactions in multilevel models, but many researchers assume that the same procedures and interpretations for interactions in single-level models apply to multilevel models. However, estimating interactions in multilevel models is much more complex than in single-level models. Because uncentered (RAS) or grand mean centered (CGM) level-1 predictors in two-level models contain two sources of variability (i.e., within-cluster variability and between-cluster variability), interactions involving RAS or CGM level-1 predictors also contain more than one source of variability. In this Master’s thesis, I use simulations to demonstrate that ignoring the four sources of variability in a total level-1 interaction effect can lead to erroneous conclusions. I explain how to parse a total level-1 interaction effect into four specific interaction effects, derive equivalencies between CGM and centering within context (CWC) for this model, and describe how the interpretations of the fixed effects change under CGM and CWC. Finally, I provide an empirical example using diary data collected from working adults with chronic pain.
ContributorsMazza, Gina L (Author) / Enders, Craig K. (Thesis advisor) / Aiken, Leona S. (Thesis advisor) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2015
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
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
Description
For this thesis a Monte Carlo simulation was conducted to investigate the robustness of three latent interaction modeling approaches (constrained product indicator, generalized appended product indicator (GAPI), and latent moderated structural equations (LMS)) under high degrees of nonnormality of the exogenous indicators, which have not been investigated in previous literature. Results showed that the constrained product indicator and LMS approaches yielded biased estimates of the interaction effect when the exogenous indicators were highly nonnormal. When the violation of nonnormality was not severe (symmetric with excess kurtosis < 1), the LMS approach with ML estimation yielded the most precise latent interaction effect estimates. The LMS approach with ML estimation also had the highest statistical power among the three approaches, given that the actual Type-I error rates of the Wald and likelihood ratio test of interaction effect were acceptable. In highly nonnormal conditions, only the GAPI approach with ML estimation yielded unbiased latent interaction effect estimates, with an acceptable actual Type-I error rate of both the Wald test and likelihood ratio test of interaction effect. No support for the use of the Satorra-Bentler or Yuan-Bentler ML corrections was found across all three methods.
ContributorsCham, Hei Ning (Author) / West, Stephen G. (Thesis advisor) / Aiken, Leona S. (Committee member) / Enders, Craig K. (Committee member) / Arizona State University (Publisher)
Created2010