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 Title
 A Comparison of Three Approaches to Confidence Interval Estimation for Coefficient Omega.
 Creator

Xu, Jie, Yang, Yanyun, Becker, Betsy Jane, Almond, Russell G., Florida State University, College of Education, Department of Educational Psychology and Learning Systems
 Abstract/Description

Coefficient Omega was introduced by McDonald (1978) as a reliability coefficient of composite scores for the congeneric model. Interval estimation (Neyman, 1937) on coefficient Omega provides a range of plausible values which is likely to capture the population reliability of composite scores. The Wald method, likelihood method, and biascorrected and accelerated bootstrap method are three methods to construct confidence interval for coefficient Omega (e.g., Cheung, 2009b; Kelley & Cheng,...
Show moreCoefficient Omega was introduced by McDonald (1978) as a reliability coefficient of composite scores for the congeneric model. Interval estimation (Neyman, 1937) on coefficient Omega provides a range of plausible values which is likely to capture the population reliability of composite scores. The Wald method, likelihood method, and biascorrected and accelerated bootstrap method are three methods to construct confidence interval for coefficient Omega (e.g., Cheung, 2009b; Kelley & Cheng, 2012; Raykov, 2002, 2004, 2009; Raykov & Marcoulides, 2004; Padilla & Divers, 2013). Very limited number of studies on the evaluation of these three methods can be found in the literature (e.g., Cheung, 2007, 2009a, 2009b; Kelley & Cheng, 2012; Padilla & Divers, 2013). No simulation study has been conducted to evaluate the performance of these three methods for interval construction on coefficient Omega. In the current simulation study, I assessed these three methods by comparing their empirical performance on interval estimation for coefficient Omega. Four factors were included in the simulation design: sample size, number of items, factor loading, and degree of nonnormality. Two thousands datasets were generated in R 2.15.0 (R Core Team, 2012) for each condition. For each generated dataset, three approaches (i.e., the Wald method, likelihood method, and biascorrected and accelerated bootstrap method) were used to construct 95% confidence interval of coefficient Omega in R 2.15.0. The results showed that when the data were multivariate normally distributed, three methods performed equally well and coverage probabilities were very close to the prespecified .95 confidence level. When the data were multivariate nonnormally distributed, coverage probabilities decreased and interval widths became wider for all three methods as the degree of nonnormality increased. In general, when the data departed from the multivariate normality, the BCa bootstrap method performed better than the other two methods, with relatively higher coverage probabilities, while the Wald and likelihood methods were comparable and yielded narrower interval width than the BCa bootstrap method.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_etd9269
 Format
 Thesis
 Title
 Critical Issues in Survey MetaAnalysis.
 Creator

Gozutok, Ahmet Serhat, Becker, Betsy Jane, Huffer, Fred W., Yang, Yanyun, Paek, Insu, Florida State University, College of Education, Department of Educational Psychology and...
Show moreGozutok, Ahmet Serhat, Becker, Betsy Jane, Huffer, Fred W., Yang, Yanyun, Paek, Insu, Florida State University, College of Education, Department of Educational Psychology and Learning Systems
Show less  Abstract/Description

In research synthesis, researchers may aim at summarizing peoples' attitudes and perceptions of phenomena that have been assessed using different measures. Selfreport rating scales are among the most commonly used measurement tools to quantify such latent constructs in education and psychology. However, selfreport ratingscale questions measuring the same construct may differ from each other in many ways. Scale format, number of response options, wording of questions, and labeling of...
Show moreIn research synthesis, researchers may aim at summarizing peoples' attitudes and perceptions of phenomena that have been assessed using different measures. Selfreport rating scales are among the most commonly used measurement tools to quantify such latent constructs in education and psychology. However, selfreport ratingscale questions measuring the same construct may differ from each other in many ways. Scale format, number of response options, wording of questions, and labeling of response option categories may vary across questions. Consequently, variations across the measures of the same construct bring about the issue of comparability of the results across the studies in metaanalytic investigations. In this study, I examine the complexities of summarizing the results of different survey questions about the same construct in the metaanalytic fashion. More specifically, this study focuses on the practical problems that arise when combining survey items that differ from one another in the wording of question stems, numbers of response option categories, scale direction (i.e., unipolar and bipolar scales), response scale labeling (i.e., fullylabeled scales and endpointslabeled scales), and responseoption labeling (e.g., "extremely happy"  "completely happy"  "most happy", "pretty happy", "quite happy" "moderately happy", and "not at all happy"  "least happy"  "most unhappy"). In addition, I propose practical solutions to handle the issues that arise due to such variations when conducting a metaanalysis. I discuss the implications of the proposed solutions from the perspective of metaanalysis. Examples are obtained from the collection of studies in the World Happiness Database (Veenhoven, 2006), which includes various singleitem happiness measures.
Show less  Date Issued
 2018
 Identifier
 2018_Fall_Gozutok_fsu_0071E_14866
 Format
 Thesis
 Title
 Four Methods for Combining Dependent Effects from Studies Reporting Regression Analysis.
 Creator

Gunter, Tracey Danielle, Becker, Betsy Jane, Huffer, Fred W. (Fred William), Almond, Russell G., Paek, Insu, Florida State University, College of Education, Department of...
Show moreGunter, Tracey Danielle, Becker, Betsy Jane, Huffer, Fred W. (Fred William), Almond, Russell G., Paek, Insu, Florida State University, College of Education, Department of Educational Psychology and Learning Systems
Show less  Abstract/Description

Over the years a variety of indices have been proposed to summarize regression analyses. Unfortunately the proposed indices are only appropriate when metaanalysts want to understand the role of a single predictor variable in predicting the outcome variable. However, sometimes metaanalysts want to understand the effect of a set of variables on an outcome variable. In this paper, four methods are presented for obtaining a composite effect for two focal predictor variables from a single...
Show moreOver the years a variety of indices have been proposed to summarize regression analyses. Unfortunately the proposed indices are only appropriate when metaanalysts want to understand the role of a single predictor variable in predicting the outcome variable. However, sometimes metaanalysts want to understand the effect of a set of variables on an outcome variable. In this paper, four methods are presented for obtaining a composite effect for two focal predictor variables from a single regression model. The indices are the average of the standardized regression coefficients (ASC), the average of the standardized regression coefficients using Hedges and Olkin's (1985) approach (AHO), the sheaf coefficient (SC), and the squared multiple semipartial correlation coefficient (MSP). A simulation study was conducted to examine the behavior of the indices and their variance when the number of predictor variables in the model, the sample size, the correlations between the focal predictor variables in the model, and the correlations between the focal and nonfocal predictor variables in the model were manipulated. The results of the study show that the average bias values of the ASC and AHO estimates are small even when the sample size is small. Furthermore, the ASC and AHO estimates and their estimated variances are more precise than the other indices under all conditions examined. Therefore, when metaanalysts are interested in estimating the effect of a set of predictor variables on an outcome variable from a single regression model, the ASC or AHO procedures are preferred.
Show less  Date Issued
 2015
 Identifier
 FSU_2015fall_Gunter_fsu_0071E_12829
 Format
 Thesis
 Title
 The Impact of Rater Variability on Relationships among Different EffectSize Indices for InterRater Agreement between Human and Automated Essay Scoring.
 Creator

Yun, Jiyeo, Becker, Betsy Jane, Huffer, Fred W. (Fred William), Paek, Insu, Zhang, Qian, Florida State University, College of Education, Department of Educational Psychology and...
Show moreYun, Jiyeo, Becker, Betsy Jane, Huffer, Fred W. (Fred William), Paek, Insu, Zhang, Qian, Florida State University, College of Education, Department of Educational Psychology and Learning Systems
Show less  Abstract/Description

Since researchers investigated automatic scoring systems in writing assessments, they have dealt with relationships between human and machine scoring, and then have suggested evaluation criteria for interrater agreement. The main purpose of my study is to investigate the magnitudes of and relationships among indices for interrater agreement used to assess the relatedness of human and automated essay scoring, and to examine impacts of rater variability on interrater agreement. To implement...
Show moreSince researchers investigated automatic scoring systems in writing assessments, they have dealt with relationships between human and machine scoring, and then have suggested evaluation criteria for interrater agreement. The main purpose of my study is to investigate the magnitudes of and relationships among indices for interrater agreement used to assess the relatedness of human and automated essay scoring, and to examine impacts of rater variability on interrater agreement. To implement the investigations, my study consists of two parts: empirical and simulation studies. Based on the results from the empirical study, the overall effects for interrater agreement were .63 and .99 for exact and adjacent proportions of agreement, .48 for kappas, and between .75 and .78 for correlations. Additionally, significant differences between 6point scales and the other scales (i.e., 3, 4, and 5point scales) for correlations, kappas and proportions of agreement existed. Moreover, based on the results of the simulated data, the highest agreements and lowest discrepancies achieved in the matched rater distribution pairs. Specifically, the means of exact and adjacent proportions of agreement, kappa and weighted kappa values, and correlations were .58, .95, .42, .78, and .78, respectively. Meanwhile the average standardized mean difference was .0005 in the matched rater distribution pairs. Acceptable values for interrater agreement as evaluation criteria for automated essay scoring, impacts of rater variability on interrater agreement, and relationships among interrater agreement indices were discussed.
Show less  Date Issued
 2017
 Identifier
 FSU_FALL2017_Yun_fsu_0071E_14144
 Format
 Thesis
 Title
 Investigating the ChiSquareBased ModelFit Indexes for WLSMV and ULSMV Estimators.
 Creator

Xia, Yan, Yang, Yanyun, Huffer, Fred W. (Fred William), Almond, Russell G., Becker, Betsy Jane, Paek, Insu, Florida State University, College of Education, Department of...
Show moreXia, Yan, Yang, Yanyun, Huffer, Fred W. (Fred William), Almond, Russell G., Becker, Betsy Jane, Paek, Insu, Florida State University, College of Education, Department of Educational Psychology and Learning Systems
Show less  Abstract/Description

In structural equation modeling (SEM), researchers use the model chisquare statistic and modelfit indexes to evaluate modeldata fit. Root mean square error of approximation (RMSEA), comparative fit index (CFI), and TuckerLewis index (TLI) are widely applied modelfit indexes. When data are ordered and categorical, the most popular estimator is the diagonally weighted least squares (DWLS) estimator. Robust corrections have been proposed to adjust the uncorrected chisquare statistic from...
Show moreIn structural equation modeling (SEM), researchers use the model chisquare statistic and modelfit indexes to evaluate modeldata fit. Root mean square error of approximation (RMSEA), comparative fit index (CFI), and TuckerLewis index (TLI) are widely applied modelfit indexes. When data are ordered and categorical, the most popular estimator is the diagonally weighted least squares (DWLS) estimator. Robust corrections have been proposed to adjust the uncorrected chisquare statistic from DWLS so that its first and second order moments are in alignment with the target central chisquare distribution under correctly specified models. DWLS with such a correction is called the mean and varianceadjusted weighted least squares (WLSMV) estimator. An alternative to WLSMV is the meanand varianceadjusted unweighted least squares (ULSMV) estimator, which has been shown to perform as well as, or slightly better than WLSMV. Because the chisquare statistic is corrected, the chisquarebased RMSEA, CFI, and TLI are thus also corrected by replacing the uncorrected chisquare statistic with the robust chisquare statistic. The robust model fit indexes calculated in such a way are named as the populationcorrected robust (PR) model fit indexes following BrosseauLiard, Savalei, and Li (2012). The PR model fit indexes are currently reported in almost every application when WLSMV or ULSMV is used. Nevertheless, previous studies have found the PR model fit indexes from WLSMV are sensitive to several factors such as sample sizes, model sizes, and thresholds for categorization. The first focus of this dissertation is on the dependency of model fit indexes on the thresholds for ordered categorical data. Because the weight matrix in the WLSMV fit function and the correction factors for both WLSMV and ULSMV include the asymptotic variances of thresholds and polychoric correlations, the model fit indexes are very likely to depend on the thresholds. The dependency of model fit indexes on the thresholds is not a desirable property, because when the misspecification lies in the factor structures (e.g., cross loadings are ignored or two factors are considered as a single factor), model fit indexes should reflect such misspecification rather than the threshold values. As alternatives to the PR model fit indexes, BrosseauLiard et al. (2012), BrosseauLiard and Savalei (2014), and Li and Bentler (2006) proposed the samplecorrected robust (SR) model fit indexes. The PR fit indexes are found to converge to distorted asymptotic values, but the SR fit indexes converge to their definitions asymptotically. However, the SR model fit indexes were proposed for continuous data, and have been neither investigated nor implemented in SEM software when WLSMV and ULSMV are applied. This dissertation thus investigates the PR and SR model fit indexes for WLSMV and ULSMV. The first part of the simulation study examines the dependency of the model fit indexes on the thresholds when the model misspecification results from omitting crossloadings or collapsing factors in confirmatory factor analysis. The study is conducted on extremely large computergenerated datasets in order to approximate the asymptotic values of model fit indexes. The results find that only the SR fit indexes from ULSMV are independent of the population threshold values, given the other design factors. The PR fit indexes from ULSMV, and the PR and SR fit indexes from WLSMV are influenced by thresholds, especially when data are binary and the hypothesized model is greatly misspecified. The second part of the simulation varies the sample sizes from 100 to 1000 to investigate whether the SR fit indexes under finite samples are more accurate estimates of the defined values of RMSEA, CFI, and TLI, compared with the uncorrected model fit indexes without robust correction and the PR fit indexes. Results show that the SR fit indexes are the more accurate in general. However, when the thresholds are different across items, data are binary, and sample size is less than 500, all versions of these indexes can be very inaccurate. In such situations, larger sample sizes are needed. In addition, the conventional cutoffs developed from continuous data with maximum likelihood (e.g., RMSEA < .06, CFI > .95, and TLI > .95; Hu & Bentler, 1999) have been applied to WLSMV and ULSMV regardless of the arguments against such a practice (e.g., Marsh, Hau, & Wen, 2004). For comparison purposes, this dissertation reports the RMSEA, CFI, and TLI based on continuous data using maximum likelihood before the variables are categorized to create ordered categorical data. Results show that the model fit indexes from maximum likelihood are very different from those from WLSMV and ULSMV, suggesting that the conventional rules should not be applied to WLSMV and ULSMV.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SU_Xia_fsu_0071E_13379
 Format
 Thesis
 Title
 MetaAnalysis of Factor Analyses: Comparison of Univariate and Multivariate Approaches Using Correlation Matrices and Factor Loadings.
 Creator

Cho, Kyunghwa, Becker, Betsy Jane, Huffer, Fred W. (Fred William), Paek, Insu, Yang, Yanyun, Florida State University, College of Education, Department of Educational Psychology...
Show moreCho, Kyunghwa, Becker, Betsy Jane, Huffer, Fred W. (Fred William), Paek, Insu, Yang, Yanyun, Florida State University, College of Education, Department of Educational Psychology and Learning Systems
Show less  Abstract/Description

Currently, more sophisticated techniques such as factor analyses are frequently applied in primary research thus may need to be metaanalyzed. This topic has been given little attention in the past due to its complexity. Because factor analysis is becoming more popular in research in many areas including education, social work, social science, and so on, the study of methods for the metaanalysis of factor analyses is also becoming more important. The first main purpose of this dissertation...
Show moreCurrently, more sophisticated techniques such as factor analyses are frequently applied in primary research thus may need to be metaanalyzed. This topic has been given little attention in the past due to its complexity. Because factor analysis is becoming more popular in research in many areas including education, social work, social science, and so on, the study of methods for the metaanalysis of factor analyses is also becoming more important. The first main purpose of this dissertation is to compare the results of seven different approaches to doing metaanalysis of confirmatory factor analyses. Specifically, five approaches are based on univariate metaanalysis methods. The next two approaches use multivariate metaanalysis to obtain the results of factor loadings and the standard errors of factor loadings. The results from each approach are compared. Given the fact that factor analyses are commonly used in many areas, the second purpose of this dissertation is to explore the appropriate approach or approaches to use for the metaanalysis of factor analyses, especially Confirmatory Factor Analysis (CFA). When the average sample size was small, the results of IRD, WMC, WMFL, and GLSMFL approaches showed better performance than those of UMC, MFL, and GLSMC approaches to estimating parameters. With large average sample sizes (larger than 150), the performance to estimate the parameters across all seven approaches seemed to be similar in this dissertation. Based on my simulation results, researchers who want to conduct metaanalytic confirmatory factor analysis can apply any of these approaches to synthesize the results from primary studies it their studies have n > 150.
Show less  Date Issued
 2015
 Identifier
 FSU_migr_etd9570
 Format
 Thesis
 Title
 A WeaklyInformative GroupSpecific Prior Distribution for MetaAnalysis.
 Creator

Thompson, Christopher, Becker, Betsy Jane, Clark, Kathleen M., Almond, Russell G., Aloe, Ariel M., Yang, Yanyun, Florida State University, College of Education, Department of...
Show moreThompson, Christopher, Becker, Betsy Jane, Clark, Kathleen M., Almond, Russell G., Aloe, Ariel M., Yang, Yanyun, Florida State University, College of Education, Department of Educational Psychology and Learning Systems
Show less  Abstract/Description

While Bayesian metaanalysis has flourished both in methodological and substantive work, groupspecific Bayesian modeling remains scarce. Common practice for choosing prior distributions entails using typical noninformative priors. Currently, there is a push to use more informative prior distributions. In this dissertation I propose a group specific weakly informative prior distribution. The new prior distribution uses a frequentist estimate of betweenstudies heterogeneity as the...
Show moreWhile Bayesian metaanalysis has flourished both in methodological and substantive work, groupspecific Bayesian modeling remains scarce. Common practice for choosing prior distributions entails using typical noninformative priors. Currently, there is a push to use more informative prior distributions. In this dissertation I propose a group specific weakly informative prior distribution. The new prior distribution uses a frequentist estimate of betweenstudies heterogeneity as the noncentrality parameter in a folded noncentral t distribution. This new distribution is then modeled individually for groups based on some categorical factor. An extensive simulation study was performed to assess the performance of the new groupspecific prior distribution to several noninformative prior distributions in a variety of metaanalytic scenarios. An application using data from a previously published metaanalysis on dynamic geometry software is also provided.
Show less  Date Issued
 2016
 Identifier
 FSU_2016SP_Thompson_fsu_0071E_13051
 Format
 Thesis