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Towards a Network Psychometrics Approach to Assessment Towards A Network Psychometrics Approach to Assessment: Simulations for Redundancy, Dimensionality, and Loadings Alexander P. Christensen University of North Carolina at Greensboro Doctoral Dissertation 2020 All three simulation studies in this dissertation have been updated and revised for publication purposes. Below is a list of the most recent versions of these manuscripts: Redundancy Christensen, A. P., Garrido, L. E., & Golino, H. (2020). Unique Variable Analysis: A novel approach for detecting redundant variables in multivariate data. PsyArXiv. https://doi.org/10.31234/osf.io/4kra2 Dimensionality Christensen, A. P., & Golino, H. (2020). Estimating factors with psychometric networks: A Monte Carlo simulation comparing community detection algorithms. PsyArXiv. https://doi.org/10.31234/osf.io/hz89e Loadings Christensen, A. P., & Golino, H. (2020). On the equivalency of factor and network loadings. Behavior Research Methods. https://doi.org/10.3758/s13428-020-01500-6 CHRISTENSEN, ALEXANDER P., Ph.D. Towards a Network Psychometrics Approach to Assessment: Simulations for Redundancy, Dimensionality, and Loadings. (2020) Directed by Dr. Paul J. Silvia. 104 pp. Research using network models in psychology has proliferated over the last decade. The popularity of network models has largely been driven by their alternative explanation for the emergence of psychological attributes—observed variables co-occur because they are causally coupled and dynamically reinforce each other, forming cohesive systems. Despite their rise in popularity, the growth of network models as a psychometric tool has remained relatively stagnant, mainly being used as a novel measurement perspective. In this dissertation, the goal is to expand the role of network models in modern psychometrics and to move towards using these models as a tool for the validation of assessment instruments. This paper presents three simulation studies and an empirical example that are designed to evaluate different aspects of the psychometric network approach to assessment: reducing redundancy, detecting dimensions, and estimating loadings. The first simulation evaluated two novel approaches for determining whether items are redundant, which is a key component for the accuracy and interpretation of network measures. The second simulation evaluated several different community detection algorithms, which are designed to detect dimensions in networks. The third simulation evaluated an adapted formulation of the network measure, node strength, and how it compares to factor loadings estimated by exploratory and confirmatory factor analysis. The results of the simulations demonstrate that network models can be used as an effective psychometric tool and one that is on par with more traditional methods. Finally, in the empirical example, the methods from the simulations are applied to a real-world dataset measuring personality. This example demonstrated that these methods are not only effective, but they can validate whether an assessment instrument is consistent with theoretical and empirical expectations. With these methods in hand, network models are poised to take the next step towards becoming a robust psychometric tool. TOWARDS A NETWORK PSYCHOMETRICS APPROACH TO ASSESSMENT: SIMULATIONS FOR REDUNDANCY, DIMENSIONALITY, AND LOADINGS by Alexander P. Christensen A Dissertation Submitted to the Faculty of The Graduate School at The University of North Carolina at Greensboro in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Greensboro 2020 Approved by Paul J. Silvia _____________________________ Committee Chair To Gilbert, my furry collaborator. ii APPROVAL PAGE This dissertation written by ALEXANDER P. CHRISTENSEN has been approved by the following committee of the Faculty of The Graduate School at the University of North Carolina at Greensboro. Committee Chair___________________________Paul J. Silvia Committee Members___________________________Brittany S. Cassidy ___________________________Peter F. Delaney ___________________________John T. Willse ____________________________03/13/2020 Date of Acceptance by Committee __________________________03/13/2020 Date of Final Oral Examination iii ACKNOWLEDGEMENTS First and foremost, I would like to thank my committee for their insightful comments and instructive feedback. Second, I would like to thank the many collaborators, specifically, Roger Beaty, Yoed Kenett, and Hudson Golino, that have influenced the development of my research program. Third, I would like to especially thank Hudson Golino for graciously allowing me to use his workstation to complete the series of simulations performed in this dissertation. Last but least, I would like to thank Paul Silvia whose mentorship was beyond exception and expectation. iv TABLE OF CONTENTS Page LIST OF TABLES ............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii CHAPTER I. INTRODUCTION .................................................................................................1 Aims of the Present Research ......................................................................3 II. REDUNDANCY ...................................................................................................5 Detecting Redundancy in Networks ............................................................6 Present Research ..........................................................................................8 Method .........................................................................................................8 Data Generation ...............................................................................8 Psychometric Network Model .......................................................10 Redundant Node Approaches ........................................................11 Design ............................................................................................14 Simulating Redundancy .................................................................15 Statistical Analyses ........................................................................16 Results ........................................................................................................17 False Discovery Rate .....................................................................17 False Negative Rate .......................................................................18 Critical Success Index ....................................................................19 Discussion ..................................................................................................20 III. DIMENSIONALITY ...........................................................................................23 Recent Simulation Studies .........................................................................24 Present Research ........................................................................................27 Method .......................................................................................................28 Data Generation .............................................................................28 Psychometric Network Models ......................................................28 Modularity......................................................................................31 Community Detection Algorithms .................................................31 Unidimensionality Adjustment ......................................................35 Parallel Analysis ............................................................................36 Design ............................................................................................37 v Statistical Analyses ........................................................................37 Results ........................................................................................................39 Accuracy and Bias .........................................................................39 Item Placement...............................................................................42 Best Algorithms .............................................................................44 Discussion ..................................................................................................45 IV. LOADINGS ........................................................................................................48 Review of Hallquist, Wright, and Molenaar (2019) ..................................50 Present Research ........................................................................................52 Method .......................................................................................................53 Data Generation .............................................................................53 Psychometric Network Model .......................................................53 Network Loadings ..........................................................................54 EFA Loadings ................................................................................55 CFA Loadings ................................................................................55 Design ............................................................................................56 Statistical Analyses ........................................................................56
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