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Introductory Remarks Introductory Remarks
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Range of Applications Range of Applications
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Scope of Chapter Scope of Chapter
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Chapter Organization Chapter Organization
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Terminological Foundations, Suggested Readings, and Chapter Notation Terminological Foundations, Suggested Readings, and Chapter Notation
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Terminological Foundations Terminological Foundations
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Observations Versus Variables Observations Versus Variables
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Variable Types Versus Measurement Scales Variable Types Versus Measurement Scales
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Non-Parametric Versus Parametric/Model-Based Techniques Non-Parametric Versus Parametric/Model-Based Techniques
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Exploratory Versus Confirmatory Techniques Exploratory Versus Confirmatory Techniques
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Suggested Readings Suggested Readings
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Introductory Books for Multivariate Statistics Introductory Books for Multivariate Statistics
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Specialized Books for Particular Techniques Specialized Books for Particular Techniques
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Peer-Reviewed Publications and Professional Associations Peer-Reviewed Publications and Professional Associations
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Chapter Notation Chapter Notation
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Nonparametric Techniques Nonparametric Techniques
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Hierarchical Techniques Hierarchical Techniques
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Basic Concepts Basic Concepts
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Agglomerative Versus Divisive Approaches Agglomerative Versus Divisive Approaches
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Stopping Rules and Numerical Representation of Cluster Membership Stopping Rules and Numerical Representation of Cluster Membership
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Graphical Representation of Cluster Structure and Membership Graphical Representation of Cluster Structure and Membership
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Key Pre-Processing Choices for Hierarchical Techniques Key Pre-Processing Choices for Hierarchical Techniques
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Standardization Approaches for Variables Standardization Approaches for Variables
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Selection Procedures for Variables Selection Procedures for Variables
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Distance Measures for the Multivariate Space Distance Measures for the Multivariate Space
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Measures of Intercluster Distance Measures of Intercluster Distance
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Partitioning Clustering Methods Partitioning Clustering Methods
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K-Means Clustering K-Means Clustering
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Mechanics of K-Means Clustering Mechanics of K-Means Clustering
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Initial Selection of Cluster Centers for K-Means Initial Selection of Cluster Centers for K-Means
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Selected Technical Advances for K-Means Clustering Selected Technical Advances for K-Means Clustering
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Alternatives to K-Means Clustering Alternatives to K-Means Clustering
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Software Packages for Nonparametric Techniques Software Packages for Nonparametric Techniques
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Additional Example Additional Example
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Finite Mixture and Latent Class Models Finite Mixture and Latent Class Models
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Finite Mixture Models for Single Quantitative Response Variables Finite Mixture Models for Single Quantitative Response Variables
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Finite Mixture Models for Multiple Quantitative Response Variables Finite Mixture Models for Multiple Quantitative Response Variables
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Unconstrained Latent Class Models Unconstrained Latent Class Models
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Instrument Calibration Versus Respondent Scaling Instrument Calibration Versus Respondent Scaling
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Class-Specific Item Response Probabilities Class-Specific Item Response Probabilities
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Local/Conditional Independence Assumption Local/Conditional Independence Assumption
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Statistical Structure of Unrestricted Latent Class Model Statistical Structure of Unrestricted Latent Class Model
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Constrained Latent Class Models/Diagnostic Classification Models Constrained Latent Class Models/Diagnostic Classification Models
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Latent Classes as Attribute Profiles Latent Classes as Attribute Profiles
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Definition of Diagnostic Classification Models Definition of Diagnostic Classification Models
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Parameter Constraints via the Q-Matrix Parameter Constraints via the Q-Matrix
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Statistical Structure of Diagnostic Classification Models Statistical Structure of Diagnostic Classification Models
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Nonparametric Alternatives to Diagnostic Classification Models Nonparametric Alternatives to Diagnostic Classification Models
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Designs for Investigating The Relative Performance of Different Techniques Designs for Investigating The Relative Performance of Different Techniques
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Software Packages for Finite Mixture and Latent Class Models Software Packages for Finite Mixture and Latent Class Models
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Assessing Model-Data Fit at Different Levels Assessing Model-Data Fit at Different Levels
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Relative Fit Assessment Relative Fit Assessment
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Absolute Fit Assessment Absolute Fit Assessment
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Item-Fit Assessment Item-Fit Assessment
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Person-Fit Assessment Person-Fit Assessment
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Concluding Remarks Concluding Remarks
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Author Note Author Note
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References References
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24 Clustering and Classification
Get accessAndré A. Rupp, Department of Measurement, Statistics, and Evaluation (EDMS), University of Maryland, College Park, MD
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Published:01 October 2013
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Abstract
In this chapter I first describe core terminology, notation, and related readings for certain core clustering and classification techniques. I then discuss the theoretical underpinnings and practical applications of nonparametric techniques that do not require distributional assumptions on outcome variables followed by parametric/model-based techniques that do require such assumptions. In the former set, I specifically discuss hierarchical clustering techniques and K-means clustering techniques. In the latter set I specifically discuss univariate and multivariate finite mixture models, unrestricted latent class models, and restricted latent class models. I further show how so-called diagnostic classification models are a particularly useful class of restricted latent class models for calibration and scaling purposes in educational and psychological measurement.
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