An Introduction to Latent Class Analysis: Methods and Applications

Description

This book provides methods and applications of latent class analysis, and the following topics are taken up in the focus of discussion: basic latent structure models in a framework of generalized linear models, exploratory latent class analysis, latent class analysis with ordered latent classes, a latent class model approach for analyzing learning structures, the latent Markov analysis for longitudinal data, and path analysis with latent class models. The maximum likelihood estimation procedures for latent class models are constructed via the expectation–maximization (EM) algorithm, and along with it, latent profile and latent trait models are also treated. Entropy-based discussions for latent class models are given as advanced approaches, for example, comparison of latent classes in a latent class cluster model, assessing latent class models, path analysis, and so on. In observing human behaviors and responses to various stimuli and test items, it is valid to assume they are dominated by certain factors. This book plays a significant role in introducing latent structure analysis to not only young researchers and students studying behavioral sciences, but also to those investigating other fields of scientific research.  Preface References Acknowledgements Contents 1 Overview of Basic Latent Structure Models 1.1 Introduction 1.2 Latent Class Model 1.3 Latent Trait Model 1.4 Latent Profile Model 1.5 Factor Analysis Model 1.6 Latent Structure Models in a Generalized Linear Model Framework 1.7 The EM Algorithm and Latent Structure Models 1.8 Discussion References 2 Latent Class Cluster Analysis 2.1 Introduction 2.2 The ML Estimation of Parameters in the Latent Class Model 2.3 Examples 2.4 Measuring Goodness-of-Fit of Latent Class Models 2.5 Comparison of Latent Classes 2.6 Latent Profile Analysis 2.7 Discussion References 3 Latent Class Analysis with Ordered Latent Classes 3.1 Introduction 3.2 Latent Distance Analysis 3.3 Assessment of the Latent Guttman Scaling 3.4 Analysis of the Association Between Two Latent Traits with Latent Guttman Scaling 3.5 Latent Ordered-Class Analysis 3.6 The Latent Trait Model (Item Response Model) 3.7 Discussion References 4 Latent Class Analysis with Latent Binary Variables: An Application for Analyzing Learning Structures 4.1 Introduction 4.2 Latent Class Model for Scaling Skill Acquisition Patterns 4.3 ML Estimation Procedure for Model (4.3) with (4.4) 4.4 Numerical Examples (Exploratory Analysis) 4.5 Dynamic Interpretation of Learning (Skill Acquisition) Structures 4.6 Estimation of Mixed Proportions of Learning Processes 4.7 Solution of the Separating Equations 4.8 Path Analysis in Learning Structures 4.9 Numerical Illustration (Confirmatory Analysis) 4.10 A Method for Ordering Skill Acquisition Patterns 4.11 Discussion References 5 The Latent Markov Chain Model 5.1 Introduction 5.2 The Latent Markov Chain Model 5.3 The ML Estimation of the Latent Markov Chain Model 5.4 A Property of the ML Estimation Procedure via the EM Algorithm 5.5 Numerical Example I 5.6 Numerical Example II 5.7 A Latent Markov Chain Model with Missing Manifest Observations 5.8 A General Version of the Latent Markov Chain Model with Missing Manifest Observations 5.9 The Latent Markov Process Model 5.10 Discussion References 6 The Mixed Latent Markov Chain Model 6.1 Introduction 6.2 Dynamic Latent Class Models 6.3 The ML Estimation of the Parameters of Dynamic Latent Class Models 6.4 A Numerical Illustration 6.5 Discussion References 7 Path Analysis in Latent Class Models 7.1 Introduction 7.2 A Multiple-Indicator, Multiple-Cause Model 7.3 An Entropy-Based Path Analysis of Categorical Variables 7.4 Path Analysis in Multiple-Indicator, Multiple-Cause Models 7.4.1 The Multiple-Indicator, Multiple-Cause Model in Fig. 7.2a 7.4.2 The Multiple-Indicator, Multiple-Cause Model in Fig. 7.2b 7.5 Numerical Illustration I 7.5.1 Model I (Fig. 7.2a) 7.5.2 Model II (Fig. 7.2b) 7.6 Path Analysis of the Latent Markov Chain Model 7.7 Numerical Illustration II 7.8 Discussion References