Higher-Order Growth Curves and Mixture Modeling with Mplus

Höfundar: Kandauda Wickrama; Tae Kyoung Lee; Catherine Walker O’Neal; Frederick Lorenz (Útgáfa: 2)
Higher-Order Growth Curves and Mixture Modeling with Mplus

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This practical introduction to second-order and growth mixture models using Mplus introduces simple and complex techniques through incremental steps. The authors extend latent growth curves to second-order growth curve and mixture models and then combine the two using normal and non-normal (e. g. , categorical) data. To maximize understanding, each model is presented with basic structural equations, figures with associated syntax that highlight what the statistics mean, Mplus applications, and an interpretation of results.

Examples from a variety of disciplines demonstrate the use of the models and exercises allow readers to test their understanding of the techniques. A comprehensive introduction to confirmatory factor analysis, latent growth curve modeling, and growth mixture modeling is provided so the book can be used by readers of various skill levels. The book’s datasets are available on the web. New to this edition: * Two new chapters providing a stepwise introduction and practical guide to the application of second-order growth curves and mixture models with categorical outcomes using the Mplus program.

Complete with exercises, answer keys, and downloadable data files. * Updated illustrative examples using Mplus 8. 0 include conceptual figures, Mplus program syntax, and an interpretation of results to show readers how to carry out the analyses with actual data. This text is ideal for use in graduate courses or workshops on advanced structural equation, multilevel, longitudinal or latent variable modeling, latent growth curve and mixture modeling, factor analysis, multivariate statistics, or advanced quantitative techniques (methods) across the social and behavioral sciences.

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Útgefandi
Taylor & Francis
ISBN
9781000465846
Print ISBN
9780367746209
Format
ePub
Útgáfa
2
Höfundar
Kandauda Wickrama; Tae Kyoung Lee; Catherine Walker O’Neal; Frederick Lorenz
Tungumál
English
Útgefið
2021-11-23
Prent takmörkun á líftíma
100
Prent takmörkun
2
Afritunar takmörkun
2

Kaflar

  • Cover
  • Endorsements
  • Half-Title
  • Series
  • Title
  • Copyright
  • Contents
  • Preface
  • Acknowledgments
  • Authors
  • PART I Growth Curve Modeling
  • 1 Introduction
  • A Layout of Incrementally Related SEMs: An Organizing Guide
  • Illustrative Example 1.1: Examining Alternative Growth Curve Models
  • Adolescents’ Internalizing Symptoms (IS) Trajectories
  • Datasets Used in Illustrations
  • Measures
  • References
  • 2 Latent Growth Curves
  • Introduction
  • Growth Curve Modeling
  • Conventional Latent Growth Curve Models (LGCM)
  • Linear Growth Curve Modeling
  • Investigating Longitudinal Covariance Patterns
  • Illustrative Example 2.1: Examining the Longitudinal Covariance Pattern of Indicators
  • Estimating an Unconditional Linear Latent Growth Curve Model (LGCM) Using Mplus
  • Illustrative Example 2.2: Estimating a Linear Latent Growth Curve Model (LGCM
  • Curvilinear Growth Curve Modeling (i.e., a Quadratic Growth Curve Model)
  • Illustrative Example 2.3: Estimating a Quadratic Latent Growth Curve Model (LGCM)
  • Model Fit Indices
  • Comparing Nested Models
  • Illustrative Example 2.4: Nested Model Comparison between Linear and Quadratic Models
  • Illustrative Example 2.5: Nested Model Comparison between Models with and without Correlated Errors
  • Illustrative Example 2.6: Non-Nested Model Comparison between Linear and Piecewise Models
  • Adding Covariates to an Unconditional Model
  • Illustrative Example 2.7: Adding a Predictor and Outcome to a Linear LGCM
  • Illustrative Example 2.8: Adding a Predictor and Outcome to a Quadratic LGCM
  • Methodological Concerns in Longitudinal Analysis: Why Growth Curves?
  • The Need to Preserve the Continuity of Change
  • The Need to Investigate Different Growth Parameters
  • The Need to Incorporate Growth Parameters as Either Predictors or Outcomes in the Same Model
  • The Need to Incorporate Time-Varying Predictors
  • Limitations
  • Beyond Latent Growth Curve Modeling
  • Revisiting the Layout of Models: Figures 1.1, 1.2, and 1.3
  • First-Order Structural Equation Models
  • Second-Order Growth Curve Modeling
  • Growth Mixture Modeling
  • Chapter 2 Exercises
  • References
  • 3 Longitudinal Confirmatory Factor Analysis and Curve-of-Factors Growth Curve Models
  • Introduction
  • Confirmatory Factor Analysis (CFA) (Step 1)
  • Specification of a Simple CFA
  • CFA Model Identification
  • Scale Setting in a CFA
  • Longitudinal Confirmatory Factor Analysis (LCFA): Model Specification (Step 2)
  • A Second-Order Growth Curve: A Curve-of-Factors Model (Step 3)
  • Specification of a Curve-of-Factors Model (CFM)
  • Why Analyze a Curve-of-Factors Model? Improvements Over a Conventional LGCM
  • Equal Contribution of Items to the Composite Measure
  • Longitudinal Measurement Invariance (Factorial Invariance)
  • Variance Components of Indicators: Measurement Error and Time-Specific Variance
  • Chapter 3 Exercises
  • References
  • 4 Estimating Curve-of-Factors Growth Curve Models
  • Introduction
  • Steps for Estimating a Curve-of-Factors Model (CFM)
  • Investigating the Longitudinal Correlation Patterns of Subdomain Indicators (Step 1)
  • Illustrative Example 4.1: Examining the Longitudinal Correlation Patterns among Indicators
  • Performing an Unconstrained Longitudinal Confirmatory Factor Analysis (LCFA) (Step 2)
  • Illustrative Example 4.2: Longitudinal Confirmatory Factor Analysis (LCFA) Using Mplus
  • Measurement Invariance of the LCFA Model (Step 3)
  • Illustrative Example 4.3: Systematic Incremental Testing Sequences for Assessing Measurement Invariance
  • Nested Model Comparison for Measurement Invariance
  • Taking Autocorrelations among Indicators in a LCFA into Account as a Trait Factor
  • Illustrative Example 4.4: Longitudinal Confirmatory Factor Analysis (LCFA) with “Trait” Factors (IT Model)
  • Estimating a Second-Order Growth Curve: A Curve-of-Factors Model (CFM) (Step 4)
  • Illustrative Example 4.5: Estimating a Curve-of-Factors Model (CFM)
  • Scale Setting Approaches and Second-Order Growth Model Parameters (Curve-of-Factors Model, CFM)
  • Marker Variable Approach
  • Illustrative Example 4.6: Using the Marker Variable Approach for CFA Scale Setting
  • Fixed Factor Approach
  • Illustrative Example 4.7: Using the Fixed Factor Scale Setting Approach in a CFA
  • Effect Coding Approach
  • Illustrative Example 4.8: Using the Effect Coding Scale Setting Approach in a CFA
  • Adding Covariates to a Curve-of-Factors Model (CFM)
  • Time-Invariant Covariate (TIC) Model
  • Incorporating a single indicator variable (W) as a predictor
  • Illustrative Example 4.9: Adding a Time-Invariant Covariate (TIC) as a CFM Predictor
  • Incorporating a Multiple-Indicator Latent Variable (P) as a Predictor
  • Illustrative Example 4.10: Adding a Multiple-Indicator Latent Factor as a CFM Predictor
  • Predicting Both Time-Specific Latent Factors and Second-Order Growth Parameters
  • Illustrative Example 4.11: Predicting Both Second-Order Growth Parameters and First-Order Latent Factors
  • Predicting Distal Outcomes (D) of Second-Order Growth Factors
  • Illustrative Example 4.12: Predicting Distal Outcomes of Second-Order Growth Factors
  • Time-Varying Covariate (TVC) Model
  • Time-Varying Covariate (TVC) as a Predictor of Manifest Outcomes
  • Illustrative Example 4.13: Incorporating a Time-Varying Covariate as a Direct Predictor of Manifest Indicators
  • A Parallel Process Second-Order Model Using a Dyadic Model Framework as an Example
  • Illustrative Example 4.14: Incorporating a Time-Varying Covariate as a Parallel Process
  • Chapter 4 Exercises
  • References
  • 5 Extending a Parallel Process Latent Growth Curve Model (PPM) to a Factor-of-Curves Model (FCM)
  • Introduction
  • Parallel Process Latent Growth Curve Model (PPM)
  • Estimating a Parallel Process Model (PPM)
  • Correlation of Measurement Errors in a PPM
  • Influence of Growth Factors of One Subdomain on the Growth Factors of Other Subdomains
  • Modeling Sequentially Contingent Processes over Time
  • Extending a Parallel Process Latent Growth Curve Model (PPM) to a Factor-of-Curves Growth Curve Model (FCM)
  • Second-Order Growth Factors
  • Chapter 5 Exercises
  • References
  • 6 Estimating a Factor-of-Curves Model (FCM) and Adding Covariates
  • Introduction
  • Estimating a Factor-of-Curves Model (FCM)
  • Investigating the Longitudinal Correlation Patterns among Repeated Measures of Each Subdomain (Step 1)
  • Illustrative Example 6.1: Investigating the Longitudinal Correlation Patterns among Repeated Measures of Each Subdomain
  • Estimating a Parallel Process Growth Curve Model (PPM) (Step 2)
  • Illustrative Example 6.2: Estimating a Parallel Process Growth Curve Model (PPM)
  • Estimating a Factor-of-Curves Model (FCM) (Step 3)
  • Illustrative Example 6.3: Estimating a Factor-of-Curves Model (FCM)
  • Illustrative Example 6.4: Comparing Two Competing Models Empirically
  • Estimating a Conditional FCM (Step 4)
  • Adding Time-Invariant Covariates (TICs) to a FCM
  • Predicting Both First-Order and Second-Order Growth Factors
  • Illustrative Example 6.5: Adding Time-Invariant Covariates (TIC) to a FCM
  • Primary and Secondary Growth Factors of the FCM as Predictors of Latent Distal Outcomes (D)
  • Illustrative Example 6.6: Incorporating a Latent Distal Outcome into a FCM
  • Adding Time-Varying Covariates (TVC) to a FCM
  • A Time-Varying Covariate (TVC) as a Direct Predictor of Indicators
  • Illustrative Example 6.7: Incorporating a Time-Varying Covariate (TVC) as a Direct Predictor
  • Incorporating a TVC as a Secondary Growth Curve: A Second-Order Parallel Process Dyadic Model
  • Illustrative Example 6.8: Incorporating a Time-Varying Predictor as a Parallel Process
  • A Multiple-Group FCM (Multi-Group Longitudinal Modeling)
  • Illustrative Example 6.9: Estimating a FCM for Multiple Groups
  • Multivariate FCM
  • Illustrative Example 6.10: Estimating a Multivariate FCM
  • Model Selection: Factor-of-Curves vs. Curve-of-Factors
  • Illustrative Example 6.11: Empirically Comparing CFM and FCM Approaches
  • Combining a CFM and a FCM: A Factor-of-Curves-of-Factors (FCF) Model
  • Illustrative Example 6.12: Estimating a Factor-of-Curves-of-Factors (FCF) Model
  • Chapter 6 Exercises
  • References
  • PART II Growth Mixture Modeling
  • 7 An Introduction to Growth Mixture Models (GMMs)
  • Introduction
  • A Conventional Latent Growth Curve Model (LGCM)
  • Potential Heterogeneity in Individual Trajectories
  • Growth Mixture Modeling (GMM)
  • Latent Class Growth Analysis (LCGA): A Simplified GMM
  • Specifying a Growth Mixture Model (GMM)
  • Specifying Trajectory Classes: Class-Specific Equations
  • Specifying a Latent Class Growth Analysis (LCGA)
  • Building A Growth Mixture Model (GMM) Using MSpecify a Traditional Growth Curve Model (LGCM) (Step 1)
  • Estimating a Latent Class Growth Analysis (LCGA) (Step Two)
  • Illustrative Example 7.1: Mplus Syntax for a Latent Class Growth Analysis (LCGA)
  • Specifying a Growth Mixture Model (GMM) (Step 3)
  • Illustrative Example 7.2: Mplus Syntax for a Growth Mixture Model (GMM)
  • Addressing Estimation Problems (Step Four)
  • Estimation Problems Related to a Non-Normal Probability Distribution
  • Illustrative Example 7.3: A Non-Normal Distribution
  • Estimation Problems Related to Local Maxima
  • Estimation Problems Due to Model Non-Identification and Inappropriate Data
  • Selecting the Optimal Class Model (Enumeration Indices) (Step 5)
  • Information Criteria (IC) Statistics
  • Entropy and Average Posterior Probabilities
  • Likelihood Ratio Test (LRT): LMR-LRT and Bootstrapped LRT (BLRT)
  • Other Considerations
  • Illustrative Example 7.4: Identifying the Optimal Model
  • Summary of a Model-Building Strategy
  • Chapter 7 Exercises
  • References
  • 8 Estimating a Conditional Growth Mixture Model (GMM)
  • Introduction
  • Growth Mixture Models: Predictors and Distal Outcomes
  • The One-Step Approach to Incorporating Covariates into a GMM
  • Predictors of Latent Classes (Multinomial Regression)
  • Illustrative Example 8.1: Incorporating a Time-Invariant Predictor into a GMM
  • Predictors of Latent Growth Factors Within Classes
  • Illustrative Example 8.2: Adding Within-Class Effects of Predictors to a GMM
  • Adding Distal Outcomes of Latent Classes (Categorical and Continuous)
  • Illustrative Example 8.3: Incorporating a Binary Distal Outcome into a GMM
  • Illustrative Example 8.4: Incorporating a Continuous Distal Outcome into a GMM
  • Uncertainty of Latent Class Membership with the Addition of Covariates
  • The Three-Step Approach: The “Manual” Method
  • Illustrative Example 8.5: The Three-Step Procedure for Incorporating Predictor(s)
  • Illustrative Example 8.6: The Three-Step Procedure for Incorporating Distal Outcome(s)
  • AUXILIARY Option for the Three-Step Approach
  • Illustrative Example 8.7: Utilizing the Auxiliary Option with the Three-Step Approach
  • Illustrative Example 8.8: Utilizing the Auxiliary Option
  • Chapter 8 Exercises
  • References
  • 9 Second-Order Growth Mixture Models (SOGMMs)
  • Introduction
  • Estimating a Second-Order Growth Mixture Model: A Curve-of-Factors Model (SOGMM of a CFM)
  • Illustrative Example 9.1: A Second-Order Growth Mixture Model of a CFM (SOGMM-CF)
  • Illustrative Example 9.2: Avoiding Convergence Problems
  • Estimating a Second-Order Growth Mixture Model: A Factor-of-Curves Model (SOGMM of a FCM)
  • Illustrative Example 9.3: A Second-Order Growth Mixture Model of a FCM (SOGMM-FC)
  • Comparison of Classification between a First-Order GMM with Composite Measures and Second-Order GMMs
  • Estimating a Conditional Model (Conditional SOGMM)
  • The Three-Step Approach (Using the AUXILIARY Option) to Add Predictors of Second-Order Trajectory Classes
  • Illustrative Example 9.4: Estimating a Conditional SOGMM with Predictors
  • The Three-Step Approach (Using the AUXILIARY Option) to Add Outcomes of Second-Order Trajectory Classes
  • Illustrative Example 9.5: Estimating a Conditional SOGMM with Outcomes
  • Estimating a Multidimensional Growth Mixture Model (MGMM)
  • Illustrative Example 9.6: Estimating a Multidimensional Growth Mixture Model
  • Conclusion
  • Chapter 9 Exercises
  • References
  • PART III Latent Growth Curves with Non-Normal Variables
  • Introduction
  • 10 Latent Growth Curve Model with Non-Normal Variables
  • Introduction
  • Latent Response Variable (LRV) Transformation
  • LRV Transformation of a Binary Response Variable Using the Standard Logistic Distribution
  • The LRV Transformation
  • Converting Logistic Coefficients to Probabilities of Yi Being 1
  • Extending Logit Transformation to Latent Growth Curves with Binary Indicator Variables
  • Illustrative Example 10.1: Estimating a Categorical LGCM with Binary Outcomes
  • A Categorical LGCM with Time-Invariant Covariates
  • Illustrative Example 10.2: Estimating a Conditional Categorical LGCM with Time-Invariant Covariates
  • Applying Probit Transformation for Categorical LGCM
  • Parameterization and Estimator
  • Illustrative Example 10.3: Estimating a Categorical LGCM with Binary Outcomes (Using Probit Transformation)
  • Extending Probit Transformations to a Categorical LGCM with Ordinal Outcomes
  • Latent Growth Curves with Count Variables
  • Poisson Model (Log-link Functioning)
  • Illustrative Example 10.4: Estimating a Count LGCM
  • Alternative Count Models (Negative Binominal and Zero-Inflated Count Models)
  • Negative Binomial (NB) Models
  • Zero-Inflated (ZI) Models
  • Illustrative Example 10.5: Estimating Count LGCMs (Using Negative Binomial and Zero-Inflated Model)
  • Conclusion
  • Chapter 10 Exercises
  • Note
  • References
  • 11 Growth Mixture Models with Non-Normal Variables
  • Introduction
  • Estimating a GMM with Binary Variables
  • Building a GMM with Binary Variables Using Mplus
  • Mplus Syntax for a LCGA with Binary Outcomes (Step 2)
  • Mplus Syntax for a GMM with Binary Outcomes (Step 3)
  • Assessing Estimation Problems (Step 4)
  • Selecting the Optimal Class Model (Step 5)
  • Interpreting Results from the Optimal Class Model with Binary Variables
  • A GMM with Time-Invariant Covariates
  • A GMM with Ordinal Variables
  • A GMM with Count Variables
  • Building a GMM with Count Variables Using Mplus
  • Illustrative Example 11.1: Estimating the Two-Class Model of a Zero-Inflated LCGA
  • Interpreting Results From the Optimal Class Model with Count Variables
  • A Brief Introduction to a Second-Order Growth Mixture Model (SOGMM) with Categorical Variables
  • Conclusion
  • Chapter 11 Exercises
  • References
  • Answers to Chapter Exercises
  • Chapter 2 Exercises
  • Chapter 3 Exercises
  • Chapter 4 Exercises
  • Chapter 5 Exercises
  • Chapter 6 Exercises
  • Chapter 7 Exercises
  • Chapter 8 Exercises
  • Chapter 9 Exercises
  • Chapter 10 Exercises
  • Chapter 11 Exercises
  • Index