Higher-order growth curves and mixture modeling with MPlus: a practical guide
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| Hauptverfasser: | , , , |
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| Format: | Buch |
| Sprache: | English |
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New York ; London
Routledge
2022
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| Ausgabe: | Second edition |
| Schriftenreihe: | Multivariate applications series
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xviii, 326 Seiten Illustrationen |
| ISBN: | 9780367711269 9780367746209 |
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MARC
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| 245 | 1 | 0 | |a Higher-order growth curves and mixture modeling with MPlus |b a practical guide |c Kandauda A.S. Wickrama, Tae Kyoung Lee, Catherine Walker O'Neal, and Frederick O. Lorenz |
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Datensatz im Suchindex
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| adam_text | Contents Preface Acknowledgments Authors xvi XľX xx PART I Growth Curve Modeling 1 Introduction 1 3 A Layout of Incrementally Related SEMs: An Organizing Guide 3 Illustrative Example 1.1: Examining Alternative Growth Curve Models 3 Adolescents’ Internalizing Symptoms (IS) Trajectories 8 Datasets Used in Illustrations 8 Measures 9 References 11 2 Latent Growth Curves Introduction 12 Growth Curve Modeling 12 Conventional Latent Growth Curve Models (LGCM) 12 Linear Growth Curve Modeling 13 Investigating Longitudinal Covariance Patterns 15 niustrative Example 2.1: Examining the Longitudinal Covariance Pattern of Indicators 17 Estimating an Unconditional Linear Latent Growth Curve Model (LGCM) Using Mplus 17 Illustrative Example 2.2: Estimating a Linear Latent Growth Curve Model (LGCM 17 Curvilinear Growth Curve Modeling (i.e., a Quadratic Growth Curve Model) 20 Illustrative Example 2.3: Estimating a Quadratic Latent Growth Curve Model (LGCM) 21 Model Fit Indices 24 Comparing Nested Models 26 12
viii Contents Illustrative Example 2.4: Nested Model Comparison between Linear and Quadratic Models 2 7 Illustrative Example 2.5: Nested Model Comparison between Models with and without Correlated Errors 27 Illustrative Example 2.6: Non-Nested Model Comparison between Linear and Piecewise Models 29 Adding Covariates to an Unconditional Model 30 Illustrative Example 2.7: Adding a Predictor and Outcome to a Linear LGCM 31 Illustrative Example 2.8: Adding a Predictor and Outcome to a Quadratic LGCM 31 Methodological Concerns in Longitudinal Analysis: Why Growth Curves? 32 The Need to Preserve the Continuity of Change 33 Tite Need to Investigate Different Growth Parameters 34 The Need to Incorporate Growth Parameters as Either Predictors or Outcomes in the Same Model 34 The Need to Incorporate Time-Varying Predictors 34 Limitations 35 Beyond Latent Growth Curve Modeling 35 Revisiting the Layout of Models: Figures 1.1, 1.2, and 1.3 36 First-Order Structural Equation Models 36 Second-Order Growth Curve Modeling 36 Growth Mixture Modeling 37 Chapter 2 Exercises 37 References 38 3 Longitudinal Confirmatory Factor Analysis and Curve-of-Factors Growth Curve Models Introduction 40 Confirmatory Factor Analysis (CFA) (Step 1) 40 Specification of a Simple CFA 41 CFA Model Identification 42 Scale Setting in a CFA 43 Longitudinal Confirmatory Factor Analysis (LCFA): Model Specification (Step 2) 43 A Second-Order Growth Curve: A Curve-of-Factors Model (Step 3) 43 Specification of a Curve-of-Factors Model (CFM) 43 Why Analyze a Curve-of-Factors Model? Improvements Over a Conventional LGCM 46
Equal Contribution of Items to the Composite Measure 46 Longitudinal Measurement Invariance (Factorial Invariance) 47 Variance Components of Indicators: Measurement Error and Time-Specific Variance 47 Chapter 3 Exercises 48 References 48
Contents 4 Estimating Curve-of-Factors Growth Curve Models Introduction 49 Steps for Estimating a Curve-of-Factors Model (CFM) 49 Investigating the Longitudinal Correlation Patterns of Subdomain Indicators (Step 1) 50 Illustrative Example 4.1: Examining the Longitudinal Correlation Patterns among Indicators 50 Performing an Unconstrained Longitudinal Confirmatory Factor Analysis (LCFA) (Step 2) 51 Illustrative Example 4.2: Longitudinal Confirmatory Factor Analysis (LCFA) Using Mplus 51 Measurement Invariance of the LCFA Model (Step 3) 57 Illustrative Example 4.3: Systematic Incremental Testing Sequences for Assessing Measurement Invariance 58 Nested Model Comparison for Measurement Invariance 63 Taking Autoconelations among Indicators in a LCFA into Account as a Trait Factor 66 Illustrative Example 4.4: Longitudinal Confirmatory Factor Analysis (LCFA) with “Trait” Factors (IT Model) 67 Estimating a Second-Order Growth Curve: A Curve-of-Factors Model (CFM) (Step 4) 68 Illustrative Example 4.5: Estimating a Curve-of-Factors Model (CFM) 70 Scale Setting Approaches and Second-Order Growth Model Parameters (Curve-ofFactors Model, CFM) 72 Marker Variable Approach 74 Illustrative Example 4.6: Using the Marker Variable Approach for CFA Scale Setting 74 Fixed Factor Approach 78 Illustrative Example 4.7: Using the Fixed Factor Scale Setting Approach in a CFA 79 Effect Coding Approach 79 Illustrative Example 4.8: Using the Effect Coding Scale Setting Approach in a CFA 82 Adding Covariates to a Curve-of-Factors Model (CFM) 85 Time-Invariant Covariate (TIC) Model 85 Incorporating a
single indicator variable (W) as a predictor 85 Illustrative Example 4.9: Adding a Time-Invariant Covariate (TIC) as a CFM Predictor 86 Incorporating a Multiple-Indicator Latent Variable (P) as a Predictor 87 niustrative Example 4.10: Adding a Multiple-Indicator Latent Factor as a CFM Predictor 87 Predicting Both Time-Specific Latent Factors and Second-Order Growth Parameters 88 Illustrative Example 4.11: Predicting Both Second-Order Growth Parameters and First-Order Latent Factors 89 ix 49
x Contents Predicting Distal Outcomes (D) of Second-Order Growth Factors 90 Illustrative Example 4.12: Predicting Distal Outcomes of Second-Order Growth Factors 91 Time- Varying Covariate (TVC) Model 93 Time-Varying Covariate (TVC) as a Predictor of Manifest Outcomes 93 Illustrative Example 4.13: Incorporating a Time-Varying Covariate as a Direct Predictor of Manifest Indicators 94 A Parallel Process Second-Order Model Using a Dyadic Model Framework as an Example 96 Illustrative Example 4.14: Incorporating a Time- Varying Covariate as a Parallel Process 91 Chapter 4 Exercises 100 References 101 5 Extending a Parallel Process Latent Growth Curve Model (PPM) to a Factor-of-Curves Model (FCM) Introduction 103 Parallel Process Latent Growth Curve Model (PPM) 103 Estimating a Parallel Process Model (PPM) 104 Correlation of Measurement Errors in a PPM 106 Influence of Growth Factors of One Subdomain on the Growth Factors of Other Subdomains 106 Modeling Sequentially Contingent Processes over Time 110 Extending a Parallel Process Latent Growth Curve Model (PPM) to a Factor-ofCurves Growth Curve Model (FCM) 112 Second-Order Growth Factors 115 Chapter 5 Exercises 119 References 119 6 Estimating a Factor-of-Curves Model (FCM) and Adding Covariates Introduction 120 Estimating a Factor-of-Curves Model (FCM) 120 Investigating the Longitudinal Correlation Patterns among Repeated Measures of Each Subdomain (Step 1) 121 Illustrative Example 6.1 : Investigating the Longitudinal Conelation Patterns among Repeated Measures of Each Subdomain 121 Estimating a Parallel Process Growth Curve Model
(PPM) (Step 2) 121 Illustrative Example 6.2: Estimating a Parallel Process Growth Curve Model (PPM) 122 Estimating a Factor-of-Curves Model (FCM) (Step 3) 125 Illustrative Example 6.3: Estimating a Factor-of-Curves Model (FCM) 125 Illustrative Example 6.4: Comparing Two Competing Models Empirically 128 Estimating a Conditional FCM (Step 4) 129 Adding Time-Invariant Covariates (TICs) to a FCM 129 Predicting Both First-Order and Second-Order Growth Factors 129
Contents xi Illustrative Example 6.5: Adding Time-Invariant Covariates (TIC) to a FCM 130 Primary and Secondary Growth Factors of the FCM as Predictors of Latent Distal Outcomes (D) 130 Illustrative Example 6.6: Incorporating a Latent Distal Outcome into a FCM 133 Adding Time-Varying Covariates (TVC) to a FCM 134 A Time-Varying Covariate (TVC) as a Direct Predidor of Indicators 134 Illustrative Example 6.7: Incorporating a Time- Varying Covariate (TVC) as a Direct Predictor 135 Incorporating a TVC as a Secondary Growth Curve: A Second-Order Parallel Process Dyadic Model 137 Ľlustrative Example 6.8: Incorporating a Time- Varying Predictor as a Parallel Process 139 A Multiple-Group FCM (Multi-Group Longitudinal Modeling) 140 Illustrative Example 6.9: Estimating a FCMfor Multiple Groups 142 Multivariate FCM 146 Illustrative Example 6.10: Estimating a Multivariate FCM 148 Model Selection: Factor-of-Curves vs. Curve-of-Factors 151 Illustrative Example 6.11: Empirically Comparing CFM and FCM Approaches 152 Combining a CFM and a FCM: A Factor-of-Curves-of-Factors (FCF) Model 154 Illustrative Example 6.12: Estimating a Factor-of-Curves-of-Factors (FCF) Model 154 Chapter 6 Exercises 157 References 158 PART II Growth Mixture Modeling 7 An Introduction to Growth Mixture Models (GMMs) Introduction 161 A Conventional Latent Growth Curve Model (LGCM) 162 Potential Heterogeneity in Individual Trajedori.es 162 Growth Mixture Modeling (GMM) 163 Latent Class Growth Analysis (LCGA): A Simplified GMM 165 Specifying a Growth Mixture Model (GMM) 166 Specifying Trajectory Classes: Class-Specific
Equations 167 Specifying a Latent Class Growth Analysis (LCGA) 168 Building A Growth Mixture Model (GMM) Using MSpecify a Traditional Growth Curve Model (LGCM) (Step 1) 170 Estimating a Latent Class Growth Analysis (LCGA) (Step Two) 170 Ľlustrative Example 7.1: Mplus Syntax for a Latent Class Growth Analysis (LCGA) 170 159 161
xii Contents Specifying a Growth Mixture Model (GMM) (Step 3) 1 72 Illustrative Example 7.2: A /piti s Syntax for a Growth Mixture Model (GMM) 172 Addressing Estimation Problems (Step Four) 173 Estimation Problems Related to a Non-Normal Probability Distribution 174 Illustrative Example 7.3: A Non-Normal Distribution 174 Estimation Problems Related to Local Maxima 176 Estimation Problems Due to Model Non-Identification and Inappropriate Data 179 Selecting the Optimal Class Model (Enumeration Indices) (Step 5) 179 Information Criteria (IC) Statistics 180 Entropy and Average Posterior Probabilities 180 Likelihood Ratio Test (LRT): LMR-LRT and Bootstrapped LRT (BERT) 180 Other Considerations 181 Illustrative Example 7.4: Identifying the Optimal Model 182 Summary of a Model-Building Strategy 186 Chapter 7 Exercises 187 References 189 8 Estimating a Conditional Growth Mixture Model (GMM) Introduction 191 Growth Mixture Models: Predictors and Distal Outcomes 191 The One-Step Approach to Incorporating Covariates into a GMM 192 Predictors of Latent Classes (Multinomial Regression) 192 Illustrative Example 8.1: Incorporating a Time-Invariant Predictor into a GMM 193 Predictors of Latent Growth Factors Within Classes 194 Illustrative Example 8.2: Adding Within-Class Effects of Predictors to a GMM 195 Adding Distal Outcomes of Latent Classes (Categorical and Continuous) 196 Illustrative Example 8.3: Incorporating a Binary Distal Outcome into a GMM 197 Illustrative Example 8. 4: Incorporating a Continuous Distal Outcome into a GMM 199 Uncertainty of Latent Class Membership with the
Addition of Covariates 200 Die Three-Step Approach: The “Manual” Method 200 Illustrative Example 8.5: The Three-Step Procedure for Incorporating Predictor(s) 201 Illustrative Example 8.6: The Three-Step Procedurefor Incorporating Distal Outcome(s) 206 AUXILIARY Option for the Three-Step Approach 207 Illustrative Example 8.7: Utilizing the Auxiliary Option with the Three-Step Approach 208
Contents xiii Illustrative Example 8.8: Utilizing the Auxiliary Option 208 Chapter 8 Exercises 211 References 213 9 Second-Order Growth Mixture Models (SOGMMs) 214 Introduction 214 Estimating a Second-Order Growth Mixture Model: A Curve-of-Factors Model (SOGMMofa CFM) 215 Illustrative Example 9.1: A Second-Order Growth Mixture Model of a CFM (SOGMM-CF) 217 Illustrative Example 9.2: Avoiding Convergence Problems 222 Estimating a Second-Order Growth Mixture Model: A Factor-of-Curves Model (SOGMM of a FCM) 224 Illustrative Example 9.3: A Second-Order Growth Mixture Model of a FCM (SOGMM-FC) 227 Comparison of Classification between a First-Order GMM with Composite Measures and Second-Order GMMs 232 Estimating a Conditional Model (Conditional SOGMM) 232 The Three-Step Approach (Using the AUXILIARY Option) to Add Predictors of Second-Order Trajectory Classes 233 Illustrative Example 9.4: Estimating a Conditional SOGMM with Predictors 233 Иге Three-Step Approach (Using the AUXILIARY Option) to Add Outcomes of Second-Order Trajectory Classes 237 Illustrative Example 9.5: Estimating a Conditional SOGMM with Outcomes 237 Estimating a Multidimensional Growth Mixture Model (MGMM) 239 Illustrative Example 9.6: Estimating a Multidimensional Growth Mixture Model 239 Conclusion 242 Chapter 9 Exercises 244 References 246 PART III Latent Growth Curves with Non-Normal Variables 10 Latent Growth Curve Model with Non-Normal Variables Introduction 247 Introduction 249 Latent Response Variable (LRV) Transformation 249 LRV Transformation of a Binary Response Variable Using the Standard Logistic
Distribution 251 The LRV Transformation 251 Converting Logistic Coefficients to Probabilities ofY. Being 1 253 247 249
xiv Contents Extending Logit Transformation to Latent Growth Curves with Binary Indicator Variables 254 Illustrative Example 10.1: Estimating a Categorical LGCM with Binary Outcomes 255 A Categorical LGCM with Time-Invariant Covariates 257 Illustrative Example 10.2: Estimating a Conditional Categorical LGCM with Time-Invariant Covariates 259 Applying Probit Transformation for Categorical LGCM 260 Parameterization and Estimator 260 Illustrative Example 10.3: Estimating a Categorical LGCM with Binary Outcomes (Using Probit Transformation) 261 Extending Probit Transformations to a Categorical LGCM with Ordinal Outcomes 261 Latent Growth Curves with Count Variables 263 Poisson Model (Log-link Functioning) 264 Illustrative Example 10.4: Estimating a Count LGCM 265 Alternative Count Models (Negative Binominal and Zero-Inflated Count Models) 266 Negative Binomial (NB) Models 267 Zero-Inflated (ZI) Models 268 Illustrative Example 10.5: Estimating Count LGCMs (Using Negative Binomial and Zero-Inflated Model) 269 Conclusion 270 Chapter 10 Exercises 271 Note 273 References 273 11 Growth Mixture Models with Non-Normal Variables Introduction 275 Estimating a GMM with Binary Variables 275 Building a GMM with Binary Variables Using Mplus 276 Mplus Syntaxfor a LCGA with Binary Outcomes (Step 2) 276 Mplus Syntax for a GMM with Binary Outcomes (Step 3) 278 Assessing Estimation Problems (Step 4) 278 Selecting the Optimal Class Model (Step 5) 279 Interpreting Results from the Optimal Class Model with Binary Variables 280 A GMM with Time-Invariant Covariates 281 A GMM with Ordinal Variables 283
A GMM with Count Variables 283 Building a GMM with Count Variables Using Mplus 284 Illustrative Example 11.1: Estimating the Two-Class Model of a Zero-Inflated LCGA 285 Interpreting Results From the Optimal Class Model with Count Variables 287
Contents XV A Brief Introduction to a Second-Order Growth Mixture Model (SOGMM) with Categorical Variables 288 Conclusion 290 Chapter 11 Exercises 291 References 293 Answers to Chapter Exercises 294 Chapter 2 Exercises 294 Chapter 3 Exercises 296 Chapter 4 Exercises 296 Chapter 5 Exercises 300 Chapter 6 Exercises 300 Chapter 7 Exercises 305 Chapter 8 Exercises 307 Chapter 9 Exercises 309 Chapter 10 Exercises 312 Chapter 11 Exercises 315 Index 321
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Contents Preface Acknowledgments Authors xvi XľX xx PART I Growth Curve Modeling 1 Introduction 1 3 A Layout of Incrementally Related SEMs: An Organizing Guide 3 Illustrative Example 1.1: Examining Alternative Growth Curve Models 3 Adolescents’ Internalizing Symptoms (IS) Trajectories 8 Datasets Used in Illustrations 8 Measures 9 References 11 2 Latent Growth Curves Introduction 12 Growth Curve Modeling 12 Conventional Latent Growth Curve Models (LGCM) 12 Linear Growth Curve Modeling 13 Investigating Longitudinal Covariance Patterns 15 niustrative Example 2.1: Examining the Longitudinal Covariance Pattern of Indicators 17 Estimating an Unconditional Linear Latent Growth Curve Model (LGCM) Using Mplus 17 Illustrative Example 2.2: Estimating a Linear Latent Growth Curve Model (LGCM 17 Curvilinear Growth Curve Modeling (i.e., a Quadratic Growth Curve Model) 20 Illustrative Example 2.3: Estimating a Quadratic Latent Growth Curve Model (LGCM) 21 Model Fit Indices 24 Comparing Nested Models 26 12
viii Contents Illustrative Example 2.4: Nested Model Comparison between Linear and Quadratic Models 2 7 Illustrative Example 2.5: Nested Model Comparison between Models with and without Correlated Errors 27 Illustrative Example 2.6: Non-Nested Model Comparison between Linear and Piecewise Models 29 Adding Covariates to an Unconditional Model 30 Illustrative Example 2.7: Adding a Predictor and Outcome to a Linear LGCM 31 Illustrative Example 2.8: Adding a Predictor and Outcome to a Quadratic LGCM 31 Methodological Concerns in Longitudinal Analysis: Why Growth Curves? 32 The Need to Preserve the Continuity of Change 33 Tite Need to Investigate Different Growth Parameters 34 The Need to Incorporate Growth Parameters as Either Predictors or Outcomes in the Same Model 34 The Need to Incorporate Time-Varying Predictors 34 Limitations 35 Beyond Latent Growth Curve Modeling 35 Revisiting the Layout of Models: Figures 1.1, 1.2, and 1.3 36 First-Order Structural Equation Models 36 Second-Order Growth Curve Modeling 36 Growth Mixture Modeling 37 Chapter 2 Exercises 37 References 38 3 Longitudinal Confirmatory Factor Analysis and Curve-of-Factors Growth Curve Models Introduction 40 Confirmatory Factor Analysis (CFA) (Step 1) 40 Specification of a Simple CFA 41 CFA Model Identification 42 Scale Setting in a CFA 43 Longitudinal Confirmatory Factor Analysis (LCFA): Model Specification (Step 2) 43 A Second-Order Growth Curve: A Curve-of-Factors Model (Step 3) 43 Specification of a Curve-of-Factors Model (CFM) 43 Why Analyze a Curve-of-Factors Model? Improvements Over a Conventional LGCM 46
Equal Contribution of Items to the Composite Measure 46 Longitudinal Measurement Invariance (Factorial Invariance) 47 Variance Components of Indicators: Measurement Error and Time-Specific Variance 47 Chapter 3 Exercises 48 References 48
Contents 4 Estimating Curve-of-Factors Growth Curve Models Introduction 49 Steps for Estimating a Curve-of-Factors Model (CFM) 49 Investigating the Longitudinal Correlation Patterns of Subdomain Indicators (Step 1) 50 Illustrative Example 4.1: Examining the Longitudinal Correlation Patterns among Indicators 50 Performing an Unconstrained Longitudinal Confirmatory Factor Analysis (LCFA) (Step 2) 51 Illustrative Example 4.2: Longitudinal Confirmatory Factor Analysis (LCFA) Using Mplus 51 Measurement Invariance of the LCFA Model (Step 3) 57 Illustrative Example 4.3: Systematic Incremental Testing Sequences for Assessing Measurement Invariance 58 Nested Model Comparison for Measurement Invariance 63 Taking Autoconelations among Indicators in a LCFA into Account as a Trait Factor 66 Illustrative Example 4.4: Longitudinal Confirmatory Factor Analysis (LCFA) with “Trait” Factors (IT Model) 67 Estimating a Second-Order Growth Curve: A Curve-of-Factors Model (CFM) (Step 4) 68 Illustrative Example 4.5: Estimating a Curve-of-Factors Model (CFM) 70 Scale Setting Approaches and Second-Order Growth Model Parameters (Curve-ofFactors Model, CFM) 72 Marker Variable Approach 74 Illustrative Example 4.6: Using the Marker Variable Approach for CFA Scale Setting 74 Fixed Factor Approach 78 Illustrative Example 4.7: Using the Fixed Factor Scale Setting Approach in a CFA 79 Effect Coding Approach 79 Illustrative Example 4.8: Using the Effect Coding Scale Setting Approach in a CFA 82 Adding Covariates to a Curve-of-Factors Model (CFM) 85 Time-Invariant Covariate (TIC) Model 85 Incorporating a
single indicator variable (W) as a predictor 85 Illustrative Example 4.9: Adding a Time-Invariant Covariate (TIC) as a CFM Predictor 86 Incorporating a Multiple-Indicator Latent Variable (P) as a Predictor 87 niustrative Example 4.10: Adding a Multiple-Indicator Latent Factor as a CFM Predictor 87 Predicting Both Time-Specific Latent Factors and Second-Order Growth Parameters 88 Illustrative Example 4.11: Predicting Both Second-Order Growth Parameters and First-Order Latent Factors 89 ix 49
x Contents Predicting Distal Outcomes (D) of Second-Order Growth Factors 90 Illustrative Example 4.12: Predicting Distal Outcomes of Second-Order Growth Factors 91 Time- Varying Covariate (TVC) Model 93 Time-Varying Covariate (TVC) as a Predictor of Manifest Outcomes 93 Illustrative Example 4.13: Incorporating a Time-Varying Covariate as a Direct Predictor of Manifest Indicators 94 A Parallel Process Second-Order Model Using a Dyadic Model Framework as an Example 96 Illustrative Example 4.14: Incorporating a Time- Varying Covariate as a Parallel Process 91 Chapter 4 Exercises 100 References 101 5 Extending a Parallel Process Latent Growth Curve Model (PPM) to a Factor-of-Curves Model (FCM) Introduction 103 Parallel Process Latent Growth Curve Model (PPM) 103 Estimating a Parallel Process Model (PPM) 104 Correlation of Measurement Errors in a PPM 106 Influence of Growth Factors of One Subdomain on the Growth Factors of Other Subdomains 106 Modeling Sequentially Contingent Processes over Time 110 Extending a Parallel Process Latent Growth Curve Model (PPM) to a Factor-ofCurves Growth Curve Model (FCM) 112 Second-Order Growth Factors 115 Chapter 5 Exercises 119 References 119 6 Estimating a Factor-of-Curves Model (FCM) and Adding Covariates Introduction 120 Estimating a Factor-of-Curves Model (FCM) 120 Investigating the Longitudinal Correlation Patterns among Repeated Measures of Each Subdomain (Step 1) 121 Illustrative Example 6.1 : Investigating the Longitudinal Conelation Patterns among Repeated Measures of Each Subdomain 121 Estimating a Parallel Process Growth Curve Model
(PPM) (Step 2) 121 Illustrative Example 6.2: Estimating a Parallel Process Growth Curve Model (PPM) 122 Estimating a Factor-of-Curves Model (FCM) (Step 3) 125 Illustrative Example 6.3: Estimating a Factor-of-Curves Model (FCM) 125 Illustrative Example 6.4: Comparing Two Competing Models Empirically 128 Estimating a Conditional FCM (Step 4) 129 Adding Time-Invariant Covariates (TICs) to a FCM 129 Predicting Both First-Order and Second-Order Growth Factors 129
Contents xi Illustrative Example 6.5: Adding Time-Invariant Covariates (TIC) to a FCM 130 Primary and Secondary Growth Factors of the FCM as Predictors of Latent Distal Outcomes (D) 130 Illustrative Example 6.6: Incorporating a Latent Distal Outcome into a FCM 133 Adding Time-Varying Covariates (TVC) to a FCM 134 A Time-Varying Covariate (TVC) as a Direct Predidor of Indicators 134 Illustrative Example 6.7: Incorporating a Time- Varying Covariate (TVC) as a Direct Predictor 135 Incorporating a TVC as a Secondary Growth Curve: A Second-Order Parallel Process Dyadic Model 137 Ľlustrative Example 6.8: Incorporating a Time- Varying Predictor as a Parallel Process 139 A Multiple-Group FCM (Multi-Group Longitudinal Modeling) 140 Illustrative Example 6.9: Estimating a FCMfor Multiple Groups 142 Multivariate FCM 146 Illustrative Example 6.10: Estimating a Multivariate FCM 148 Model Selection: Factor-of-Curves vs. Curve-of-Factors 151 Illustrative Example 6.11: Empirically Comparing CFM and FCM Approaches 152 Combining a CFM and a FCM: A Factor-of-Curves-of-Factors (FCF) Model 154 Illustrative Example 6.12: Estimating a Factor-of-Curves-of-Factors (FCF) Model 154 Chapter 6 Exercises 157 References 158 PART II Growth Mixture Modeling 7 An Introduction to Growth Mixture Models (GMMs) Introduction 161 A Conventional Latent Growth Curve Model (LGCM) 162 Potential Heterogeneity in Individual Trajedori.es 162 Growth Mixture Modeling (GMM) 163 Latent Class Growth Analysis (LCGA): A Simplified GMM 165 Specifying a Growth Mixture Model (GMM) 166 Specifying Trajectory Classes: Class-Specific
Equations 167 Specifying a Latent Class Growth Analysis (LCGA) 168 Building A Growth Mixture Model (GMM) Using MSpecify a Traditional Growth Curve Model (LGCM) (Step 1) 170 Estimating a Latent Class Growth Analysis (LCGA) (Step Two) 170 Ľlustrative Example 7.1: Mplus Syntax for a Latent Class Growth Analysis (LCGA) 170 159 161
xii Contents Specifying a Growth Mixture Model (GMM) (Step 3) 1 72 Illustrative Example 7.2: A /piti s Syntax for a Growth Mixture Model (GMM) 172 Addressing Estimation Problems (Step Four) 173 Estimation Problems Related to a Non-Normal Probability Distribution 174 Illustrative Example 7.3: A Non-Normal Distribution 174 Estimation Problems Related to Local Maxima 176 Estimation Problems Due to Model Non-Identification and Inappropriate Data 179 Selecting the Optimal Class Model (Enumeration Indices) (Step 5) 179 Information Criteria (IC) Statistics 180 Entropy and Average Posterior Probabilities 180 Likelihood Ratio Test (LRT): LMR-LRT and Bootstrapped LRT (BERT) 180 Other Considerations 181 Illustrative Example 7.4: Identifying the Optimal Model 182 Summary of a Model-Building Strategy 186 Chapter 7 Exercises 187 References 189 8 Estimating a Conditional Growth Mixture Model (GMM) Introduction 191 Growth Mixture Models: Predictors and Distal Outcomes 191 The One-Step Approach to Incorporating Covariates into a GMM 192 Predictors of Latent Classes (Multinomial Regression) 192 Illustrative Example 8.1: Incorporating a Time-Invariant Predictor into a GMM 193 Predictors of Latent Growth Factors Within Classes 194 Illustrative Example 8.2: Adding Within-Class Effects of Predictors to a GMM 195 Adding Distal Outcomes of Latent Classes (Categorical and Continuous) 196 Illustrative Example 8.3: Incorporating a Binary Distal Outcome into a GMM 197 Illustrative Example 8. 4: Incorporating a Continuous Distal Outcome into a GMM 199 Uncertainty of Latent Class Membership with the
Addition of Covariates 200 Die Three-Step Approach: The “Manual” Method 200 Illustrative Example 8.5: The Three-Step Procedure for Incorporating Predictor(s) 201 Illustrative Example 8.6: The Three-Step Procedurefor Incorporating Distal Outcome(s) 206 AUXILIARY Option for the Three-Step Approach 207 Illustrative Example 8.7: Utilizing the Auxiliary Option with the Three-Step Approach 208
Contents xiii Illustrative Example 8.8: Utilizing the Auxiliary Option 208 Chapter 8 Exercises 211 References 213 9 Second-Order Growth Mixture Models (SOGMMs) 214 Introduction 214 Estimating a Second-Order Growth Mixture Model: A Curve-of-Factors Model (SOGMMofa CFM) 215 Illustrative Example 9.1: A Second-Order Growth Mixture Model of a CFM (SOGMM-CF) 217 Illustrative Example 9.2: Avoiding Convergence Problems 222 Estimating a Second-Order Growth Mixture Model: A Factor-of-Curves Model (SOGMM of a FCM) 224 Illustrative Example 9.3: A Second-Order Growth Mixture Model of a FCM (SOGMM-FC) 227 Comparison of Classification between a First-Order GMM with Composite Measures and Second-Order GMMs 232 Estimating a Conditional Model (Conditional SOGMM) 232 The Three-Step Approach (Using the AUXILIARY'Option) to Add Predictors of Second-Order Trajectory Classes 233 Illustrative Example 9.4: Estimating a Conditional SOGMM with Predictors 233 Иге Three-Step Approach (Using the AUXILIARY Option) to Add Outcomes of Second-Order Trajectory Classes 237 Illustrative Example 9.5: Estimating a Conditional SOGMM with Outcomes 237 Estimating a Multidimensional Growth Mixture Model (MGMM) 239 Illustrative Example 9.6: Estimating a Multidimensional Growth Mixture Model 239 Conclusion 242 Chapter 9 Exercises 244 References 246 PART III Latent Growth Curves with Non-Normal Variables 10 Latent Growth Curve Model with Non-Normal Variables Introduction 247 Introduction 249 Latent Response Variable (LRV) Transformation 249 LRV Transformation of a Binary Response Variable Using the Standard Logistic
Distribution 251 The LRV Transformation 251 Converting Logistic Coefficients to Probabilities ofY. Being 1 253 247 249
xiv Contents Extending Logit Transformation to Latent Growth Curves with Binary Indicator Variables 254 Illustrative Example 10.1: Estimating a Categorical LGCM with Binary Outcomes 255 A Categorical LGCM with Time-Invariant Covariates 257 Illustrative Example 10.2: Estimating a Conditional Categorical LGCM with Time-Invariant Covariates 259 Applying Probit Transformation for Categorical LGCM 260 Parameterization and Estimator 260 Illustrative Example 10.3: Estimating a Categorical LGCM with Binary Outcomes (Using Probit Transformation) 261 Extending Probit Transformations to a Categorical LGCM with Ordinal Outcomes 261 Latent Growth Curves with Count Variables 263 Poisson Model (Log-link Functioning) 264 Illustrative Example 10.4: Estimating a Count LGCM 265 Alternative Count Models (Negative Binominal and Zero-Inflated Count Models) 266 Negative Binomial (NB) Models 267 Zero-Inflated (ZI) Models 268 Illustrative Example 10.5: Estimating Count LGCMs (Using Negative Binomial and Zero-Inflated Model) 269 Conclusion 270 Chapter 10 Exercises 271 Note 273 References 273 11 Growth Mixture Models with Non-Normal Variables Introduction 275 Estimating a GMM with Binary Variables 275 Building a GMM with Binary Variables Using Mplus 276 Mplus Syntaxfor a LCGA with Binary Outcomes (Step 2) 276 Mplus Syntax for a GMM with Binary Outcomes (Step 3) 278 Assessing Estimation Problems (Step 4) 278 Selecting the Optimal Class Model (Step 5) 279 Interpreting Results from the Optimal Class Model with Binary Variables 280 A GMM with Time-Invariant Covariates 281 A GMM with Ordinal Variables 283
A GMM with Count Variables 283 Building a GMM with Count Variables Using Mplus 284 Illustrative Example 11.1: Estimating the Two-Class Model of a Zero-Inflated LCGA 285 Interpreting Results From the Optimal Class Model with Count Variables 287
Contents XV A Brief Introduction to a Second-Order Growth Mixture Model (SOGMM) with Categorical Variables 288 Conclusion 290 Chapter 11 Exercises 291 References 293 Answers to Chapter Exercises 294 Chapter 2 Exercises 294 Chapter 3 Exercises 296 Chapter 4 Exercises 296 Chapter 5 Exercises 300 Chapter 6 Exercises 300 Chapter 7 Exercises 305 Chapter 8 Exercises 307 Chapter 9 Exercises 309 Chapter 10 Exercises 312 Chapter 11 Exercises 315 Index 321 |
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| discipline | Soziologie Mathematik |
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| id | DE-604.BV047877102 |
| illustrated | Illustrated |
| index_date | 2024-07-03T19:21:26Z |
| indexdate | 2024-07-10T09:23:59Z |
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| isbn | 9780367711269 9780367746209 |
| language | English |
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| publishDate | 2022 |
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| spelling | Wickrama, Kandauda A. S. Verfasser (DE-588)170930645 aut Higher-order growth curves and mixture modeling with MPlus a practical guide Kandauda A.S. Wickrama, Tae Kyoung Lee, Catherine Walker O'Neal, and Frederick O. Lorenz Second edition New York ; London Routledge 2022 xviii, 326 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Multivariate applications series Mplus (DE-588)7716737-5 gnd rswk-swf Lineares Modell (DE-588)4134827-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s Lineares Modell (DE-588)4134827-8 s Mplus (DE-588)7716737-5 s DE-604 Lee, Tae Kyoung 1979- Verfasser (DE-588)1107569907 aut O'Neal, Catherine Walker 1985- Verfasser (DE-588)1107587905 aut Lorenz, Frederick O. 1948- Verfasser (DE-588)1107588898 aut Erscheint auch als Online-Ausgabe, Taylor & Francis 978-1-00-315876-9 Erscheint auch als Online-Ausgabe, ProQuest 978-1-00-046580-8 Erscheint auch als Online-Ausgabe, Endnutzer 978-1-00-046584-6 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033259508&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wickrama, Kandauda A. S. Lee, Tae Kyoung 1979- O'Neal, Catherine Walker 1985- Lorenz, Frederick O. 1948- Higher-order growth curves and mixture modeling with MPlus a practical guide Mplus (DE-588)7716737-5 gnd Lineares Modell (DE-588)4134827-8 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)7716737-5 (DE-588)4134827-8 (DE-588)4056995-0 |
| title | Higher-order growth curves and mixture modeling with MPlus a practical guide |
| title_auth | Higher-order growth curves and mixture modeling with MPlus a practical guide |
| title_exact_search | Higher-order growth curves and mixture modeling with MPlus a practical guide |
| title_exact_search_txtP | Higher-order growth curves and mixture modeling with MPlus a practical guide |
| title_full | Higher-order growth curves and mixture modeling with MPlus a practical guide Kandauda A.S. Wickrama, Tae Kyoung Lee, Catherine Walker O'Neal, and Frederick O. Lorenz |
| title_fullStr | Higher-order growth curves and mixture modeling with MPlus a practical guide Kandauda A.S. Wickrama, Tae Kyoung Lee, Catherine Walker O'Neal, and Frederick O. Lorenz |
| title_full_unstemmed | Higher-order growth curves and mixture modeling with MPlus a practical guide Kandauda A.S. Wickrama, Tae Kyoung Lee, Catherine Walker O'Neal, and Frederick O. Lorenz |
| title_short | Higher-order growth curves and mixture modeling with MPlus |
| title_sort | higher order growth curves and mixture modeling with mplus a practical guide |
| title_sub | a practical guide |
| topic | Mplus (DE-588)7716737-5 gnd Lineares Modell (DE-588)4134827-8 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mplus Lineares Modell Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033259508&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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