Higher-order growth curves and mixture modeling with Mplus: a practical guide / K.A.S.Wickrama, T.K.Lee, C.W.O'Neal, F.O.Lorenz. - London: Routledge, 2016. - xviii, 326 p.: ill. - Incl. bibl. ref. - Auth. ind.: p.:320-322. - Sub. ind.: p.323-326. - ISBN 978-1-138-92514-4 Шифр: 01  Место хранения:   01 | ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Preface ........................................................ xv About the Authors ............................................. xix PART I. Introduction ............................................ 1 1 Introduction ................................................. 3 A Layout of Incrementally-Related SEMs: An Organizing Guide .. 3 Illustrative Example 1.1: Examining Alternative Growth Curve Models ............................................. 4 Adolescents' Internalizing Symptoms (IS) Trajectories ........ 9 Datasets used in Illustrations ............................. 9 Measures .................................................. 10 2 Latent Growth Curves ........................................ 13 Introduction ................................................ 13 Growth Curve Modeling ....................................... 13 Conventional Latent Growth Curve Models (LGCM) ............ 14 Illustrative Example 2.1: Examining the Longitudinal Covariance Pattern of Indicators ........................ 19 Estimating an Unconditional Linear Latent Growth Curve Model (LGCM) Using Mplus ................................ 20 Illustrative Example 2.2: Estimating a Linear Latent Growth Curve Model (LGCM) ............................... 20 Curvilinear Growth Curve Modeling (i.e., A Quadratic Growth Curve Model) ....................................... 20 Illustrative Example 2.3: Estimating a Quadratic Latent Growth Curve Model (LGCM) ............................... 24 Model Fit Indices ......................................... 27 Comparing Nested Models ................................... 30 Illustrative Example 2.4: Nested Model Comparison Between Linear and Quadratic Models ............................. 30 Illustrative Example 2.5: Nested Model Comparison Between Models with and Without Correlated Errors ............... 31 Illustrative Example 2.6: Non-nested Model Comparison Between Linear and Piecewise Models ..................... 31 Adding Covariates to an Unconditional Model ................. 33 Illustrative Example 2.7: Adding a Predictor and Outcome to a Linear LGCM ........................................ 35 Illustrative Example 2.8: Adding a Predictor and Outcome to a Quadratic LGCM ..................................... 36 Methodological Concerns in Longitudinal Analysis: Why Growth Curves? ........................................ 38 The Need to Preserve the Continuity of Change ............. 38 The Need to Investigate Different Growth Parameters ....... 39 The Need to Incorporate Growth Parameters as Either Predictors or Outcomes in the Same Model ................ 39 The Need to Incorporate Time- Varying Predictors .......... 40 Limitations ................................................. 40 Beyond Latent Growth Curve Modeling ......................... 41 Revisiting the Layout of Models: Figures 1.1,1-2, and 1.3 ... 41 First-Order Structural Equation Models .................... 42 Second-Order Grotvth Curve Modeling ....................... 42 Growth Mixture ModeHng .................................... 42 Chapter 2 Exercises ......................................... 43 3 Longitudinal Confirmatory Factor Analysis and Curve-of-Factors Growth Curve Models ........................ 47 Introduction ................................................ 47 Confirmatory Factor Analysis (CFA) (Step One) ............... 47 Specification of a Simple CFA ............................. 48 CFA Model Identification .................................. 50 Scale Setting in a CFA .................................... 50 Longitudinal Confirmatory Factor Analysis (LCFA): Model Specification (Step Two) ............................ 51 A Second-Order Growth Curve: A Curve-of-Factors Model (Step Three) ........................................ 51 Specification of a Curve-of-Factors Model (CFM) ........... 51 Why Analyze a Curve-of-Factors Model? Improvements Over a Conventional LGCM .................................. 54 Chapter 3 Exercises ......................................... 57 4 Estimating Curve-of-Factors Growth Curve Models ............. 59 Introduction ................................................ 59 Steps for Estimating a Curve-of-Factors Model (CFM) ......... 59 Investigating the Longitudinal Correlation Patterns of Subdomain indicators (Step One) ......................... 60 Illustrative Example 4.1: Examining the Longitudinal Correlation Patterns Among Indicators ................... 60 Performing an Unconstrained Longitudinal Confirmatory Factor Analysis (LCFA) (Step Two) ....................... 62 Illustrative Example 4.2; Longitudinal Confirmatory Factor Analysis (LCFA) Using Mplus ...................... 62 Measurement Invariance of the LCFA Model (Step Three) ..... 70 Illustrative Example 4.3: Systematic Incremental Testing Sequences for Assessing Measurement Invariance .......... 71 Illustrative Example 4.4: Longitudinal Confirmatory Factor Analysis (LCFA) with "Trait" Factors (IT model) .. 81 Estimating a Second-Order Growth Curve: A Curve-of-Factors Model (CFM) (Step Four) .............. 84 Illustrative Example 4.5: Estimating a Curve-of-Factors Model (CFM) ............................................. 85 Scale Setting Approaches and Second-Order Growth Model Parameters (Curve-of-Factors Model, CFM) .................. 90 Marker Variable Approach .................................. 90 Illustrative Example 4.6: Using the Marker Variable Approach for CFA Scale Setting .......................... 90 Fixed Factor Approach ..................................... 94 Illustrative Example 4.7: Using the Fixed Factor Scale Setting Approach in a CFA ............................... 94 Effect Coding Approach .................................... 96 Illustrative Example 4.8: Using the Effect Coding Scale Setting Approach in a CFA ............................... 98 Adding Covariates to a Curve-of-Factors Model (CFM) ........ 100 Time-Invariant Covariate (TIC) Model ..................... 100 Illustrative Example 4.9: Adding a Time-Invariant Covariate (TIC) as a CFM Predictor ..................... 102 Illustrative Example 4.10: Adding a Multiple-Indicator Latent Factor as a CFM Predictor ....................... 104 Illustrative Example 4.11: Predicting Both Second-Order Growth Parameters and First-Order Latent Factors ....... 106 Illustrative Example 4.12: Predicting Distal Outcomes of Second-order Growth Factors ............................ 108 Time-Varying Covariate (TVC) Model ....................... 110 Illustrative Example 4.13: Incorporating a Time-Varying Covariate as a Direct Predictor of Manifest Indicators ............................................. 111 Illustrative Example 4.14: Incorporating a Time-Varying Covariate as a Parallel Process ........................ 115 Chapter 4 Exercises ........................................ 118 5 Extending a Parallel Process Latent Growth Curve Model (PPM) to a Factor-of-Curves Model (PCM) .............. 122 Introduction ............................................... 122 Parallel Process Latent Growth Curve Model (PPM) ......... 122 Estimating a Parallel Process Model (PPM) ................ 124 Correlation of Measurement Errors in a PPM ............... 126 Influence of Growth Factors of One Subdomain on the Growth Factors of Other Suhdomains ..................... 128 Modeling Sequentially Contingent Processes over Time ..... 132 Extending a Parallel Process Latent Growth Curve Model (PPM) to a Factor-of-Curves Growth Curve Model (FCM) ..... 134 Second-Order Growth Factors ................................ 136 Chapter 5 Exercises ........................................ 141 6 Estimating a Factor-of-Curves Model (FCM) and Adding Covariates ................................................. 142 Introduction ............................................... 142 Estimating a Factor-of-Curves Model (FCM) .................. 142 Investigating the Longitudinal Correlation Patterns Among Repeated Measures of Each Suhdotnain (Step One) .... 143 Illustrative Example 6.1: Investigating the Longitudinal Correlation Patterns Among Repeated Measures of Each Subdomain ............................. 144 Estimating a Parallel Process Growth Curve Model (PPM) (Step Two) .............................................. 144 Illustrative Example 6.2: Estimating a Parallel Process Growth Curve Model (PPM) ............................... 144 Estimating a Factor-of-Curves Model (FCM) (Step Three) ... 146 Illustrative Example 6.3; Estimating a Factor-of-Curves Model (FCM) ............................................ 148 Illustrative Example 6.4; Comparing Two Competing Models Empirically ............................................ 152 Estimating a Conditional FCM (Step Four) ................. 153 Illustrative Example 6.5; Adding Time-Invariant Covariates (TIC) to a FCM .............................. 154 Illustrative Example 6.6; Incorporating a Latent Distal Outcome into a FCM ..................................... 156 Illustrative Example 6.7; Incorporating a Time-Varying Covariate (TVC) as a Direct Predictor .................. 160 Illustrative Example 6.8; Incorporating a Time-Varying Predictor as a Parallel Process ........................ 164 A Multiple-Group FCM (Multi-Group Longitudmal Modeling) .... 165 Illustrative Example 6.9; Estimating a FCM for Multiple Groups ................................................... 167 Multivariate FCM ........................................... 172 Illustrative Example 6.10: Estimating a Multivariate FCM ... 174 Model Selection; Factor-of-Curves vs. Curve-of-Factors ..... 177 Illustrative Example 6.11; Empirically Comparing CFM and FCM Approaches ........................................... 179 Combining a CFM and a FCM; A Factor-of-Curves-of-Factors (FCF) Model .............................................. 182 Illustrative Example 6.12; Estimating a Factor-of-Curves- of-Factors (FCF) Model ................................... 183 Chapter 6 Exercises ........................................ 185 PART 2. Growth Mixture Modeling ............................... 189 7 An Introduction to Growth Mixture Models (GMMs) ........... 191 Introduction ............................................... 191 A Conventional Latent Growth Curve Model (LGCM) ............ 192 Potential Heterogeneity in Individual Trajectories ......... 192 Growth Mixture Modehng (GMM) ............................... 195 Latent Class Growth Analysis (LCGA); A Simplified GMM ...... 196 Specifying a Growth Mixture Model (GMM) .................... 197 Specifying Trajectory Classes: Class-Specific Equations .. 199 Specifying a Latent Class Growth Analysis (LCGA) ......... 199 Building A Growth Mixture Model (GMM) Using Mplus .......... 201 Specify a Traditional Growth Curve Model (LGCM) (Step One) ................................................... 201 Estimating a Latent Class Growth Analysis (LCGA) (Step Two) ................................................... 202 Illustrative Example 7.1: Mplus Syntax for a Latent Class Growth Analysis (LCGA) ........................... 204 Specifying a Growth Mixture Model (GMM) (Step Three) ..... 204 Illustrative Example 7.2: Mplus Syntax for a Growth Mixture Model (GMM) ............................. 205 Addressing Estimation Problems (Step Four) ............... 206 Illustrative Example 7.3: A Non-Normal Distribution ...... 207 Selecting the Optimal Class Model (Enumeration Indices) (Step Five) ............................................ 213 Illustrative Example 7.4: Identifying the Optimal Model .. 216 Summary of a Model Building Strategy ....................... 221 Chapter 7 Exercises ........................................ 223 8 Estimating a Conditional Growth Mixture Model (GMM) ........ 227 Introduction ............................................... 227 Growth Mixture Models: Predictors and Distal Outcomes ...... 228 The One-Step Approach to Incorporating Covariates into a GMM .................................................... 229 Predictors of Latent Classes (Multinomial Regression) .... 229 Illustrative Example 8.1: Incorporating a Time-Invariant Predictor into a GMM ................................... 230 Predictors of Latent Growth Factors Within Classes ....... 230 Illustrative Example 8.2: Adding Within-Class Effects of Predictors to a GMM ................................. 232 Adding Distal Outcomes of Latent Classes (Categorical and Continuous) ........................................ 234 Illustrative Example 8.3: Incorporating a Binary Distal Outcome into a GMM ..................................... 234 Illustrative Example 8.4: Incorporating a Continuous Distal Outcome into a GMM .............................. 236 Uncertainty of Latent Class Membership With the Addition of Covariates .......................................... 237 The Three-Step Approach: The "Manual" Method ............... 238 Illustrative Example 8.5: The Three-Step Procedure for Incorporating Predictor(s) ............................. 239 Illustrative Example 8.6: The Three-Step Procedure for Incorporating Distal Outcome(s) ........................ 243 AUXILIARY Option for the Three-Step Approach ............... 247 Illustrative Example 8.7: Utilizing the Auxiliary Option with the 3-Step Approach ............................... 247 Illustrative Example 8.8: Utilizing the Auxiliary Option with "Lanza Commands" .................................. 249 Chapter 8 Exercises ........................................ 253 9 Second-Order Growth Mixture Models (SOGMMs) ................ 256 Introduction ............................................... 256 Estimating a Second-Order Growth Mixture Model: A Curve-of-Factors Model (SOGMM of a CFM) ................ 257 Illustrative Example 9.1: A Second-Order Growth Mixture Model of a CFM (SOGMM-CF) ........................ 259 Illustrative Example 9.2: Avoiding Convergence Problems .. 265 Estimating a Second-Order Growth Mixture Model: A Factor-of-Curves Model (SOGMM of a FCM) ................ 272 Illustrative Example 9.3: A Second-Order Growth Mixture Model of a FCM (SOGMM-FC) ...................... 273 Comparison of Classification Between a First-Order GMMWith Composite Measures and Second-Order GMMs ................. 277 Estimating a Conditional Model (Conditional SOGMM) ......... 279 The Three-Step Approach (Using the AUXILIARY Optioti) to Add Predictors of Second-Order Trajectory Classes ...... 281 Illustrative Example 9.4: Estimating a Conditional SOGMM with Predictors .................................. 281 The Three-Step Approach (Using the AUXILIARY Option) to Add Outcomes of Second-Order Trajectory Classes ........ 285 Illustrative Example 9.5: Estimating a Conditional SOGMM with Outcomes .................................... 285 Estimating a Multidimensional Growth Mixture Model (MGMM) ................................................... 287 Illustrative Example 9.6: Estimating a Multidimensional Growth Mixture Model ................................... 289 Conclusion ................................................. 291 Chapter 9 Exercises ........................................ 293 Answers to Chapter Exercises .................................. 297 Author Index .................................................. 320 Subject Index ................................................. 323