Longitudinal Multivariate Psychology

Contents......Page 3
Foreword......Page 6
Intro & Section Overview......Page 8
Section I: Extensions of Latent Change Score Models......Page 9
Section II: Measurement and Testing Issues in Longitudinal Modeling......Page 10
Section III: Novel Applications of Multivariate Longitudinal Methodology......Page 11
--- Extensions of Latent Change Score Models......Page 14
1 Methodological Issues & Extensions to Latent Difference Score Framework......Page 15
The Bivariate Dual Change Score (BDCS) Model......Page 17
IC Specifications in the BDCS......Page 19
Stochastic BDCS Model......Page 23
Empirical Illustration......Page 30
Discussion......Page 35
Limitations......Page 37
References......Page 38
Sample dynr Code for Fitting the Stochastic BDCS Models in the Illustrative Example.......Page 42
Development of Fluid Reasoning......Page 44
Models to Examine Changes in Fluid Reasoning across Measurement Occasions......Page 45
Models to Examine Dynamics of Fluid Reasoning and Underlying Developmental Mechanisms......Page 46
Data Description......Page 50
Change in Fluid Reasoning Across Measurement Occasions......Page 51
Developmental Changes in Fluid Reasoning......Page 56
Summary of Findings......Page 58
Methodological and Substantive Implications......Page 59
References......Page 60
Sample Code for Analyses......Page 62
3 Individually Varying Time Metrics in Latent Change Score Models......Page 67
Latent Change Score Models......Page 69
Structural Equation Modeling Framework......Page 70
Nonlinear Multilevel Modeling Framework......Page 72
JAGS......Page 74
Data......Page 76
SAS Programming......Page 77
NLMIXED Output......Page 78
JAGS......Page 79
Structural Equation Modeling Software......Page 80
Discussion......Page 81
References......Page 83
Introduction......Page 86
Methods......Page 89
Latent Constant Change Score Model......Page 90
Latent Quadratic Constant Change Score Model......Page 91
A Latent Change Score Model Representing Latent Basis Curve Model......Page 94
Bivariate Latent Quadratic Curve Model Based on Latent Change Score Approach......Page 98
Bivariate Quadratic Constant Latent Change Score Model with Coupling Effect......Page 100
Bivariate Quadratic Constant Latent Change Score Model with Self-Feedback and Coupling Effect......Page 104
Discussion......Page 107
References......Page 113
Regularized Estimation of Multivariate Latent Change Score Models......Page 115
Latent Change Score Framework......Page 116
Rationale......Page 119
Regularization......Page 120
Univariate LCS Regularization......Page 122
Time-Varying Effects Regularization......Page 124
Bivariate LCS Regularization......Page 126
Discussion......Page 127
References......Page 129
Setting the Stage......Page 132
The Breakthrough: RAM Algebra and RAM Path Analysis......Page 137
Some Personal History......Page 141
How Our Thinking About Modeling Has Changed......Page 143
Notes......Page 145
References......Page 146
--- Measurement & Testing Issues in Longitudinal Modeling......Page 149
Small Sample Corrections to Model Fit Criteria for Latent Change Score Models......Page 150
Methods......Page 157
Modeling Framework......Page 158
Number of Time Points......Page 161
Missing Data Corrections......Page 162
RMSEA......Page 163
Empirical Example......Page 164
Discussion......Page 165
References......Page 168
Introduction......Page 171
Latent Curve Modeling......Page 172
Specific vs. Generalized Variance Tests......Page 174
Unconstrained vs. Constrained Estimation and the Boundary Issue......Page 175
How Are the Tests Conducted in Practice?......Page 177
Type I Error Rates......Page 178
Statistical Power......Page 179
A Real Data Analysis Example......Page 181
Consequences of Over-Simplifying Covariance Structures in Linear Growth Curve Modeling......Page 184
Point Estimates of the Latent Factor Means or Fixed Effects......Page 185
Standard Error Estimates of the Latent Factor Mean Estimates......Page 187
Robust Standard Error Estimates......Page 188
General Discussion......Page 189
Note......Page 190
References......Page 191
Introduction......Page 194
A Univariate Latent Change Score Model......Page 196
A Bivariate Latent Change Score Model......Page 198
Statistical Power Analysis Based on Monte Carlo Simulation......Page 199
R Package......Page 202
Online Interface......Page 204
Example 9.1: Type I Error Rate Investigation for a Univariate LCSM......Page 205
Example 9.2: Power Analysis for a Univariate LCSM......Page 206
Example 9.3: Generate a Power Curve for Different Sample Sizes for a Univariate LCSM......Page 207
Example 9.4: Generate a Power Curve for Different Number of Occasions for a Univariate LCSM......Page 208
Example 9.5: Power Analysis for a Bivariate LCSM......Page 209
Discussion and Future Directions......Page 211
References......Page 213
10 Investigating the Performance of cart- & Random Forest-based Procedures for Dealing with Longitudinal Dropout in Small Sample Designs under mnar Missing Data......Page 217
Introduction to CART and Random Forests......Page 218
Using CART and Random Forests to Address Missing Data......Page 219
The Present Research......Page 221
Data Generation Model......Page 222
Factors Manipulated in the Simulation......Page 223
Analyses Conducted on Each Simulated Dataset......Page 226
Percent Bias......Page 228
Discussion......Page 238
Notes......Page 241
References......Page 242
Introduction......Page 245
Latent Variable Measurement, Indeterminacy, and Model Equivalence......Page 246
Problems with Longitudinal Measurement Modeling......Page 249
Factor of Curves Model......Page 250
Measurement Model of Derivatives......Page 252
Derivative Estimation......Page 253
Full Dimensionality......Page 254
Interpretable......Page 255
Multidimensional Measurement Modeling......Page 256
Redefining MMOD for Item-Level Data......Page 257
Defining Residual Dynamic Structure......Page 259
Discussion......Page 260
FOCUS, CUFFS, and Cross-Classified Data......Page 261
Notes......Page 262
References......Page 263
--- Novel Applications of Multivariate Longitudinal Methodology......Page 266
12 Role of Interval Measurement in Developmental Studies......Page 267
Validity......Page 268
Importance of Interval Scaling......Page 269
Mechanistic Modeling......Page 271
Rasch Measurement......Page 273
Need for Pragmatism......Page 274
Recommendations......Page 276
References......Page 278
Growth Modeling using the Differential Form: Translations from Study of Fish Growth......Page 281
Reformulating Growth Models in the Differential Form......Page 282
Translating Models from Ecology to Developmental Science......Page 285
A von Bertalanffy Growth Model for Fish Growth: The Integral Form......Page 286
Bioenergetic Determinants of Growth: The Differential Form......Page 289
Connecting the Differential and Integral Forms......Page 292
Example Extensions......Page 295
Future Directions......Page 298
Epilogue......Page 300
References......Page 301
Introduction......Page 305
Psychometric and Biometric Factor Models......Page 306
Latent Growth Modeling......Page 309
Conclusions......Page 314
References......Page 317
15 Making the Cut......Page 319
Research Can’t Answer Every Question......Page 321
Understand Your Audience......Page 322
You Need More and Better Data......Page 323
References......Page 325
Jack’s Successful Team-Approach in Working with Minority Researchers and Organizations......Page 327
Individualism......Page 328
Collectivism......Page 329
Trusting Relationships......Page 330
Training Approach......Page 331
Projects......Page 332
Methodologies and Statistical Analyses......Page 333
Strategically Planning for the Long Term......Page 337
References......Page 340
Index......Page 345