## Advances in Latent Variable Mixture ModelsThe current volume, Advances in Latent Variable Mixture Models, contains chapters by all of the speakers who participated in the 2006 CILVR conference, providing not just a snapshot of the event, but more importantly chronicling the state of the art in latent variable mixture model research. The volume starts with an overview chapter by the CILVR conference keynote speaker, Bengt Muthen, offering a "lay of the land" for latent variable mixture models before the volume moves to more specific constellations of topics. Part I, Multilevel and Longitudinal Systems, deals with mixtures for data that are hierarchical in nature either due to the data's sampling structure or to the repetition of measures (of varied types) over time. Part II, Models for Assessment and Diagnosis, addresses scenarios for making judgments about individuals' state of knowledge or development, and about the instruments used for making such judgments. Finally, Part III, Challenges in Model Evaluation, focuses on some of the methodological issues associated with the selection of models most accurately representing the processes and populations under investigation. It should be stated that this volume is not intended to be a first exposure to latent variable methods. Readers lacking such foundational knowledge are encouraged to consult primary and/or secondary didactic resources in order to get the most from the chapters in this volume. Once armed with that basic understanding of latent variable methods, we believe readers will find this volume incredibly exciting." |

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### Contents

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LONGITUDINAL MODELING OF POPULATION HETEROGENEITY Methodological Challenges to the Analysis of Empirically Derived Criminal ... | 53 |

EXAMINING CONTINGENT DISCRETE CHANGE OVER TIME WITH ASSOCIATIVE LATENT TRANSITION ANALYSIS | 77 |

MODELING MEASUREMENT ERROR IN EVENT OCCURRENCE FOR SINGLE NONRECURRING EVENTS IN DISCRETETIME SURVIVAL A... | 105 |

MODELS FOR ASSESSMENT AND DIAGNOSIS | 147 |

EVIDENTIARY FOUNDATIONS OF MIXTURE ITEM RESPONSE THEORY MODELS | 149 |

APPLICATIONS OF STOCHASTIC ANALYSES FOR COLLABORATIVE LEARNING AND COGNITIVE ASSESSMENT | 217 |

THE MIXTURE GENERAL DIAGNOSTIC MODEL | 255 |

CHALLENGES IN MODEL EVALUATION | 275 |

CATEGORIES OR CONTINUA? The Correspondence Between Mixture Models and Factor Models | 277 |

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IDENTIFYING THE CORRECT NUMBER OF CLASSES IN GROWTH MIXTURE MODELS | 317 |

CHOOSING A CORRECT FACTOR MIXTURE MODEL Power Limitations and Graphical Data Exploration | 343 |

ABOUT THE CONTRIBUTORS | 363 |

EXAMINING DIFFERENTIAL ITEM FUNCTIONING FROM A LATENT MIXTURE PERSPECTIVE | 177 |

MIXTURE MODELS IN A DEVELOPMENTAL CONTEXT | 199 |

### Other editions - View all

Advances in Latent Variable Mixture Models Gregory R. Hancock,Karen M. Samuelsen Limited preview - 2008 |

### Common terms and phrases

3-class alcohol algorithm ALTA model applications approach assessment assumption behavior categorical class membership cluster cognitive components covariates Davier described diagnostic model distribution error event indicators examinees example factor mixture models factor model Figure frequency GoM model growth mixture model growth model hazard probabilities Hidden Markov Models identified individual intercept IRT model item response theory Journal latent class analysis latent class model latent class variable latent profile latent transition LC model LCGA logistic regression longitudinal manifest groups Markov chain Markov Models matrix measurement Mislevy Mplus multivariate Muthen Neural Network nodes nonparametric number of classes observed variables population Psychological psychometric random effects Rasch model regression SABIC sample scores sequence skill slope solution specific strategy structural equation modeling subpopulations substantive survival analysis Table tasks tion tobacco trajectories values variance variance-covariance matrix vector within-class

### Popular passages

Page 23 - J. (2002). General growth mixture modeling for randomized preventive interventions. Biostatistics, 3, 459-475. Muthen, BO, & Curran, PJ (1997).