Multilevel Mixture Modeling (with co-author Bengt Muthén)

This presentation describes the general framework of multilevel mixture models that is implemented in the Mplus software, and illustrates the framework with specific examples such as multilevel mixture item response theory, multilevel latent transition analysis, and multilevel growth mixture modeling.

The Two-Point Mixture Index of Model Fit

This presentation will deal with a variety of applications of the descriptive measure of model fit proposed by Rudas, Clogg, and Lindsay.  This index will be compared with more traditional indices and its relative advantages/disadvantages discussed in the context of several real-data analyses.

Identifying the Correct Number of Classes in Growth Mixture Models (with first author Davood Tofighi, Arizona State University )

This presentation will discuss strategies for correctly identifying the number of latent classes in a growth mixture model. A number of fit indices exist for the purpose of identifying the number of underlying classes, but the utility of these indices is largely untested at this point in time. This presentation reports results from a simulation study that examines the utility of several different indices, and outlines the propensity of each index to over- or under-extract the correct number of classes.

Examining Contingent Discrete Change Over Time With Associative Latent Transition Analysis

This presentation will introduce the parameterization of the latent class model for modeling change over time in a single discrete latent variable, and a related parameterization for modeling associations between two discrete latent variables.  A method will then be introduced to test for broad patterns of association between the discrete latent variables using parameter restrictions.  This will be illustrated with an empirical example, and specific hypothesis testing will be demonstrated.

Methodological challenges to a population-based analysis of antecedents and consequences of empirically derived criminal trajectory profiles (with co-author Bengt Muthén)

Over the last 25 years, a life-course/developmental perspective of
criminal behavior has become more and more prominent in criminological literature. The theoretical development of this perspective goes hand in hand with the development of statistical modeling techniques for longitudinal data, in particular latent class growth models, growth mixture models, and parallel processes to name just a few. However while there is a growing body of literature applying these statistical techniques to empirical data, the usage and usability of these techniques has been challenged. This paper will revisit the rationale for applying group-based modeling techniques, compare modeling alternatives, and discuss model extensions that might be better suited to meet the needs of criminological theory. In addition we will evaluate model sensitivity and discussion replication issues. (Key words: latent class growth modeling, growth mixture modeling, zero-inflated Poisson distribution, developmental trajectory groups)

Categories or Continua: The Correspondence Between Factor and Mixture Models (with co-author Peter Molenaar, The Pennsylvania State University )

Mixture models have become extremely popular in recent years as researchers try to represent heterogeneity in populations.  In many applications, however, factor models and mixture models can provide similar fit to the observed covariance structure of data.  This talk will look closely at an empirical example to explore the general formal correspondences between solutions for mixtures of multivariate normals and common orthogonal factor models.

Discriminating Between Continuous and Categorical Latent Variables

This presentation will address the problem of finding the correct number of classes and within-class factors when modeling data from a potentially heterogeneous population using factor mixture models.

Modeling Measurement Error In Event Occurrence For Discrete-Time Survival Analysis

This presentation will cover the use of a second-order latent class model where the first-order latent class variables represent the latent (unobserved) event status for individuals at discrete points in time, as measured by a set of observed indicators, and the second-order latent class variable models the population heterogeneity in the event history process. This model would be ideally suited for research aimed at modeling, for example, the time between clinical depression episodes, the time from alcohol use onset to alcohol use disorder, etc., where the outcome event of interest is not directly observed and the time dependence of the event process is of particular interest. Special concerns for model implementation, including identification and measurement invariance, will be discussed.

Bayesian Perspective on Structured mixtures of IRT Models (with co-authors Roy Levy, Marc Kroopnick, and Daisy Wise, University of Maryland)

This presentation would fit under the general framework of mixtures of IRT models.   Of particular interest are situations when substantive theory suggests the structure of the components—for example, when there are different solution strategies and theory indicates the features of tasks that make them difficult under the different solutions.  The issues surrounding inference and model-building for circumstances such as these will be illustrated using real data examples.

Keynote Address

The worlds of mixture models and latent variable models have long existed in isolation. With a reframing of finite mixtures as latent class models, and with the divisions among latent variable methods becoming less and less clear or even necessary, the general role for mixtures across latent variable methods is coming into focus. This keynote address will discuss the role of mixtures within the general context of latent variable models, as well as the rich application potential for such models in addressing problems of substance.

Examining Differential Item Functioning from a Latent Class Perspective

This presentation will first discuss the two major problems with the current procedures for identifying differential item functioning (DIF).  The first issue relates to the use of manifest grouping variables, such as sex, race, and ethnicity.  The second related issue deals with the lack of information gained regarding the cause of the DIF.  A latent class procedure for DIF detection using the mixed Rasch model will then be applied to real data.  Manifest groups will be mapped onto the latent classes so that the issues identified regarding manifest DIF procedures can be again discussed within the mixture model framework.

Artificial Intelligence Methods for Modeling and Assessing Collaborative Distance Learning

Two different applications will be presented in which artificial intelligence modeling methods are used to assist an instructor or online coach in assessing and mediating online student interaction, with the aim of improving the quality of students' distance learning experiences. The first application, EPSILON, applies a combination of latent mixed Markov modeling and Multidimensional Scaling for modeling, analyzing, and supporting the process of online student knowledge sharing. These analysis techniques are used to train a system to dynamically recognize (a) when students are having trouble learning the new concepts they share with each other, and (b) why they are having trouble. In the second application, IMMEX Collaborative, a combination of iterative nonlinear machine learning algorithms is applied to identify latent classes of student problem solving strategies. The approach is used to predict students’ future behaviors within a scientific inquiry environment and provide targeted non-intrusive facilitation.

Mixtures of Diagnostic Skill Profile

This presentation will cover an introduction to the general diagnostic model (GDM) that can be viewed as a family of multidimensional discrete item response theory models. The talk will focus on recent work on these models in the framework of large scale educational assessment, using a model extension that allows estimating mixture and multiple-group versions of the GDM. Methods to impose constraints for the purpose of linking across groups and/or mixture components will be discussed and illustrated using real data examples.

Mixture Models In a Developmental Context (with co-author Karen Draney, University of California, Berkeley)

This presentation will cover the topic of designing mixture models that are suited to the sorts of theories that arise in research in developmental studies. The SALTUS model, which includes parameters that reflect stage mastery thereby allowing an increase in the probability of correctly responding to an item for examinees who have reached certain stages, is an example of such a mixture model.