| Invited Lectures |
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Ralitza Gueorguieva
(Yale Univ) |
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Modeling Longitudinal Trajectories Using Growth and Growth Mixture Models |
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Recent advances in longitudinal statistical modeling allow realistic description of patterns of change over time, use of all available data on an individual and assessment of the effects of both stationary and time-dependent variables. Traditional growth modeling assumes that every individual follows the same type of trajectory over time, while growth mixture models allow data-driven identification of distinct classes of developmental trajectories within a population. The latter models also allow characterization of the individuals most likely to belong to each class, assessment of treatment or intervention effects on trajectory membership and simultaneous modeling of trajectories of related behaviors. In this presentation we will describe trajectory-based approaches, will discuss their advantages and disadvantages, and will formulate recommendations for the implementation of such models. We will use examples from randomized clinical trials in alcohol dependence to illustrate identification of patterns of change over time, selection of number of trajectory classes, assessment of treatment effects and effects of time-dependent covariates, and joint modeling of treatment and compliance trajectories. Software for fitting such models will also be briefly discussed. [Supported by the Department of Veterans Affairs Cooperative Study Program, the Center for Translational Neuroscience of Alcoholism (P50 AA012870- 05).]
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Kristin Javaras
(Harvard Univ) |
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Latent Variable Models for Likert Attitude Data |
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Likert attitude scales are widely used to measure individuals' attitudes toward a particular entity, an example being attitudes towards one's own nation ("national pride"). Individuals are presented with several attitudinal statements about the entity and asked to indicate their level of agreement with each statement by choosing from ordered response categories. The resulting responses reflect individuals' underlying attitudes, but also their response style, which is defined as a consistent and content-independent pattern of response category selection, such as a tendency to agree with all statements ("acquiescence"). In the real data example we use here, differences in British and American responses to a Likert scale assessing national pride may reflect national differences in acquiescence, as well as national differences in national pride. Failure to control for response style can confound inferences about attitudes. We introduce a new measurement model for Likert attitude data, an "unfolding" latent variable model that allows not only multiple underlying attitudes, but also response style, to affect responses. In simulation experiments where response style differs between individuals, our model yields less biased inferences about attitudes than do other models, including the popular Likert scoring method, especially when there are unequal proportions of favorable and unfavorable statements.
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Michael Lee
(UC Irvine) |
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Bayesian Graphical Modeling in Cognitive Science |
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Graphical modeling provides an easily understood and powerful framework for implementing Bayesian analyses in the cognitive sciences. Graphical models specify a probabilistic generative process for observed data in terms of psychologically meaningful parameters, and allow Bayesian inferences about parameters, data, and models to be made using computational sampling methods. We give a series of tutorial examples, trying to highlight those features of the Bayesian graphical modeling approach most likely to foster theoretical progress in understanding human cognition. These examples include models of stimulus representation, memory retention, and heuristic decision-making. We also give a brief survey of more advanced recent applications, spanning a range of topics in higher-order cognition, to try and indicate the generality and potential of the graphical modeling approach.
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Jacqueline Leighton
(Univ Alberta) |
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Cognitive Diagnostic Assessment for Education: Theory and Applications |
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Billions of public dollars are spent every year in the United States, Canada, and abroad on large-scale student testing. Federal legislation such as the No Child Left Behind (NCLB) Act in the US and international testing programs such as the Organization for Economic Co-operation and Developments Programme for International Student Assessment (PISA) and the National Center for Education Statistics Trends in International Mathematics and Science Studies (TIMSS) reflect increasing expectations and demands for accountability by means of educational testing. While unidimensional summative scores have generally been useful for making comparisons among students, states, provinces, and even countries, this information has been less useful for revealing students academic strengths and weaknesses, and helping teachers and administrators improve learning and instruction. Consequently, there is a call for educational tests in science, math, and reading that can be used not only to evaluate students overall proficiency but also to identify students' cognitive strengths and weaknesses. This kind of cognitive diagnostic information could be used to rank students on a summative scale as well as to directly facilitate students learning and teachers instructional practices. The philosophy and practice of a newly emerging form of assessment, Cognitive Diagnostic Assessment (CDA), is described in this presentation.
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Sophia Rabe-Hesketh
(UC Berkeley) |
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Comparison of Methods for Handling Endogenous Covariates in Longitudinal Data |
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A strength of longitudinal data is that they allow estimation of within-subject effects of time-varying covariates. Such estimates do not suffer from bias due to unobserved subject-specific covariates that are correlated with the observed time-varying covariates, a special kind of endogeneity. Within-subject effects are typically estimated by mean-centering the time-varying covariates, or similar approaches. An alternative is to specify a random intercept model as a structural equation model and allow the time-varying covariates to be correlated with the random intercept. In this talk, another alternative will be proposed. Some approaches will be shown to correspond to equivalent models in the sense that they are reparameterizations of each other. Furthermore, the equivalent models yield identical maximum likelihood estimates of within-subject effects. However, estimates of the effects of exogenous subject-specific covariates differ, and are consistent only for some of the approaches.
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Shohei Shimizu
(The Institute of Statistical
Mathematics, Tokyo) |
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Linear Non-Gaussian Structural Equation Models |
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Linear structural equation models (linear SEMs) are widely applied in many empirical studies including social sciences, neuroinformatics and bioinformatics. Estimation of linear SEMs for continuous variables typically uses covariance structure of data alone and poses serious identifiability problems so that many important models including path analysis models are indistinguishable with no prior knowledge on the structures. A linear acyclic model which is a special case of path analysis models is typically used to analyze causal influences. Covariance information alone is not sufficient to uniquely estimate such a linear acyclic model and in most cases cannot identify the full structure (path coefficients and directions) of the model. Bentler (1983, PMK) proposed that non-Gaussian structures of data could be useful to overcome such identifiability problems of covariance-based estimation of SEMs. Recently we showed that use of non-Gaussianity allows the full structure of a linear acyclic model to be identified without pre-specifying any path directions between the variables (Shimizu et al., 2006, JMLR). The new method is based on a fairly recent statistical technique called independent component analysis (Hyvarinen et al., 2001, Wiley). We will first present an overview of linear non-Gaussian SEMs and then go to some recent advances we have made.
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