| State-of-the-Art Lectures |
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Marieke Timmerman
(Univ Groningen,
The Netherlands) |
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Principal Component Analysis and Generalizations |
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Principal Component Analysis (PCA) is a popular technique for condensing information in a large set of variables into a smaller set of components. Although the definition of Principal Components (PCs) is straightforward, the technique has several facets that are important to know of and to connect with each other. We will provide an introduction of the technique and discuss issues important in applications, including the different criteria underlying PCA, rotation criteria and inferential aspects. In psychology, PCA is often used in test- and questionnaire construction to detect the structure in the variables. It has been debated contentiously whether PCA is an appropriate method in this context, or whether Common Factor Analysis (CFA) should be preferred. The essential differences between the two approaches will be explained, as well as their implications for the choice between PCA and CFA. Attention will be paid to frequently encountered misconceptions. Finally, we will provide an overview of the numerous generalizations of PCA and their applications. Examples of such generalizations are non-linear PCA, Redundancy Analysis, Common Principal Components, Multilevel Component analysis and Three-way Component Analysis.
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David Cella
(Northwestern Univ) |
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IRT Modeling Applied to Self-reported Health and Quality of Life: The Patient Reported Outcomes Measurement Information System (PROMIS) |
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PROMIS is a publicly-funded research group of investigators from academic institutions and the National Institutes of Health (http://www.nihpromis.org). From 2004-2008, we developed, refined and tested nearly 1,000 self-report questions about physical, mental and social health. We administered these questions on an electronic (internet) platform, to a cross sectional sample of approximately 20,000 people from the general US population and selected clinical samples. Using a combination of classical methods to test dimensionality and item response theory (IRT) modeling, we derived nine (9) calibrated item banks that measure unidimensional concepts of fatigue, pain impact, pain behavior, physical function, depression, anxiety, anger, satisfaction with participation in social roles, and satisfaction with participation in discretionary social activities. We also developed and tested item banks in parallel domains for pediatrics, as well as adult banks of sleep/wake disturbance and cancer-specific issues. This presentation will review item bank development and testing, and compare the precision of these item banks and their derivative tools (short forms and computerized adaptive testing; CAT) with existing "legacy" instruments measuring the same concepts. It will illustrate that the precision of CAT and PROMIS short forms outperforms the "legacy standards." Opportunities for collaboration with PROMIS investigators going forward will also be discussed.
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Michael Edwards
(Ohio State Univ) |
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Item Factor Analysis: Where We've Been and Where We Might Be Going |
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Most of original developments in factor analysis were for scores from experiments or questionnaires (this is true of much of Spearman's and Thurstone's original work). In these cases, a linear relationship between the latent variables and observed scores was often plausible. As time passed, researchers became increasing interested in conducting factor analyses on item level data. In fact, in many circles, this has become the dominant form of factor analysis. Item factor analysis (IFA), can provide valuable evidence during scale construction regarding dimensionality and item performance, as well as other useful pieces of information. Unlike the sorts of measured variables originally used in factor analytic work, item-level data are often categorical in nature. This violates many of the assumptions that are traditionally made by the model and estimation method. Initial efforts to overcome these difficulties emerged in both the structural equation and item response frameworks. Through much of the 20th centuries these solutions were quite different, despite the underlying links between the models. In the past decade, the line between these two frameworks has become increasingly blurry. In this talk I will review the historical development of IFA, provide a snapshot of where we stand today, and discuss where we might find ourselves a decade from now.
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Brian Junker
(Carnegie Mellon Univ) |
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Beyond MCMC |
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Markov Chain Monte Carlo (MCMC) techniques have simplified the development of model estimation and simulation methods, extending our reach as applied statisticians and abetting a revolution in model development and unification in psychometrics. For example, more than one in four recent papers in {\em Psychometrika} make use of MCMC techniques in areas such as Bayesian structural equation modeling, mixtures of vector and ideal point latent utility models for preference data, computation of the exact null distribution for frequentist hypothesis tests in Rasch and social network models, model evaluation and comparison in cognitive diagnosis modeling, item response models for guessing behavior, and dependence models for conjoint choice experiments. MCMC methods can be viewed as instances of successive substitution methods, reaching back to Gauss-Seidel; as instances of numerical integration methods; or as alternatives/extensions to E-M for dealing with data augmentation and other forms of missing data. In this talk I will place MCMC in the context of other optimization and integration methods, and survey some extensions, refinements and alternatives to MCMC. A central challenge for the future of psychometrics is posed by the enormous data gathering and data storage capacities of modern computing and communications technology. Although MCMC methods will always be a sensible early estimation choice while developing new parametric models, they do not always scale up well as the dimension or sample size of the data increases. I will point to some situations where MCMC does not scale well, and indicate some computational alternatives that may work better.
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Douglas Steinley
(Univ Missouri-Columbia) |
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K-Means Clustering: State-of-the-Art Methodological Developments |
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The presentation synthesizes the results and methodology of current research conducted in the area of K-means clustering. The K-means method is introduced and several recommendations are provided for the stages of cluster analytic decisions. Such decisions included variable standardization, variable selection, data reduction, and algorithmic initialization techniques.
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Jeroen Vermunt
(Univ Tilburg,
The Netherlands) |
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Latent Class and Finite Mixture Models: Recent Developments |
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Though latent class and finite mixture models have a rather long history, only recently we see an increase in the application of these methods in psychological, sociological, educational, and biomedical research. Not only has the number of applied papers increased enormously, also the number of methodological contributions has grown tremendously the last ten to twenty year. Methodological contributions include papers on new models such as mixture regression models, mixture SEM and factor analysis, mixture growth models, latent class models with multiple latent variables, latent class behavioral and diagnostic models, and multilevel mixture models. Moreover, papers have been written on model selection issues (number of latent classes), improved algorithms to prevent local maxima, methods to check model identification, improved algorithms to speed up computations, etc. Another trend is the further integration between discrete (latent class models) and continuous (IRT, factor analysis, and random effects models) latent variable models. In this 'state-of-the-art' lecture, I will provide an overview of these recent developments.
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