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70
Latent class models
 In
, 2004
"... The latent class (LC) models that have been developed so far assume that observations are independent. Parametric and nonparametric randomcoefficient LC models are proposed here, which will make it possible to modify this assumption. For example, the models can be used for the analysis of data coll ..."
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Cited by 95 (18 self)
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The latent class (LC) models that have been developed so far assume that observations are independent. Parametric and nonparametric randomcoefficient LC models are proposed here, which will make it possible to modify this assumption. For example, the models can be used for the analysis of data collected with complex sampling designs, data with a multilevel structure, and multiplegroup data for more than a few groups. An adapted EM algorithm is presented that makes maximumlikelihood estimation feasible. The new model is illustrated with examples from organizational, educational, and crossnational comparative research. 1.
in press). Generalized multilevel structural equation modeling
, 2002
"... A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a respon ..."
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Cited by 73 (13 self)
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A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent variables. The response model generalizes GLMMs to incorporate factor structures in addition to random intercepts and coefficients. As in GLMMs, the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lowerlevel units in the higherlevel units and missing data. A wide range of response processes can be modeled including ordered and unordered categorical responses, counts, and responses of mixed types. The structural model is similar to the structural part of a SEM except that it may include latent and observed variables varying at different levels. For example, unitlevel latent variables (factors or random coefficients) can be regressed on clusterlevel latent variables. Special cases of this framework are explored and data from the British Social Attitudes Survey are used for illustration. Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata. Key words: multilevel structural equation models, generalized linear mixed models, latent variables, random
Item factor analysis: Current approaches and future directions
 PSYCHOLOGICAL METHODS
, 2007
"... The rationale underlying factor analysis applies to continuous and categorical variables alike; however, the models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for itemlevel data that are categorical in nature. The authors provide a targeted review ..."
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Cited by 39 (4 self)
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The rationale underlying factor analysis applies to continuous and categorical variables alike; however, the models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for itemlevel data that are categorical in nature. The authors provide a targeted review and synthesis of the item factor analysis (IFA) estimation literature for orderedcategorical data (e.g., Likerttype response scales) with specific attention paid to the problems of estimating models with many items and many factors. Popular IFA models and estimation methods found in the structural equation modeling and item response theory literatures are presented. Following this presentation, recent developments in the estimation of IFA parameters (e.g., Markov chain Monte Carlo) are discussed. The authors conclude with considerations for future research on IFA, simulated examples, and advice for applied researchers.
Have multilevel models been structural equation models all along
 Multivariate Behavioral Research
, 2003
"... A core assumption of the standard multiple regression model is independence of residuals, the violation of which results in biased standard errors and test statistics. The structural equation model (SEM) generalizes the regression model in several key ways, but the SEM also assumes independence of ..."
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Cited by 38 (2 self)
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A core assumption of the standard multiple regression model is independence of residuals, the violation of which results in biased standard errors and test statistics. The structural equation model (SEM) generalizes the regression model in several key ways, but the SEM also assumes independence of residuals. The multilevel model (MLM) was developed to extend the regression model to dependent data structures. Attempts have been made to extend the SEM in similar ways, but several complications currently limit the general application of these techniques in practice. Interestingly, it is well known that under a broad set of conditions SEM and MLM longitudinal "growth curve" models are analytically and empirically identical. This is intriguing given the clear violation of independence in growth modeling that does not detrimentally affect the standard SEM. Better understanding the source and potential implications of this isomorphism is my focus here. I begin by exploring why SEM and MLM are analytically equivalent methods in the presence of nesting due to repeated observations over time. I then capitalize on this equivalency to allow for the extension of SEMs to a general class of nested data structures. I conclude with a description of potential opportunities for multilevel SEMs and directions for future developments. The structural equation model (SEM) is a flexible and powerful analytical method that has become a mainstay in many areas of social science research. The generality of this approach is evidenced in the ability to parameterize the SEM to estimate well known members of the general linear modeling (GLM) family including the ttest, ANOVA, ANCOVA, MANOVA, MANCOVA, and the multiple regression model. However, the
People are variables too: multilevel structural equations modeling
 Psychol. Methods
, 2005
"... The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (MLSEM) and to demonstrate the equivalence of general mixedeffects models and MLSEM. An intuitively appealing graphical representation of complex MLSEMs is introduced ..."
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Cited by 33 (0 self)
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The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (MLSEM) and to demonstrate the equivalence of general mixedeffects models and MLSEM. An intuitively appealing graphical representation of complex MLSEMs is introduced that succinctly describes the underlying model and its assumptions. The use of definition variables (i.e., observed variables used to fix model parameters to individual specific data values) is extended to the case of MLSEMs for clustered data with random slopes. Empirical examples of multilevel CFA and MLSEM with random slopes are provided along with scripts for fitting such models in SAS Proc Mixed, Mplus, and Mx. Methodological issues regarding estimation of complex MLSEMs and the evaluation of model fit are discussed. Further potential applications of MLSEMs are explored.
Bayesian analysis of latent variable models using Mplus. Version 4. Retrieved from http://www.statmodel.com/download/BayesAdvantages18.pdf Asparouhov
 University of Barcelona
, 1996
"... In this paper we describe some of the modeling possibilities that are now available in Mplus Version 6 with the Bayesian methodology. This new methodology offers many new possibilities but also many challenges. The paper is intended to spur more research rather than to provide complete an ..."
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Cited by 22 (7 self)
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In this paper we describe some of the modeling possibilities that are now available in Mplus Version 6 with the Bayesian methodology. This new methodology offers many new possibilities but also many challenges. The paper is intended to spur more research rather than to provide complete an
Bayesian modeling of measurement error in predictor variables using item response theory. Psychometrika 2003; 68:169191
"... It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, axe treated as latent variables. The normal ogive model is used to describe the relation between t ..."
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Cited by 17 (3 self)
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It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, axe treated as latent variables. The normal ogive model is used to describe the relation between the latent variables and dichotomous observed variables, which may be responses to tests or questionnaires. It will be shown that the multilevel model with measurement error in the observed predictor variables can be estimated in a Bayesian framework using Gibbs sampling. In this article, handling measurement error via the normal ogive model is compared with alternative approaches using the classical true score model. Examples using real data are given.
Multilevel structural equation models for the analysis of comparative data on educational performance
 Journal of Educational and Behavioral Statistics
, 2007
"... Paris The Programme for International Student Assessment comparative study of reading performance among 15yearolds is reanalyzed using statistical procedures that allow the full complexity of the data structures to be explored. The article extends existing multilevel factor analysis and structura ..."
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Cited by 15 (2 self)
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Paris The Programme for International Student Assessment comparative study of reading performance among 15yearolds is reanalyzed using statistical procedures that allow the full complexity of the data structures to be explored. The article extends existing multilevel factor analysis and structural equation models and shows how this can extract richer information from the data and provide better fits to the data. It shows how these models can be used fully to explore the dimensionality of the data and to provide efficient, singlestage models that avoid the need for multiple imputation procedures. Markov Chain Monte Carlo methodology for parameter estimation is described.
Randomized Item Response Theory Models
 Bonner Hall, The State University of New York at
, 2005
"... The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR technique is the probability of the true response modeled by ..."
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Cited by 8 (0 self)
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The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR technique is the probability of the true response modeled by an item response theory (IRT) model. The RR technique links the observed item response with the true item response. Attitudes can be measured without knowing the true individual answers. This approach makes also a hierarchical analysis possible, with explanatory variables, given observed RR data. All model parameters can be estimated simultaneously using Markov chain Monte Carlo. The randomized item response technique was applied in a study on cheating behavior of students at a Dutch University. In this study, it is of interest if students ’ cheating behavior differs across studies and if there are indicators that can explain differences in cheating behavior.
Integrative data analysis: The simultaneous analysis of multiple data sets
 Psychological Methods
, 2009
"... There are both quantitative and methodological techniques that foster the development and maintenance of a cumulative knowledge base within the psychological sciences. Most noteworthy of these techniques is metaanalysis, which allows for the synthesis of summary statistics drawn from multiple studi ..."
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Cited by 8 (1 self)
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There are both quantitative and methodological techniques that foster the development and maintenance of a cumulative knowledge base within the psychological sciences. Most noteworthy of these techniques is metaanalysis, which allows for the synthesis of summary statistics drawn from multiple studies when the original data are not available. However, when the original data can be obtained from multiple studies, many advantages stem from the statistical analysis of the pooled data. The authors define integrative data analysis (IDA) as the analysis of multiple data sets that have been pooled into one. Although variants of IDA have been incorporated into other scientific disciplines, the use of these techniques is much less evident in psychology. In this article the authors present an overview of IDA as it may be applied within the psychological sciences, discuss the relative advantages and disadvantages of IDA, describe analytic strategies for analyzing pooled individual data, and offer recommendations for the use of IDA in practice.