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Nickolay T Trendafilov, Sara Fontanella, Kohei Adachi
Sparse principal component analysis is a very active research area in the last decade. It produces component loadings with many zero entries which facilitates their interpretation and helps avoid redundant variables. The classic factor analysis is another popular dimension reduction technique which shares similar interpretation problems and could greatly benefit from sparse solutions. Unfortunately, there are very few works considering sparse versions of the classic factor analysis. Our goal is to contribute further in this direction...
July 13, 2017: Psychometrika
Hailemichael M Worku, Mark De Rooij
The ideal point classification (IPC) model was originally proposed for analysing multinomial data in the presence of predictors. In this paper, we studied properties of the IPC model for analysing bivariate binary data with a specific focus on three quantities: (1) the marginal probabilities; (2) the association structure between the two binary responses; and (3) the joint probabilities. We found that the IPC model with a specific class point configuration represents either the marginal probabilities or the association structure...
June 13, 2017: Psychometrika
So Yeon Chun, Michael W Browne, Alexander Shapiro
Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness of fit of a model under analysis. One of the most popular test statistics used in covariance structure analysis is the asymptotically distribution-free (ADF) test statistic introduced by Browne (Br J Math Stat Psychol 37:62-83, 1984). The ADF statistic can be used to test models without any specific distribution assumption (e...
June 8, 2017: Psychometrika
Michel Tenenhaus, Arthur Tenenhaus, Patrick J F Groenen
A new framework for sequential multiblock component methods is presented. This framework relies on a new version of regularized generalized canonical correlation analysis (RGCCA) where various scheme functions and shrinkage constants are considered. Two types of between block connections are considered: blocks are either fully connected or connected to the superblock (concatenation of all blocks). The proposed iterative algorithm is monotone convergent and guarantees obtaining at convergence a stationary point of RGCCA...
May 23, 2017: Psychometrika
Blakeley B McShane, Ulf Böckenholt
We introduce multilevel multivariate meta-analysis methodology designed to account for the complexity of contemporary psychological research data. Our methodology directly models the observations from a set of studies in a manner that accounts for the variation and covariation induced by the facts that observations differ in their dependent measures and moderators and are nested within, for example, papers, studies, groups of subjects, and study conditions. Our methodology is motivated by data from papers and studies of the choice overload hypothesis...
May 19, 2017: Psychometrika
Po-Hsien Huang
Model selection is a popular strategy in structural equation modeling (SEM). To select an "optimal" model, many selection criteria have been proposed. In this study, we derive the asymptotics of several popular selection procedures in SEM, including AIC, BIC, the RMSEA, and a two-stage rule for the RMSEA (RMSEA-2S). All of the results are derived under weak distributional assumptions and can be applied to a wide class of discrepancy functions. The results show that both AIC and BIC asymptotically select a model with the smallest population minimum discrepancy function (MDF) value regardless of nested or non-nested selection, but only BIC could consistently choose the most parsimonious one under nested model selection...
April 26, 2017: Psychometrika
Michelle M LaMar
Within-task actions can provide additional information on student competencies but are challenging to model. This paper explores the potential of using a cognitive model for decision making, the Markov decision process, to provide a mapping between within-task actions and latent traits of interest. Psychometric properties of the model are explored, and simulation studies report on parameter recovery within the context of a simple strategy game. The model is then applied to empirical data from an educational game...
April 26, 2017: Psychometrika
Steffen Grønneberg, Njål Foldnes
We propose a new and flexible simulation method for non-normal data with user-specified marginal distributions, covariance matrix and certain bivariate dependencies. The VITA (VIne To Anything) method is based on regular vines and generalizes the NORTA (NORmal To Anything) method. Fundamental theoretical properties of the VITA method are deduced. Two illustrations demonstrate the flexibility and usefulness of VITA in the context of structural equation models. R code for the implementation is provided.
April 24, 2017: Psychometrika
Laura Bocci, Donatella Vicari
A Generalized INDCLUS model, termed GINDCLUS, is presented for clustering three-way two-mode proximity data. In order to account for the heterogeneity of the data, both a partition of the subjects into homogeneous classes and a covering of the objects into groups are simultaneously determined. Furthermore, the availability of information which is external to the three-way data is exploited to better account for such heterogeneity: the weights of both classifications are linearly linked to external variables allowing for the identification of meaningful classes of subjects and groups of objects...
June 2017: Psychometrika
Cristina Mollica, Luca Tardella
The elicitation of an ordinal judgment on multiple alternatives is often required in many psychological and behavioral experiments to investigate preference/choice orientation of a specific population. The Plackett-Luce model is one of the most popular and frequently applied parametric distributions to analyze rankings of a finite set of items. The present work introduces a Bayesian finite mixture of Plackett-Luce models to account for unobserved sample heterogeneity of partially ranked data. We describe an efficient way to incorporate the latent group structure in the data augmentation approach and the derivation of existing maximum likelihood procedures as special instances of the proposed Bayesian method...
June 2017: Psychometrika
Michael Sobel, David Madigan, Wei Wang
We construct a framework for meta-analysis and other multi-level data structures that codifies the sources of heterogeneity between studies or settings in treatment effects and examines their implications for analyses. The key idea is to consider, for each of the treatments under investigation, the subject's potential outcome in each study or setting were he to receive that treatment. We consider four sources of heterogeneity: (1) response inconsistency, whereby a subject's response to a given treatment would vary across different studies or settings, (2) the grouping of nonequivalent treatments, where two or more treatments are grouped and treated as a single treatment under the incorrect assumption that a subject's responses to the different treatments would be identical, (3) nonignorable treatment assignment, and (4) response-related variability in the composition of subjects in different studies or settings...
June 2017: Psychometrika
Jimmy de la Torre, Chia-Yi Chiu
This rejoinder responds to the commentary by Liu (Psychometrika, 2015) entitled "On the consistency of Q-matrix estimation: A commentary" on the paper "A general method of empirical Q-matrix validation" by de la Torre and Chiu (Psychometrika, 2015). It discusses and addresses three concerns raised in the commentary, namely the estimation accuracy when a provisional Q-matrix is used, the consistency of the Q-matrix estimator, and the computational efficiency of the proposed method.
June 2017: Psychometrika
Ji Yeh Choi, Heungsun Hwang, Michio Yamamoto, Kwanghee Jung, Todd S Woodward
Functional principal component analysis (FPCA) and functional multiple-set canonical correlation analysis (FMCCA) are data reduction techniques for functional data that are collected in the form of smooth curves or functions over a continuum such as time or space. In FPCA, low-dimensional components are extracted from a single functional dataset such that they explain the most variance of the dataset, whereas in FMCCA, low-dimensional components are obtained from each of multiple functional datasets in such a way that the associations among the components are maximized across the different sets...
June 2017: Psychometrika
Steffen Nestler, Mitja D Back
Whether, when, and why perceivers are able to accurately infer the personality traits of other individuals is a key topic in psychological science. Studies examining this question typically ask a number of perceivers to judge a number of targets with regard to a specific trait. The resulting data are then analyzed by averaging the judgments across perceivers or by computing the respective statistic for each single perceiver. Here, we discuss the limitations of the average-perceiver and single-perceiver approaches...
June 2017: Psychometrika
Jingchen Liu
This commentary concerns the theoretical properties of the estimation procedure in "A General Method of Empirical Q-matrix Validation" by Jimmy de la Torre and Chia-Yi Chiu. It raises the consistency issue of the estimator, proposes some modifications to it, and also makes some conjectures.
June 2017: Psychometrika
Po-Hsien Huang, Hung Chen, Li-Jen Weng
A penalized likelihood (PL) method for structural equation modeling (SEM) was proposed as a methodology for exploring the underlying relations among both observed and latent variables. Compared to the usual likelihood method, PL includes a penalty term to control the complexity of the hypothesized model. When the penalty level is appropriately chosen, the PL can yield an SEM model that balances the model goodness-of-fit and model complexity. In addition, the PL results in a sparse estimate that enhances the interpretability of the final model...
April 17, 2017: Psychometrika
Alwin Stegeman
A new model for simultaneous component analysis (SCA) is introduced that contains the existing SCA models with common loading matrix as special cases. The new SCA-T3 model is a multi-set generalization of the Tucker3 model for component analysis of three-way data. For each mode (observational units, variables, sets) a different number of components can be chosen and the obtained solution can be rotated without loss of fit to facilitate interpretation. SCA-T3 can be fitted on centered multi-set data and also on the corresponding covariance matrices...
April 6, 2017: Psychometrika
J R Lockwood, Daniel F McCaffrey
This article considers the application of the simulation-extrapolation (SIMEX) method for measurement error correction when the error variance is a function of the latent variable being measured. Heteroskedasticity of this form arises in educational and psychological applications with ability estimates from item response theory models. We conclude that there is no simple solution for applying SIMEX that generally will yield consistent estimators in this setting. However, we demonstrate that several approximate SIMEX methods can provide useful estimators, leading to recommendations for analysts dealing with this form of error in settings where SIMEX may be the most practical option...
March 29, 2017: Psychometrika
Sacha Epskamp, Mijke Rhemtulla, Denny Borsboom
We introduce the network model as a formal psychometric model, conceptualizing the covariance between psychometric indicators as resulting from pairwise interactions between observable variables in a network structure. This contrasts with standard psychometric models, in which the covariance between test items arises from the influence of one or more common latent variables. Here, we present two generalizations of the network model that encompass latent variable structures, establishing network modeling as parts of the more general framework of structural equation modeling (SEM)...
March 13, 2017: Psychometrika
Elena A Erosheva, S McKay Curtis
This paper considers the reflection unidentifiability problem in confirmatory factor analysis (CFA) and the associated implications for Bayesian estimation. We note a direct analogy between the multimodality in CFA models that is due to all possible column sign changes in the matrix of loadings and the multimodality in finite mixture models that is due to all possible relabelings of the mixture components. Drawing on this analogy, we derive and present a simple approach for dealing with reflection in variance in Bayesian factor analysis...
March 13, 2017: Psychometrika
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