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Multivariate Behavioral Research

Daniel McNeish, Denis Dumas
Recent methodological work has highlighted the promise of nonlinear growth models for addressing substantive questions in the behavioral sciences. In this article, we outline a second-order nonlinear growth model in order to measure a critical notion in development and education: potential. Here, potential is conceptualized as having three components-ability, capacity, and availability-where ability is the amount of skill a student is estimated to have at a given timepoint, capacity is the maximum amount of ability a student is predicted to be able to develop asymptotically, and availability is the difference between capacity and ability at any particular timepoint...
December 2, 2016: Multivariate Behavioral Research
Okan Bulut, Mark L Davison, Michael C Rodriguez
Subscores are of increasing interest in educational and psychological testing due to their diagnostic function for evaluating examinees' strengths and weaknesses within particular domains of knowledge. Previous studies about the utility of subscores have mostly focused on the overall reliability of individual subscores and ignored the fact that subscores should be distinct and have added value over the total score. This study introduces a profile reliability approach that partitions the overall subscore reliability into within-person and between-person subscore reliability...
November 29, 2016: Multivariate Behavioral Research
E L Hamaker, N K Schuurman, E A O Zijlmans
In this article, we show that the underlying dimensions obtained when factor analyzing cross-sectional data actually form a mix of within-person state dimensions and between-person trait dimensions. We propose a factor analytical model that distinguishes between four independent sources of variance: common trait, unique trait, common state, and unique state. We show that by testing whether there is weak factorial invariance across the trait and state factor structures, we can tackle the fundamental question first raised by Cattell; that is, are within-person state dimensions qualitatively the same as between-person trait dimensions? Furthermore, we discuss how this model is related to other trait-state factor models, and we illustrate its use with two empirical data sets...
November 23, 2016: Multivariate Behavioral Research
Sunmee Kim, Ji Yeh Choi, Heungsun Hwang
Multiple correspondence analysis (MCA) is a useful tool for investigating the interrelationships among dummy-coded categorical variables. MCA has been combined with clustering methods to examine whether there exist heterogeneous subclusters of a population, which exhibit cluster-level heterogeneity. These combined approaches aim to classify either observations only (one-way clustering of MCA) or both observations and variable categories (two-way clustering of MCA). The latter approach is favored because its solutions are easier to interpret by providing explicitly which subgroup of observations is associated with which subset of variable categories...
November 21, 2016: Multivariate Behavioral Research
Steven P Reise, Dale S Kim, Maxwell Mansolf, Keith F Widaman
Although the structure of the Rosenberg Self-Esteem Scale (RSES) has been exhaustively evaluated, questions regarding dimensionality and direction of wording effects continue to be debated. To shed new light on these issues, we ask (a) for what percentage of individuals is a unidimensional model adequate, (b) what additional percentage of individuals can be modeled with multidimensional specifications, and (c) what percentage of individuals respond so inconsistently that they cannot be well modeled? To estimate these percentages, we applied iteratively reweighted least squares (IRLS) to examine the structure of the RSES in a large, publicly available data set...
November 11, 2016: Multivariate Behavioral Research
Heining Cham, Evgeniya Reshetnyak, Barry Rosenfeld, William Breitbart
Researchers have developed missing data handling techniques for estimating interaction effects in multiple regression. Extending to latent variable interactions, we investigated full information maximum likelihood (FIML) estimation to handle incompletely observed indicators for product indicator (PI) and latent moderated structural equations (LMS) methods. Drawing on the analytic work on missing data handling techniques in multiple regression with interaction effects, we compared the performance of FIML for PI and LMS analytically...
November 11, 2016: Multivariate Behavioral Research
Jeffrey R Harring, Shelley A Blozis
Nonlinear mixed-effects (NLME) models are used when analyzing continuous repeated measures data taken on each of a number of individuals where the focus is on characteristics of complex, nonlinear individual change. Challenges with fitting NLME models and interpreting analytic results have been well documented in the statistical literature. However, parameter estimates as well as fitted functions from NLME analyses in recent articles have been misinterpreted, suggesting the need for clarification of these issues before these misconceptions become fact...
November 11, 2016: Multivariate Behavioral Research
Miao Yang, Ke-Hai Yuan
Moderation analysis has many applications in social sciences. Most widely used estimation methods for moderation analysis assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the results from a classical moderation analysis can be misleading. For more reliable moderation analysis, this article proposes two robust methods with a two-level regression model when the predictors do not contain measurement error. One method is based on maximum likelihood with Student's t distribution and the other is based on M-estimators with Huber-type weights...
November 2, 2016: Multivariate Behavioral Research
Mark H C Lai, Oi-Man Kwok
Although previous research has discussed an effect size estimator for partially nested cluster randomized designs, the existing estimator (a) is not efficient when used with primary data, (b) can be biased when the homogeneity of variance assumption is violated, and (c) has not yet been empirically evaluated for its finite sample properties. The present paper addresses these limitations by proposing an alternative maximum likelihood estimator for obtaining standardized mean difference effect size and the corresponding sampling variance for partially nested data, as well as the variants that do not make an assumption of homogeneity of variance...
November 1, 2016: Multivariate Behavioral Research
Patrick Mair, Ingwer Borg, Thomas Rusch
Judging goodness of fit in multidimensional scaling requires a comprehensive set of diagnostic tools instead of relying on stress rules of thumb. This article elaborates on corresponding strategies and gives practical guidelines for researchers to obtain a clear picture of the goodness of fit of a solution. Special emphasis will be placed on the use of permutation tests. The second part of the article focuses on goodness-of-fit assessment of an important variant of multidimensional scaling called unfolding, which can be applied to a broad range of psychological data settings...
November 1, 2016: Multivariate Behavioral Research
Daniel McNeish
For mixed models generally, it is well known that modeling data with few clusters will result in biased estimates, particularly of the variance components and fixed effect standard errors. In linear mixed models, small sample bias is typically addressed through restricted maximum likelihood estimation (REML) and a Kenward-Roger correction. Yet with binary outcomes, there is no direct analog of either procedure. With a larger number of clusters, estimation methods for binary outcomes that approximate the likelihood to circumvent the lack of a closed form solution such as adaptive Gaussian quadrature and the Laplace approximation have been shown to yield less-biased estimates than linearization estimation methods that instead linearly approximate the model...
November 1, 2016: Multivariate Behavioral Research
Eun Sook Kim, Robert F Dedrick, Chunhua Cao, John M Ferron
We provide reporting guidelines for multilevel factor analysis (MFA) and use these guidelines to systematically review 72 MFA applications in journals across a range of disciplines (e.g., education, health/nursing, management, and psychology) published between 1994 and 2014. Results are organized in terms of the (a) characteristics of the MFA application (e.g., construct measured), (b) purpose (e.g., measurement validation), (c) data source (e.g., number of cases at Level 1 and Level 2), (d) statistical approach (e...
October 18, 2016: Multivariate Behavioral Research
Jolynn Pek, R Philip Chalmers, Georges Monette
When statistical models are employed to provide a parsimonious description of empirical relationships, the extent to which strong conclusions can be drawn rests on quantifying the uncertainty in parameter estimates. In multiple linear regression (MLR), regression weights carry two kinds of uncertainty represented by confidence sets (CSs) and exchangeable weights (EWs). Confidence sets quantify uncertainty in estimation whereas the set of EWs quantify uncertainty in the substantive interpretation of regression weights...
October 18, 2016: Multivariate Behavioral Research
Machteld Vandecandelaere, Stijn Vansteelandt
This rejoinder, in response to the commentaries of Steiner, Park, and Kim (this issue) and Reshetnyak, Cham, and Hughes (this issue), discusses remaining challenges in grade retention research. First, a same-age comparison assumes that the instruments used in different grades measure ability equally well. We discuss the importance of evaluating the properties of the scaling process to address whether this assumption has been met. Second, we discuss issues in the selection of covariates to be included in the weights...
October 12, 2016: Multivariate Behavioral Research
Matthew S Fritz, David A Kenny, David P MacKinnon
Mediation analysis requires a number of strong assumptions be met in order to make valid causal inferences. Failing to account for violations of these assumptions, such as not modeling measurement error or omitting a common cause of the effects in the model, can bias the parameter estimates of the mediated effect. When the independent variable is perfectly reliable, for example when participants are randomly assigned to levels of treatment, measurement error in the mediator tends to underestimate the mediated effect, while the omission of a confounding variable of the mediator-to-outcome relation tends to overestimate the mediated effect...
September 2016: Multivariate Behavioral Research
Dereje W Gudicha, Verena D Schmittmann, Fetene B Tekle, Jeroen K Vermunt
The latent Markov (LM) model is a popular method for identifying distinct unobserved states and transitions between these states over time in longitudinally observed responses. The bootstrap likelihood-ratio (BLR) test yields the most rigorous test for determining the number of latent states, yet little is known about power analysis for this test. Power could be computed as the proportion of the bootstrap p values (PBP) for which the null hypothesis is rejected. This requires performing the full bootstrap procedure for a large number of samples generated from the model under the alternative hypothesis, which is computationally infeasible in most situations...
September 2016: Multivariate Behavioral Research
Maxwell Mansolf, Steven P Reise
Analytic bifactor rotations have been recently developed and made generally available, but they are not well understood. The Jennrich-Bentler analytic bifactor rotations (bi-quartimin and bi-geomin) are an alternative to, and arguably an improvement upon, the less technically sophisticated Schmid-Leiman orthogonalization. We review the technical details that underlie the Schmid-Leiman and Jennrich-Bentler bifactor rotations, using simulated data structures to illustrate important features and limitations. For the Schmid-Leiman, we review the problem of inaccurate parameter estimates caused by the linear dependencies, sometimes called "proportionality constraints," that are required to expand a p correlated factors solution into a (p + 1) (bi)factor space...
September 2016: Multivariate Behavioral Research
Jana Holtmann, Tobias Koch, Katharina Lochner, Michael Eid
Multilevel structural equation models are increasingly applied in psychological research. With increasing model complexity, estimation becomes computationally demanding, and small sample sizes pose further challenges on estimation methods relying on asymptotic theory. Recent developments of Bayesian estimation techniques may help to overcome the shortcomings of classical estimation techniques. The use of potentially inaccurate prior information may, however, have detrimental effects, especially in small samples...
September 2016: Multivariate Behavioral Research
Han Du, Lijuan Wang
In conventional frequentist power analysis, one often uses an effect size estimate, treats it as if it were the true value, and ignores uncertainty in the effect size estimate for the analysis. The resulting sample sizes can vary dramatically depending on the chosen effect size value. To resolve the problem, we propose a hybrid Bayesian power analysis procedure that models uncertainty in the effect size estimates from a meta-analysis. We use observed effect sizes and prior distributions to obtain the posterior distribution of the effect size and model parameters...
September 2016: Multivariate Behavioral Research
Peter M Steiner, Soojin Park, Yongnam Kim
This commentary discusses causal estimands of same-age and same-grade comparisons for assessing grade-retention effects on student ability and performance. Using potential outcomes notation, we show that same-age and same-grade comparisons refer to different retention-promotion contrasts and therefore assess different causal questions. We also comment on deleting versus censoring records of students who dropped out of the study or do not belong to the treatment regimes under investigation. Whereas deleting entire student records potentially induces collider bias, censoring circumvents bias if censoring is ignorable given the observed pretreatment covariates...
August 19, 2016: Multivariate Behavioral Research
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