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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
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
Bhargab Chattopadhyay, Ken Kelley
The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation...
August 11, 2016: Multivariate Behavioral Research
Dylan Molenaar, Daniel Oberski, Jeroen Vermunt, Paul De Boeck
Current approaches to model responses and response times to psychometric tests solely focus on between-subject differences in speed and ability. Within subjects, speed and ability are assumed to be constants. Violations of this assumption are generally absorbed in the residual of the model. As a result, within-subject departures from the between-subject speed and ability level remain undetected. These departures may be of interest to the researcher as they reflect differences in the response processes adopted on the items of a test...
August 11, 2016: Multivariate Behavioral Research
Evgeniya Reshetnyak, Heining Cham, Jan N Hughes
Vandecandelaere, Vansteelandt, De Fraine, and Van Damme (this issue) described marginal structural modeling (MSM) and used it to estimate the effects of a time-varying intervention, retention (holding back) in school grades, on students' math achievement. This commentary supplements Vandecandelaere et al. (this issue) and discusses several topics in retention studies and MSM. First, we discuss the importance of equating time-varying confounders in retention studies. Second, we discuss same-grade and same-age comparisons in retention studies...
August 2, 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
Emilie M Shireman, Douglas Steinley, Michael J Brusco
It is common knowledge that mixture models are prone to arrive at locally optimal solutions. Typically, researchers are directed to utilize several random initializations to ensure that the resulting solution is adequate. However, it is unknown what factors contribute to a large number of local optima and whether these coincide with the factors that reduce the accuracy of a mixture model. A real-data illustration and a series of simulations are presented that examine the effect of a variety of data structures on the propensity of local optima and the classification quality of the resulting solution...
July 2016: Multivariate Behavioral Research
Dirk Lubbe, Christof Schuster
A novel factor-analytic model-the differential discrimination model-for assessing individual differences in scale use has been recently introduced, together with a three-stage estimation approach for model fitting. Unfortunately, the second-stage estimator and, as a consequence, the third-stage estimator of this procedure are not consistent. In this article we show that (a) the differential discrimination model can be expressed in a structural equation model framework, and (b) consistent and simultaneous estimation of all model parameters can be achieved using standard SEM software...
July 2016: Multivariate Behavioral Research
Niels G Waller
For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives...
July 2016: Multivariate Behavioral Research
Insu Paek, Zhen Li, Hyun-Jeong Park
When categorical ordinal item response data are collected over multiple timepoints from a repeated measures design, an item response theory (IRT) modeling approach whose unit of analysis is an item response is suitable. This study proposes a few longitudinal IRT models and illustrates how a popular compensatory multidimensional IRT model can be utilized to formulate such longitudinal IRT models, which permits an investigation of ability growth at both individual and population levels. The equivalence of an existing multidimensional IRT model and those longitudinal IRT models is also elaborated so that one can make use of an existing multidimensional IRT model to implement the longitudinal IRT models...
July 2016: Multivariate Behavioral Research
Zhao-Hua Lu, Sy-Miin Chow, Eric Loken
Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor-loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, Muthén & Asparouhov proposed a Bayesian structural equation modeling (BSEM) approach to explore the presence of cross loadings in CFA models. We show that the issue of determining factor-loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov's approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP)...
July 2016: Multivariate Behavioral Research
Jean-Paul Fox, Sukaesi Marianti
With computerized testing, it is possible to record both the responses of test takers to test questions (i.e., items) and the amount of time spent by a test taker in responding to each question. Various models have been proposed that take into account both test-taker ability and working speed, with the many models assuming a constant working speed throughout the test. The constant working speed assumption may be inappropriate for various reasons. For example, a test taker may need to adjust the pace due to time mismanagement, or a test taker who started out working too fast may reduce the working speed to improve accuracy...
July 2016: Multivariate Behavioral Research
Daniel McNeish, Laura M Stapleton
Small-sample inference with clustered data has received increased attention recently in the methodological literature, with several simulation studies being presented on the small-sample behavior of many methods. However, nearly all previous studies focus on a single class of methods (e.g., only multilevel models, only corrections to sandwich estimators), and the differential performance of various methods that can be implemented to accommodate clustered data with very few clusters is largely unknown, potentially due to the rigid disciplinary preferences...
July 2016: Multivariate Behavioral Research
Kimberly A Barchard, Vincent Brouwers
Researchers now know that when theoretical reliability increases, power can increase, decrease, or stay the same. However, no analytic research has examined the relationship of power to the most commonly used type of reliability-internal consistency-and the most commonly used measures of internal consistency, coefficient alpha and ICC(A,k). We examine the relationship between the power of independent samples t tests and internal consistency. We explicate the mathematical model upon which researchers usually calculate internal consistency, one in which total scores are calculated as the sum of observed scores on K measures...
July 2016: Multivariate Behavioral Research
Niels G Waller, Colin G DeYoung, Thomas J Bouchard
Tellegen and Waller advocated a complex and time-consuming scale construction method that they called "exploratory test construction." Scales that are constructed by this method-such as the Multidimensional Personality Questionnaire (MPQ)-are presumed to be more "psychologically coherent" and "robust" than scales constructed by other means. Using a novel procedure that we call the "recaptured scale technique," we tested this conjecture by conducting a megafactor analysis on data from the 411 adult participants of the Minnesota Study of Twins Reared Apart who completed the MPQ, the MMPI, and the CPI...
July 2016: Multivariate Behavioral Research
Kristof Vansteelandt, Geert Verbeke
Affective instability, the tendency to experience emotions that fluctuate frequently and intensively over time, is a core feature of several mental disorders including borderline personality disorder. Currently, affect is often measured with Ecological Momentary Assessment protocols, which yield the possibility to quantify the instability of affect over time. A number of linear mixed models are proposed to examine (diagnostic) group differences in affective instability. The models contribute to the existing literature by estimating simultaneously both the variance and serial dependency component of affective instability when observations are unequally spaced in time with the serial autocorrelation (or emotional inertia) declining as a function of the time interval between observations...
July 2016: Multivariate Behavioral Research
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