Variances Of Latent Variables Research Articles

Understanding the role of subpopulations and reliability in between-group studies.

The replication crisis has led to a renewed discussion about the impacts of measurement quality on the precision of psychology research. High measurement quality is associated with low measurement error, yet the role of reliability in the quality of experimental research is not always well understood. In this study, we attempt to understand the role of reliability through its relationship with power while focusing on between-group designs for experimental studies. We outline a latent variable framework to investigate this nuanced relationship through equations. An under-evaluated aspect of the relationship is the variance and homogeneity of the subpopulation from which the study sample is drawn. Higher homogeneity implies a lower reliability, but yields higher power. We proceed to demonstrate the impact of this relationship between reliability and power by imitating different scenarios of large-scale replications with between-group designs. We find negative correlations between reliability and power when there are sizable differences in the latent variable variance and negligible differences in the other parameters across studies. Finally, we analyze the data from the replications of the ego depletion effect (Hagger et al., 2016) and the replications of the grammatical aspect effect (Eerland et al., 2016), each time with between-group designs, and the results align with previous findings. The applications show that a negative relationship between reliability and power is a realistic possibility with consequences for applied work. We suggest that more attention be given to the homogeneity of the subpopulation when study-specific reliability coefficients are reported in between-group studies.

The EV Scaling Method for Variances of Latent Variables

Abstract. The paper describes EV scaling for variances of latent variables included in confirmatory factor models. EV-scaled variances can be achieved in two ways: the estimation of variance parameters based on adjusted factor loadings and alternatively the summation of squared factor loadings obtained under the condition that the variance parameter is set equal to one. By definition, the second procedure yields values that are always positive. EV-scaled variances of latent variables show sizes similar to eigenvalues. The outcome of applying this scaling method is demonstrated in empirical data. The results of a simulation study reveal that the outcomes of the two ways virtually always correspond if the data are generated to include the contribution of a latent source. If there is no such source, the exclusion of solutions with negative error variances virtually always leads to correspondence.

Estimating Optimal Weights for Compound Scores: A Multidimensional IRT Approach

A method is proposed for constructing indices as linear functions of variables such that the reliability of the compound score is maximized. Reliability is defined in the framework of latent variable modeling [i.e., item response theory (IRT)] and optimal weights of the components of the index are found by maximizing the posterior variance relative to the total latent variable variance. Three methods for estimating the weights are proposed. The first is a likelihood-based approach, that is, marginal maximum likelihood (MML). The other two are Bayesian approaches based on Markov chain Monte Carlo (MCMC) computational methods. One is based on an augmented Gibbs sampler specifically targeted at IRT, and the other is based on a general purpose Gibbs sampler such as implemented in OpenBugs and Jags. Simulation studies are presented to demonstrate the procedure and to compare the three methods. Results are very similar, so practitioners may be suggested the use of the easily accessible latter method. A real-data set pertaining to the 28-joint Disease Activity Score is used to show how the methods can be applied in a complex measurement situation with multiple time points and mixed data formats.

Can Variances of Latent Variables be Scaled in Such a Way That They Correspond to Eigenvalues?

The paper reports an investigation of whether sums of squared factor loadings obtained in confirmatory factor analysis correspond to eigenvalues of exploratory factor analysis. The sum of squared factor loadings reflects the variance of the corresponding latent variable if the variance parameter of the confirmatory factor model is set equal to one. Hence, the computation of the sum implies a specific type of scaling of the variance. While the investigation of the theoretical foundations suggested the expected correspondence between sums of squared factor loadings and eigenvalues, the necessity of procedural specifications in the application, as for example the estimation method, revealed external influences on the outcome. A simulation study was conducted that demonstrated the possibility of exact correspondence if the same estimation method was applied. However, in the majority of realized specifications the estimates showed similar sizes but no correspondence.

Simplificación del gradiente de la función de máxima verosimilitud del análisis factorial confirmatorio

En este artículo se presenta el proceso de simplificación del gradiente de la función de máxima verosimilitud, utilizada en la estimación del Análisis Factorial Confirmatorio. El gradiente obtenido se presenta en función de las matrices tradicionales del AFC: Λ, Φ y Θε (coeficientes de regresión, varianzas de las variables latentes y varianzas de los errores). Esta simplificación se realizó mediante las leyes de derivación de matrices y permitió obtener una expresión para el gradiente de fácil programación.

The World of Assessment: How Simple Is It?

The World of Assessment: How Simple Is It?

Scaling Variances of Latent Variables by Standardizing Loadings: Applications to Working Memory and the Position Effect

The standardization of loadings gives a metric to the corresponding latent variable and thus scales the variance of this latent variable. By assigning an appropriately estimated weight to all the loadings on the same latent variable it can be achieved that the average squared loading is 1 as the result of standardization. As a consequence, there is comparability of the variances of the latent variables of a confirmatory factor model. A precondition of comparability is that the latent variables must have loadings of the same manifest variables and that the variances are estimated with respect to the same covariance matrix. The usefulness of this standardization method is demonstrated by applying it for the evaluation of the sources of performance in a working memory task and for the evaluation of the impact of the position effect on performance in completing a reasoning measure. In these examples the scaled variances of the latent variables provided useful information.

Improving the Interpretability of the Variances of Latent Variables by Uniform and Factor-Specific Standardizations of Loadings

The variances of latent variables are presented as statistics that support the evaluation of a model in confirmatory factor analysis. Appropriate standardization even improves the benefit of investigating variances. The variances integrate the information concerning the individual loadings and are associated with an error probability. The estimation of the variances of latent variables requires the estimation of the loadings in the first step and their replacement by constraints according to the estimates in the second step. Uniform or factor-specific standardization is necessary for achieving comparability of the variances. The usefulness of standardization is demonstrated in models from optimism research. Three ways of standardization were considered: uniform standardization, factor-specific standardization, and standardization by setting one loading equal to one. Generally valid results were achieved by uniform standardization. If some loadings were set equal to zero, factor-specific standardization even yielded better results. The results of the remaining way were very specific.

Construct Equivalence of a National Certification Examination That Uses Dual Languages and Audio Assistance

This study used confirmatory factor analysis (CFA) to examine the comparability of the National Nurse Aide Assessment Program (NNAAP™) test scores across language and administration condition groups for calibration and validation samples that were randomly drawn from the same population. Fit statistics supported both the calibration and validation samples in language and administration condition groups. Furthermore, evidence of the invariance of factor structure of the NNAAP™ scores across language and administration groups was found in all fit statistics when model structure, factor loading, and latent variable variance were constrained to be equal across groups, except unique variance. Thus, the results suggested that this construct was similarly structured (fair) across different language and administration condition groups.

Bootstrapping and the identification of exogenous latent variables within structural equation models

In traditional applications of latent variable models, each exogenous latent variable must either have its variance parameter fixed or a loading path to a measured indicator variable fixed (either customarily to 1). Without doing so the measurement model will suffer from underidentification, thereby yielding no unique solution when estimating the parameters of interest. The choice of whether to fix the variance or the loading is somewhat arbitrary, guided primarily by the researcher's need for inference regarding particular parameters within the model. Under conditions of multivariate nonnormal data, the method by which one makes identified the measurement of exogenous latent variables may not be as arbitrary. Specifically, as addressed briefly by Arbuckle (1997), when one is utilizing a bootstrapping approach for generating empirical standard errors for parameters of interest, the researcher must choose to fix an indicator path rather than the latent variable variance in order for the empirical standard errors to be gensrated properly. This article offers an illustrative explanation of why such an approach is necessary. Given the increased attention toward bootstrapping techniques within structural equation modeling, our hope is that a greater awareness and understanding of this unique situation will be facilitated.

A quasi-score approach to the analysis of ordered categorical data via a mixed heteroskedastic threshold model

This article presents an extension of the methodology developed by Gilmour et al. (19), for ordered categorical data, taking into account the hetero- geneity of residual variances of latent variables. Heterogeneity of residual variances is described via a structural linear model on log-variances. This method involves ' two main steps: i) a 'marginalization' with respect to the random effects leading to quasi-score estimators; ii) an approximation of the variance-covariance matrix of the observations which leads to an analogue of the Henderson mixed model equations for continuous Gaussian data. This methodology is illustrated by a numerical example of footshape in sheep. © Inra/Elsevier, Paris