Examining the Dynamic of Clustering Effects in Multilevel Designs: A Latent Variable Method Application.

This note is concerned with the study of temporal development in several indices reflecting clustering effects in multilevel designs that are frequently utilized in educational and behavioral research. A latent variable method-based approach is outlined, which can be used to point and interval estimate the growth or decline in important functions of level-specific variances in two-level and three-level settings. The procedure may also be employed for the purpose of examining stability over time in clustering effects.

Can One Pool Over Site in a Multi-Site Study With Categorical Item Measuring Instruments?: A Multiple Testing Procedure.

We outline a procedure for examining collapsibility over site in multiple-location settings that are frequently utilized in contemporary educational and behavioral research. The method is based on a test of cross-site identity of the response distributions of polytomous items in multi-component measuring instruments, which implies the possibility to pool over study location. The approach is readily applicable in empirical studies using popular and widely circulated software and is generalizable to various types of items.

Studying Factorial Invariance With Nominal Items: A Note on a Latent Variable Modeling Procedure.

A latent variable modeling procedure for studying factorial invariance and differential item functioning for multi-component measuring instruments with nominal items is discussed. The method is based on a multiple testing approach utilizing the false discovery rate concept and likelihood ratio tests. The procedure complements the Revuelta, Franco-Martinez, and Ximenez approach to factorial invariance examination, and permits localization of individual invariance violations.

A Note on Evaluation of Polytomous Item Locations With the Rating Scale Model and Testing Its Fit.

A procedure is outlined for point and interval estimation of location parameters associated with polytomous items, or raters assessing studied subjects or cases, which follow the rating scale model. The method is developed within the framework of latent variable modeling, and is readily applied in empirical research using popular software. The approach permits testing the goodness of fit of this widely used model, which represents a rather parsimonious item response theory model as a means of description and explanation of an analyzed data set.

On Latent Structure Examination of Behavioral Measuring Instruments in Complex Empirical Settings.

A multiple-step procedure is outlined that can be used for examining the latent structure of behavior measurement instruments in complex empirical settings. The method permits one to study their latent structure after assessing the need to account for clustering effects and the necessity of its examination within individual levels of fixed factors, such as gender or group membership of substantive relevance. The approach is readily applicable with binary or binary-scored items using popular and widely available software.

On the Benefits of Using Maximal Reliability in Educational and Behavioral Research.

This note is concerned with the benefits that can result from the use of the maximal reliability and optimal linear combination concepts in educational and psychological research. Within the widely used framework of unidimensional multi-component measuring instruments, it is demonstrated that the linear combination of their components that possesses the highest possible reliability can exhibit a level of consistency considerably exceeding that of their overall sum score that is nearly routinely employed in contemporary empirical research. This optimal linear combination can be particularly useful in circumstances where one or more scale components are associated with relatively large error variances, but their removal from the instrument can lead to a notable loss in validity due to construct underrepresentation.

A Note on Comparing the Bifactor and Second-Order Factor Models: Is the Bayesian Information Criterion a Routinely Dependable Index for Model Selection?

This note demonstrates that the widely used Bayesian Information Criterion (BIC) need not be generally viewed as a routinely dependable index for model selection when the bifactor and second-order factor models are examined as rival means for data description and explanation. To this end, we use an empirically relevant setting with multidimensional measuring instrument components, where the bifactor model is found consistently inferior to the second-order model in terms of the BIC even though the data on a large number of replications at different sample sizes were generated following the bifactor model. We therefore caution researchers that routine reliance on the BIC for the purpose of discriminating between these two widely used models may not always lead to correct decisions with respect to model choice.

On the Importance of Coefficient Alpha for Measurement Research: Loading Equality Is Not Necessary for Alpha's Utility as a Scale Reliability Index.

The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be arbitrarily small in any considered population and hence practically ignorable. In addition, the set of parameter values where this discrepancy is negligible is shown to possess the same dimensionality as that of the underlying model parameter space.

Design Effect in Multilevel Settings: A Commentary on a Latent Variable Modeling Procedure for Its Evaluation.

A latent variable modeling-based procedure is discussed that permits to readily point and interval estimate the design effect index in multilevel settings using widely circulated software. The method provides useful information about the relationship of important parameter standard errors when accounting for clustering effects relative to conducting single-level analyses. The approach can also be employed as an addendum to point and interval estimation of the intraclass correlation coefficient in empirical research.

Evaluation of Second- and Third-Level Variance Proportions in Multilevel Designs With Completely Observed Populations: A Note on a Latent Variable Modeling Procedure.

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity of large-scale studies in these and cognate disciplines. The present note discusses a readily applicable procedure for point-and-interval estimation of the proportions of second- and third-level variances in such multilevel settings, which may also be employed in model choice considerations regarding ensuing analyses for response variables of interest.

On the Relationship Between Item Stem Formulation and Criterion Validity of Multiple-Component Measuring Instruments.

The possible dependency of criterion validity on item formulation in a multicomponent measuring instrument is examined. The discussion is concerned with evaluation of the differences in criterion validity between two or more groups (populations/subpopulations) that have been administered instruments with items having differently formulated item stems. The case of complex item stems involving two stimuli description sentences (double-barreled questions) is thereby compared with the setting where items contained a single sentence.

Model Selection and Average Proportion Explained Variance in Exploratory Factor Analysis.

A procedure for evaluating the average -squared index for a given set of observed variables in an exploratory factor analysis model is discussed. The method can be used as an effective aid in the process of model choice with respect to the number of factors underlying the interrelationships among studied measures. The approach is developed within the framework of exploratory structural equation modeling and is readily applicable with popular statistical software.

Evaluating Restrictive Models in Educational and Behavioral Research: Local Misfit Overrides Model Tenability.

The frequent practice of overall fit evaluation for latent variable models in educational and behavioral research is reconsidered. It is argued that since overall plausibility does not imply local plausibility and is only necessary for the latter, local misfit should be considered a sufficient condition for model rejection, even in the case of omnibus model tenability. The argument is exemplified with a comparison of the widely used one-parameter and two-parameter logistic models.

On the Pitfalls of Estimating and Using Standardized Reliability Coefficients.

The population discrepancy between unstandardized and standardized reliability of homogeneous multicomponent measuring instruments is examined. Within a latent variable modeling framework, it is shown that the standardized reliability coefficient for unidimensional scales can be markedly higher than the corresponding unstandardized reliability coefficient, or alternatively substantially lower than the latter. Based on these findings, it is recommended that scholars avoid estimating, reporting, interpreting, or using standardized scale reliability coefficients in empirical research, unless they have strong reasons to consider standardizing the original components of utilized scales.

Examining Multidimensional Measuring Instruments for Proximity to Unidimensional Structure Using Latent Variable Modeling.

A widely applicable procedure of examining proximity to unidimensionality for multicomponent measuring instruments with multidimensional structure is discussed. The method is developed within the framework of latent variable modeling and allows one to point and interval estimate an explained variance proportion-based index that may be considered a measure of proximity to unidimensional structure. The approach is readily utilized in educational, behavioral, and social research when it is of interest to evaluate whether a more general structure scale, test, or measuring instrument could be treated as being associated with an approximately unidimensional latent structure for some empirical purposes.

On True Score Evaluation Using Item Response Theory Modeling.

Building on prior research on the relationships between key concepts in item response theory and classical test theory, this note contributes to highlighting their important and useful links. A readily and widely applicable latent variable modeling procedure is discussed that can be used for point and interval estimation of the individual person true score on any item in a unidimensional multicomponent measuring instrument or item set under consideration. The method adds to the body of research on the connections between classical test theory and item response theory.

Examining Validity-Related Correlations and Their Differences Under Assumption Violations.

A procedure for evaluation of validity related coefficients and their differences is discussed, which is applicable when one or more frequently used assumptions in empirical educational, behavioral and social research are violated. The method is developed within the framework of the latent variable modeling methodology and accomplishes point and interval estimation of convergent and discriminant correlations as well as differences between them in cases of incomplete data sets with data not missing at random, nonnormality, and clustering effects. The procedure uses the full information maximum likelihood approach to model fitting and parameter estimation, does not assume availability of multiple indicators for underlying latent constructs, includes auxiliary variables, and accounts for within-group correlations on main response variables resulting from nesting effects involving studied respondents.

A Method for Examining the Equating of Psychometric Scales and Tests: An Application Using Dementia Screening Test Batteries.

Equating of psychometric scales and tests is frequently required and conducted in educational, behavioral, and clinical research. Construct comparability or equivalence between measuring instruments is a necessary condition for making decisions about linking and equating resulting scores. This article is concerned with a widely applicable method for examining if two scales or tests cannot be equated.

On the Connections Between Item Response Theory and Classical Test Theory: A Note on True Score Evaluation for Polytomous Items via Item Response Modeling.

This note highlights and illustrates the links between item response theory and classical test theory in the context of polytomous items. An item response modeling procedure is discussed that can be used for point and interval estimation of the individual true score on any item in a measuring instrument or item set following the popular and widely applicable graded response model. The method contributes to the body of research on the relationships between classical test theory and item response theory and is illustrated on empirical data.

Evaluation of Variance Inflation Factors in Regression Models Using Latent Variable Modeling Methods.

A procedure that can be used to evaluate the variance inflation factors and tolerance indices in linear regression models is discussed. The method permits both point and interval estimation of these factors and indices associated with explanatory variables considered for inclusion in a regression model. The approach makes use of popular latent variable modeling software to obtain these point and interval estimates.