Tenko Raykov

Estimation of Composite Reliability for Congeneric Measures

A structural equation model is described that permits estimation of the reliability index and coefficient of a composite test for congeneric measures. The method is also helpful in exploring the factorial structure of an item set, and its use in scale reliability estimation and development is illustrated. The modeling. estimator of composite reliability it yields does not possess the general underestimation property of Cronbachs coefficient a.

Coefficient Alpha and Composite Reliability With Interrelated Nonhomogeneous Items

The relationship between Cronbachs coefficient alpha (a) and the reliability of a composite of a prespecified set of interrelated nonhomogeneous components is examined. It is shown that a can over- or underestimate scale reliability at the population level. The bias is expressed in terms of structural parameters and illustrated on simulated data. The relevance of substantive considerations about, and examination of, the latent structure of an item set prior to estimation of composite reliability using at is emphasized and demonstrated using a structural equation modeling approach.

Scale Reliability, Cronbach's Coefficient Alpha, and Violations of Essential Tau-Equivalence with Fixed Congeneric Components.

The population discrepancy between Cronbachs Coefficient Alpha and scale reliability with fixed congeneric measures, uncorrelated errors, and sampling of subjects is studied. This difference is expressed in terms of individual component violations of the assumption of essential T-equivalence that is necessary and sufficient for Alpha to equal composite reliability. An upper bound of the discrepancy is obtained and its magnitude assessed in practical contexts of informed scale development. As an alternative when the difference may be considerable, a latent variable model is recommended for estimating scale reliability.

Reliability of Scales With General Structure: Point and Interval Estimation Using a Structural Equation Modeling Approach

A method for obtaining point and interval estimates of reliability for composites of measures with a general structure is discussed. The approach is based on fitting a correspondingly constrained structural equation model and generalizes earlier covariance structure analysis methods for scale reliability estimation with congeneric tests. The procedure can be used with weighted or unweighted composites, in which the weights need not be known in advance but may be estimated simultaneously. The approach allows one also to obtain an approximate standard error and confidence interval for scale reliability using the bootstrap methodology.

Behavioral scale reliability and measurement invariance evaluation using latent variable modeling

A latent variable modeling approach to reliability and measurement invariance evaluation for multiple-component measuring instruments is outlined. An initial discussion deals with the limitations of coefficient alpha, a frequently used index of composite reliability. A widely and readily applicable structural modeling framework is next described that allows point and interval estimation of scale reliability. An easily employed procedure for testing measurement and reliability invariance in multiple population and longitudinal studies is then discussed. Unlike coefficient alpha that is in general a misestimator of scale reliability already at the population level, the article is based on the formal definition of the reliability coefficient, and its underlying modeling approach does not share alphas limitations. The described reliability and measurement invariance evaluation procedures are illustrated on a set of data resulting from a Social Interaction Anxiety Scale, and source codes for one of the most popular structural modeling programs, LISREL, are provided, which can be used to apply the outlined methods.

Estimation of congeneric scale reliability using covariance structure analysis with nonlinear constraints

A method of composite reliability estimation using covariance structure analysis with nonlinear constraints is outlined. To motivate the developments, initially a short overview of research is presented, demonstrating that in many cases the widely used coefficient alpha is an unsatisfactory index of scale reliability already at the population level. As an alternative, the proposed covariance structure analysis procedure is based on the theoretical formula of the scale reliability coefficient in terms of parameters pertaining to a given set of congeneric components. The described approach is illustrated with several numerical examples and its performance compared with that of coefficient alpha.

Bias of Coefficient afor Fixed Congeneric Measures with Correlated Errors

The population discrepancy of coefficient a from the composite reliability coefficient for fixed congeneric measures with correlated errors is studied and expressed in terms of parameters of the measures. Use of structural equation modeling methodology is recommended for identifying cases in which this discrepancy can be large. The findings are demonstrated across several empirical conditions in a scale construction context.

Analysis of Longitudinal Studies With Missing Data Using Covariance Structure Modeling With Full-Information Maximum Likelihood

A didactic discussion of covariance structure modeling in longitudinal studies with missing data is presented. Use of the full-information maximum likelihood method is considered for model fitting, parameter estimation, and hypothesis testing purposes, particularly when interested in patterns of temporal change as well as its covariates and predictors. The approach is illustrated with an application of the popular level-and-shape model to data from a cognitive intervention study of elderly adults.

Evaluation of Scale Reliability for Unidimensional Measures Using Latent Variable Modeling

This article outlines a readily and widely applicable procedure of reliability evaluation for scales with unidimensional measures. The method is developed within the framework of the popular latent variable modeling methodology, and it accomplishes point, as well as interval, estimation of measuring instrument reliability. The approach can be employed with scale components that are multinormal or, alternatively, follow a range of nonnormal distributions. In addition, the procedure can be utilized with missing data. The proposed method is illustrated with an empirical example.

On the use of confirmatory factor analysis in personality research

Abstract This paper is concerned with applications of confirmatory factor analysis (CFA) in personality research. It is argued that traditional utilizations of CFA capitalize excessively on restrictive assumptions and cannot be generally expected to be particularly informative if some of them are violated. Recent approaches to model evaluation, specifically alternative ways of fit-assessment as well as determination of the power of the model test, are then discussed and recommended for use in studies of personality.