The measurement error in principal components extracted from a set of fallible measures is discussed and evaluated. It is shown that as long as one or more measures in a given set of observed variables contains error of measurement, so also does any principal component obtained from the set. The error variance in any principal component is shown…

A critical discussion of the assumption of uncorrelated errors in classical psychometric theory and its applications is provided. It is pointed out that this assumption is essential for a number of fundamental results and underlies the concept of parallel tests, the Spearman-Brown's prophecy and the correction for attenuation formulas as well as…

A latent variable modeling method is outlined, which accomplishes estimation of criterion validity and reliability for a multicomponent measuring instrument with hierarchical structure. The approach provides point and interval estimates for the scale criterion validity and reliability coefficients, and can also be used for testing composite or…

A method for point and interval estimation of change in criterion validity of multiple-component measuring instruments as a result of revision is outlined. The procedure is developed within the framework of covariance structure modeling, which complements earlier methods for testing change in composite reliability due to addition or deletion of…

A method is outlined for evaluating the reliability and criterion validity of weighted scales based on sets of unidimensional measures. The approach is developed within the framework of latent variable modeling methodology and is useful for point and interval estimation of these measurement quality coefficients in counseling and education…

A linear combination of a set of measures is often sought as an overall score summarizing subject performance. The weights in this composite can be selected to maximize its reliability or to maximize its validity, and the optimal choice of weights is in general not the same for these two optimality criteria. We explore several relationships…

A structural equation modeling based method is outlined that accomplishes interval estimation of individual optimal scores resulting from multiple-component measuring instruments evaluating single underlying latent dimensions. The procedure capitalizes on the linear combination of a prespecified set of measures that is associated with maximal…