Reliability captures the influence of error on a measurement and, in the classical setting, is defined as one minus the ratio of the error variance to the total variance. Laenen, Alonso, and Molenberghs ("Psychometrika" 73:443-448, 2007) proposed an axiomatic definition of reliability and introduced the R[subscript T] coefficient, a measure of…

Uses classical test theory to show that it is the nature of the range restriction, rather than the nature of the available reliability coefficient, that determines the sequence for applying corrections for range restriction and unreliability. Shows how the common rule of thumb for choosing the sequence is tenable only when the correction does not…

A formally simple expression for the maximal reliability of a linear composite is provided. Its theoretical implications and its relation to existing results for reliability are discussed. (Author/SLD)

We make theoretical comparisons among five coefficients--Cronbach's [alpha], Revelle's [beta], McDonald's [omega][sub h], and two alternative conceptualizations of reliability. Though many end users and psychometricians alike may not distinguish among these five coefficients, we demonstrate formally their nonequivalence. Specifically, whereas…

The problem of scaling ordinal categorical data observed over two or more sets of categories measuring a single characteristic is addressed. Scaling is obtained by solving a constrained entropy model. A Kullback-Leibler statistic is generated that operationalizes a measure for the strength of consistency among the sets of categories. (TJH)

Explores the asymptotic theory of a method of nonparametric item characteristic curve estimation based on kernel smoothing with the theory of obtaining the proper linear ordering of examinees with respect to their true latent abilities. Results support the usefulness of estimates of the type produced by the TESTGRAF program. (SLD)

H. H. Chang and W. F. Stout (1993) presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous item response (IRT) theory models. This paper presents an extension of their results to polytomous IRT models and defines a global information…

An estimate and upper-bound estimate for the reliability of a test composed of binary items is derived from the multidimensional latent trait theory of R. D. Bock and M. Aitken (1981). The practical uses of such estimates are discussed. (SLD)

A proportional reduction in loss (PRL) measure for reliability of categorical data is explored for the situation in which each of "N" judges assigns a subject to one of "K" categories. Calculating a lower bound for reliability under more general conditions than had been proposed is demonstrated. (SLD)

A 2-facet measurement model is identified, and its coefficient of generalizability (CG) is examined. Three other multifaceted measurement models and their CGs are identified. An empirical investigation of all four procedures is conducted using data from a study of the psychopathology of 71 prison inmates. (SLD)

A method is presented for determining sample size that will achieve a pre-specified bound on confidence interval width for the interrater agreement measure "kappa." The same results can be used when a pre-specified power is desired for testing hypotheses about the value of kappa. (Author/SLD)

Sufficient conditions are derived for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis. The limiting covariance matrix is computed. (Author/SLD)

An asymptotic expression for the reliability of a linearly equated test is developed using normal theory. Reliability is expressed as the product of test reliability before equating and an adjustment term that is a function of the sample sizes used to estimate the linear equating transformation. The approach is illustrated. (SLD)

Scoring of response vectors to give maximum test-retest correlation is investigated. A general method is given for finding the best scores, deriving them for the normal factor model, and showing that for a standard model for binary response it is easy to approximate the best scores. (SLD)

A technique is presented to transform incomplete categorical data into complete data by imputing appropriate scores into missing cells. A solution of the optimization problem is suggested, and relevant psychometric theory is discussed. The average correlation should be at least 0.50 before the method becomes practical. (SLD)