Inequalities among lower bounds to reliability: With applications to test construction and factor analysis

By Peter M. Bentler, J. Woodward. 1980

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Statistical inference of minimum rank factor analysis (2002, unknown): “Equivalently, xIt has to yield the minimum of tr (D1/2£D 1/2 - D1/2XItD 1/2) subject to £-xIt _~ 0 and xIt _~ 0. The latter problem is a weighted CMTFA problem, which can be solved by an iterative algorithm ( Bentler & Woodward, 1980; ten Berge, Snijders and Zegers, 1981).”
The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability (2000, methodology): “A first numerical solution was offered by Woodhouse and Jackson (1977), and more efficient procedures were soon to follow (Bentler & Woodward, 1980, also see Ten Berge, Snijders & Zegers, 1981).”
The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality (2004, methodology): “A generalized iterative algorithm by Bentler and Woodward (1980) , also see Ten Berge, Snijders and Zegers (1981), will find the glb in all cases.”
On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha (2008, methodology): “Algorithms for solving the glb problem are discussed by Bentler and Woodward (1980) and Ten Berge, Snijders, and Zegers (1981).”
Commentary on Coefficient Alpha: A Cautionary Tale (2009, methodology): “A number of different iterative solutions have been developed to compute ρglb, including those by Woodhouse & Jackson (1977), Bentler & Woodward (1980) , and Ten Berge & Kiers (1991).”
Coefficients Alpha, Beta, Omega, and the glb: Comments on Sijtsma (2009, methodology): “We also examine two of those of Bentler and Woodward (1980) who report examples of their algorithm for computing the glb. The first set was taken from Lord and Woodward (1968), the second from Warner (1960).”
A Latent Class Approach to Estimating Test-Score Reliability (2011, background): “Bentler and Woodward (1980) and Ten Berge, Snijders, and Zegers (1981) solved the problem of finding the greatest lower bound to the reliability.”